| 1. |
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| 2. |
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| 3. |
- Boström, Anders E, 1951, et al.
(författare)
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Point-force excitation of an elastic plate with n embedded cavity
- 1985
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Ingår i: Journal of Applied Mechanics, Transactions ASME. - : ASME International. - 0021-8936 .- 1528-9036. ; 52:4, s. 937-942
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Tidskriftsartikel (refereegranskat)abstract
- The propagation of elastic waves in a thick plate containing an embedded cavity is considered. The full elastodynamic equations are solved and both time-harmonic and pulse propagation are treated. The time-harmonic problem is solved using the null field approach, a method whose main characteristics are surface integral representations and expansions in spherical and planar vector wave functions. To obtain the pulse response, a Fourier integral in frequency is employed. Numerical examples are given showing the fields in both the time and frequency domains at a few selectd locations on the plate surfaces when the plate is excited by a point force. Only low and intermediate frequencies are included and the pulse width is thus somewhat larger than the dimensions of the spheroidal cavity.
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| 4. |
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| 5. |
- Karlström, Anders, 1977, et al.
(författare)
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An extended analytical model including a layered
- 2005
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Ingår i: Environmental Vibrations, ISEV2005. - 0415390354 ; , s. 303-310
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Ground vibrations are investigated with an analytical approach. The ground is modelled as a layered half-space on which a layered embankment is placed. Situated on top of the embankment, the sleepers are modelled with an anisotropic Kirchhoff plate and the rails as Euler-Bernoulli beams. In the equation for the rails, propagating wheel loads with constant velocity are accounted for. The analyzing method is based on Fourier transforms in time and along the space coordinate parallel with the track. In the transverse direction Fourier transforms are adopted in the ground, whereas Fourier cosine and Fourier sine series are used in the embankment layers. The numerical scheme is very efficient. In particular the beam-like rectangular elastic region (embankment) is compared with the Euler-Bernoulli beam, both supported on a layered ground. With the same bending stiffness, the two solutions are seen to differ already from 0 Hz.
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| 6. |
- Karlström, Anders, 1977, et al.
(författare)
-
Efficiency of trenches along railways for trains moving at sub- or supersonic speeds
- 2007
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Ingår i: Soil Dynamics and Earthquake Engineering. ; 27, s. 625-641
-
Tidskriftsartikel (refereegranskat)abstract
- A full 3D analytical approach is adopted to account for trenches on one or both sides close to a railroad. Low-frequency ground vibrations are investigated due to passing trains, and open trenches are used as wave barriers. The modelling technique is based on Fourier transforms and Fourier series. The ground is modelled as a layered semi-infinite domain and the embankment with finite layers. The trenches are obtained by simulating the upper surface layer with two or three finite rectangular regions with appropriate widths. A particular boundary condition is adopted on the vertical sides of all finite regions to enable the solution procedure. Rails and sleepers are accounted for with Euler-Bernoulli beams and an anisotropic plate with transversal isotropy. The wheel loads from the boggie wheel pairs of the train are simulated as moving forces. Hence, no irregularities in rails or wheels are accounted for.
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| 7. |
- Kvasha, O. V., et al.
(författare)
-
The propagation of in-plane P-SV waves in a layered elastic plate with periodic interface cracks: exact versus spring boundary conditions
- 2011
-
Ingår i: Waves in Random and Complex Media. - : Informa UK Limited. - 1745-5030 .- 1745-5049. ; 21:3, s. 515-528
-
Tidskriftsartikel (refereegranskat)abstract
- The propagation of in-plane (P-SV) waves in a symmetrically three-layered thick plate with a periodic array of interface cracks is investigated. The exact dispersion relation is derived based on an integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used for the thick plate and also in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three approaches give more or less coinciding dispersion curves, and this is a confirmation that the spring boundary condition is a reasonable approximation at low frequencies.
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| 8. |
- Berbyuk, Viktor, 1953, et al.
(författare)
-
Energy-optimal control of bipedal locomtion systems
- 2002
-
Ingår i: J. Stability and Control: Theory and Application, (SACTA).. - 1563-3276. ; 4:2, s. 74-89
-
Tidskriftsartikel (refereegranskat)abstract
- The mathematical statement of the problem of energy-optimal control for a bipedal locomotion system is given. The proposed statement of the problem is characterized by broad utilization of experimental data of normal human locomotion. It is done mainly by means of the mathematical formulation of the constraints imposed both on the phase coordinates and on the controlling stimuli of a system. A numerical method for the solution of optimal control problems for highly nonlinear and complex bipedal locomotion systems is proposed. The method is based on a special procedure of converting the initial optimal control problem into a standard nonlinear programming problem. This is made by an approximation of the independent variable functions using smoothing cubic splines and by the solution of inverse dynamics problem. The key features of the method are its high numerical effectiveness and the possibility to satisfy a lot of restrictions imposed on the phase coordinates of the system automatically and accurately. The proposed method is illustrated by computer simulation of the energy-optimal anthropomorphic motion of the bipedal walking robot over a horizontal surface.
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| 9. |
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| 10. |
- Berbyuk, Viktor, 1953, et al.
(författare)
-
Modeling an design of robotic systems having spring-damper actuators
- 2000
-
Ingår i: Proceedings of the 7th Mechatronics Forum International Conference, 6-8 September 2000, Atlanta, Georgia, USA, PERGAMON, 2000.. - 0080437036
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The role of inherent dynamics for the improvement of control strategies of robotic systems is studied. A mathematical formulation of the optimal control problem that is suitable for this investigation is proposed. In solving this problem closed-form expressions have been obtained for the optimal control strategies for n degrees-of-freedom robotic systems with passive (unpowered) drives and no restrictions upon their controlling stimuli, and with non-linear viscoelastic spring-damper actuators. The obtained results can be used in designing optimal spring-damper-like passive drives for robotic systems.
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| 11. |
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| 12. |
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| 13. |
- Berbyuk, Viktor, 1953, et al.
(författare)
-
Optimization of control laws of the bipedal locomotion systems
- 1999
-
Ingår i: In Advances in Computational Multibody Dynamics, Jorge A.C. Ambrósio and Werner O. Schiehlen (Eds.), IDMEC/IST, Lisbon, Portugal, September 20-23, 1999. ; , s. 713-728
-
Konferensbidrag (refereegranskat)abstract
- The mathematical statement of the problem of energy-optimal control for a bipedal locomotion system is given. The proposed statement of the problem is characterized by broad utilization of experimental data of normal human locomotion. It is done mainly by means of the mathematical formulation of the constraints imposed both on the phase coordinates and on the controlling stimuli of a system. A numerical method for the solution of the optimal control problems for highly nonlinear and complex bipedal locomotion systems is proposed. The method is based on a special procedure of converting the initial optimal control problem into a standard nonlinear programming problem. This is made by an approximation of the independent variable functions using smoothing cubic splines and by the solution of an inverse dynamics problem. The key features of the method are its high numerical effectiveness and the possibility to satisfy a lot of restrictions imposed on the phase coordinates of the system automatically and accurately. The proposed method is illustrated by computer simulation of the energy-optimal anthropomorphic motion of the bipedal walking robot over a horizontal surface.
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| 14. |
- Berbyuk, Viktor, 1953, et al.
(författare)
-
Optimization problems of controlled multibody systems having spring-damper actuators
- 2001
-
Ingår i: International Applied Mechanics. ; 37:7, s. 935-940
-
Tidskriftsartikel (refereegranskat)abstract
- The optimal control of the motion of mechanical systems is studied. A characteristic feature of these systems is the presence of passive actuators (springs, dampers, etc.). Energy-optimal control laws and structural parameters of nonlinear springdamper actuators are determined analytically, which is necessary to impart arbitrary motion to a controllable mechanical system with n degrees of freedom. As an example, a numerical solution is presented for the problem of designing an energy-optimal spring actuator for a robot manipulator of closed kinematic structure.
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| 15. |
- Berbyuk, Viktor, 1953, et al.
(författare)
-
Optimization problems of controlled multibody systems having spring-damper actuators
- 2000
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- To incorporate spring-damper actuators into the structure of multibody systems and to design optimally their parameters can give several advantages. In this paper, we tackle optimal control problems for multibody systems having spring-damper actuators. We study a fundamental question about optimal interaction between controlling stimuli generated by external drives and proportional-differential forces described by linear and angular stiffness and damping parameters. A range of questions are also addressed about the role of inherent dynamics, and how much multibody system should be governed by external drives and how much by the system's inherent dynamics. We are in particular investigating semi-passively actuated manipulator robots and bipedal walking mechanisms having spring-damper actuators. Results obtained can help to design simpler control systems of manipulator robots and legged autonomous mechanisms having less weight and energy consumption.
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| 16. |
- Berg, Frenk van den, et al.
(författare)
-
Results of the European collaborative project "Product Uniformity Control" to improve the inline sensing of mechanical properties and microstructure of automotive steels
- 2018
-
Ingår i: e-Journal of Nondestructive Testing (eJNDT). - 1435-4934. ; 23:8
-
Tidskriftsartikel (refereegranskat)abstract
- A European consortium consisting of four major steel manufacturers and ten academic technology institutes has conducted a research and development project, called “Product Uniformity Control“ (PUC) in the period 2013 to 2017. This project aimed to develop and improve non-destructive (inline) measurement techniques to characterise the (uniformity of the) microstructure of steel strip products. In this project, a multitude of strip steel samples from various stages of production have been collected from the four participating steel manufacturers. The samples have been characterised in various ways, namely on their (1) non-destructive measurement parameters using different techniques suited for inline evaluation, (2) fundamental ultrasonic and electromagnetic properties (wave speed, ultrasonic attenuation, magnetisation loops, coercive field), (3) tensile properties (stress-strain curves) and (4) microstructure (by optical micrographs and EBSD images). The correlations between these different characterisations will be addressed. Besides the experimental characterisation, a strong accent has been on modelling activities: during the project, fundamental models have been developed to describe, starting from 2D and 3D microstructures, the ultrasonic and magnetic properties, which are next used as input to sensor models that predict the output of the inline measurement systems. This contribution presents the recent results of experimental work, which underlines the importance of associated modelling studies for the interpretation of the measurement data for the benefit of inline characterisation of the mechanical properties complementary to traditional destructive tensile testing.
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| 17. |
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| 18. |
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| 19. |
- Boström, Anders E, 1951
(författare)
-
Acoustic scattering by a sound-hard rectangle
- 1991
-
Ingår i: Journal of the Acoustical Society of America. - 1520-8524 .- 0001-4966. ; 90, s. 3344-3347
-
Tidskriftsartikel (refereegranskat)abstract
- The scattering of an incoming plane wave by a sound-hard infinitely thin rectangle is considered. Starting from a double spatial Fourier transform representation of the scattered wave, a matching of the conditions in the plane of the rectangle leads to an integral equation for the potential jump across the rectangle. The jump is expanded in a double series in Chebyshev polynomials which fulfill the right edge conditions (but no special measures are taken for the corners where the right conditions are anyway unknown). The integral equation is thus discretized and the only tricky part is the computations of double integrals in the systen matrix where special care must be excercised. A double stationary phase analysis gives the scattered far fields, and some numerical examples of total scattering cross sections are given.
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| 20. |
- Boström, Anders E, 1951
(författare)
-
Acoustic waves in a cylindrical duct with periodically varying cross section
- 1983
-
Ingår i: Wave Motion. - 0165-2125. ; 5, s. 59-67
-
Tidskriftsartikel (refereegranskat)abstract
- The null field approach is used to study the propagation of acoustic waves in a rotationally hard-walled duct with periodically varying cross section. For a radius that varies sinusoidally along the axial distance, numerical computations give the axial wave number and the passbands and stopbands of the modes of the duct. In particular, small passbands are seen to exist even for very large variations in radius, and probably all the way to the point where the duct is cut off. We also present some plots which show the pressure pattern inside the duct.
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| 21. |
- Boström, Anders E, 1951, et al.
(författare)
-
Acoustics of an obstacle inside a reactive silencer
- 1983
-
Ingår i: Journal of Sound and Vibration. - 1095-8568 .- 0022-460X. ; 87, s. 603-619
-
Tidskriftsartikel (refereegranskat)abstract
- The transmission and reflection coefficients of sound in a cylindrical duct containing several discontinuities are investigated. A building-block method, which gives the transmission and reflection coefficients for a complex system from those of the parts, is applied to bifurcations, sudden area changes with or without extended inlets, and spherical obstacles (which may be lossy). In some cases the solution can be interpreted in terns of multiple reflections. When the length between the discontinuities are small it is important to include also non-propagating modes, and this is especially true when the sudden area change is obtained from the area change with extended inlet in the limit of vanishing inlet. For an expansion chamber (a portion of the duct with a larger radius) with or without an obstacle and with or without inlets a number of numerical results with variation in frequency are presented. Numerical results for the various building-block elements of the expansion chamber are also considered.
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| 22. |
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| 23. |
- Boström, Anders E, 1951, et al.
(författare)
-
Dynamic equations for an orthotropic plate
- 2010
-
Ingår i: Proceedings of the International Conference Days on Diffraction, DD 2010. St. Petersburg, 8-11 June 2010. - 9785965105298 ; , s. 35-39
-
Konferensbidrag (refereegranskat)abstract
- A hierarchy of dynamic plate equations is derived for an orthotropic elastic plate. Using power series expansions in the thickness coordinate for the displacement components, recursion relations are obtained among the expansion functions. Using these in the boundary conditions on the plate surfaces, a set of dynamic equations are derived. These can be truncated to any order and are believed to be asymptotically correct. A comparison for the dispersion curves is made with exact 3D theory and other approximate theories.
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| 24. |
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| 25. |
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| 26. |
- Boström, Anders E, 1951, et al.
(författare)
-
Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions
- 2009
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 62:1, s. 39-52
-
Tidskriftsartikel (refereegranskat)abstract
- Elastic SH wave propagation in a layered anisotropic plate withinterface damage is modelled in several steps. A single interfacecrack between two half-spaces is first studied and an explicitsolution for the crack-opening displacement is obtained at lowfrequencies. This is then generalized to a random distribution ofcracks at the interface and the result is reformulated as a springboundary condition. As an example of its usefulness,this boundary condition is then used in thederivation of a plate equation by expanding the displacements inpower series in the thickness coordinate.
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| 27. |
- Boström, Anders E, 1951, et al.
(författare)
-
Elastic SH wave propagation in a layered anisotropic plate with periodic interface cracks: exact versus spring boundary conditions
- 2010
-
Ingår i: Journal of Mechanics of Materials and Structures. - : Mathematical Sciences Publishers. - 1559-3959. ; 5:1, s. 67-78
-
Tidskriftsartikel (refereegranskat)abstract
- The propagating antiplane (SH) modes in a symmetrically three-layered, anisotropic, thick plate with a periodic array of interface cracks are investigated. The exact dispersion relation can be derived with the help of a hypersingular integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used both for the thick plate and in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three models are shown to give the same results and this is a confirmation that the spring boundary condition is a valid approximation at low frequencies.
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| 28. |
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| 29. |
- Boström, Anders E, 1951, et al.
(författare)
-
Elastic wave scattering by a three-dimensional inhomogeneity in an elastic half space
- 1980
-
Ingår i: Wave Motion. - 0165-2125. ; 2, s. 335-353
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we will consider scattering of elastic waves in a half space. The half space is an isotropic, linear and homogeneous medium except for a finite inhomogeneity. The T-matrix method (also called the "extended boundary condition method" or "null field approach") is extended to derive expressions for the elastic field inside the half space and the surface field on the interface. The assumptions on the source that excites the half space are fairly weak. In the numerical applications found in this paper we assume a Rayleigh surface wave to be the incoming field, and we only compute the surface displacements. We make illustrations on some simple type of scatterers (spheres and spheroids; the latter ones can be arbitrarily oriented).
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| 30. |
- Boström, Anders E, 1951
(författare)
-
Elastic wave scattering from an interface crack: antiplane strain
- 1987
-
Ingår i: Journal of Applied Mechanics, Transactions ASME. - 0021-8936. ; 54, s. 503-508
-
Tidskriftsartikel (refereegranskat)abstract
- The two-dimensional scalar problem of scattering of elastic waves under antiplane strain from an interface crack between two elastic half-spaces is considered. The method used is a direct integral equation method with the crack-opening displacement as the unknown. Chebyshev polynomials are used as expansion functions and the matrix in the resulting equations is simplified by contour integration techniques. The scattered far field is expressed explicitly in simple functions and the expansion coefficients. The consequences of energy conservation are explored and are used as a check in the numerical implementation. For incoming plane waves numerical results are given for the total scattered energy and the far field amplitude.
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| 31. |
- Boström, Anders E, 1951, et al.
(författare)
-
Elastodynamic scattering from inclusions with thin interface layers
- 1988
-
Ingår i: Wave Propagation in Structural Composites AMD Vol. 90; Proceedings of the Joint ASME/SES Applied Mechanics and Engineering Sciences Conference, June 20-22, 1988. ; , s. 109-116
-
Konferensbidrag (refereegranskat)
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| 32. |
- Boström, Anders E, 1951, et al.
(författare)
-
Ground motion amplification on alluvial valleys
- 1989
-
Ingår i: Applied Mathematics and Mechanics 35; Proceedings of the Second I.U.T.A.M.-I.U.P.A.P. Symposium on Elastic Wave Propagation.
-
Konferensbidrag (refereegranskat)
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| 33. |
- Boström, Anders E, 1951, et al.
(författare)
-
In-plane P-SV waves from a piezoelectric strip actuator: exact versus effective boundary condition solutions
- 2005
-
Ingår i: IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. - 0885-3010. ; 52:9, s. 1594-1600
-
Tidskriftsartikel (refereegranskat)abstract
- A piezoelectric strip of finite width and thickness is placed on top of anisotropic elastic half-space. It operates in actuator mode and a timeharmonic voltage is thus applied across it. The piezoelectric material isof type $6mm$ oriented so that a 2D inplane (P-SV) problem results.By Fourier series expansions the problem is solved exactly and thisresult is compared to the case when the piezoelectric strip is replaced byan effective boundary condition, which is derived by series expansionsin the thickness coordinate in the piezoelectric strip. At low frequenciesthe results agree very well and this corresponds to the situation oftenmet in practice. In general, the effective boundary condition should bemuch easier to apply, for example when a FEM program is used.
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| 34. |
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| 35. |
- Boström, Anders E, 1951
(författare)
-
Multiple scattering of elastic waves by bounded obstacles
- 1980
-
Ingår i: Journal of the Acoustical Society of America. - 1520-8524 .- 0001-4966. ; 67, s. 399-413
-
Tidskriftsartikel (refereegranskat)abstract
- The transition matrix method for stationary elastic waves is extended to a great class of obstacles characterized by piecewise constant properties. First, the translation properties of the basis functions is used to treat two and, then, then several homogeneous obstacles, and thereafter an obstacle with consecutively enclosing layers is considered. It is then indicated how these two basic methods of combination can be applied tp treat more complex cases, including an obstacle consisting of several nonenclosing parts. Finally, we give some numrecal applications of configurations of spherical and nonspherical obstacles in and below the resonance region.
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| 36. |
- Boström, Anders E, 1951, et al.
(författare)
-
On the boundary conditions for ultrasonic transmission by partially closed cracks
- 1991
-
Ingår i: Journal of Nondestructive Evaluation. - 1573-4862 .- 0195-9298. ; 10, s. 139-149
-
Tidskriftsartikel (refereegranskat)abstract
- The probability of detecting crack-like defects using ultrasonic techniques can be severly reduced if the crack is closed by a static background pressure. In this paper, we model the contacting faces of a partially closed crack by an array of circular spot-welds randomly distributed over an infinite plane. We give an exact derivation of the reflection and transmission coefficients for a plane elastic wave at such a boundary in terms of the mean interfacial stresses. The latter are estimated in the limit when the contact radius is much smaller than the wavelength and the contacts are sparsely distributed. This calculation is then related to a distributed spring model of the interface. The latter replaces the real interface by an effective homogeneous linear boundary condition which relates the crack opening displacement to the boundary stresses by effective stiffnesses. These unknown parameters are chosen to ensure that the model condition predicts the exact values of the mean interfacial stresses and the reflection and transmission coefficients in the limit already described. Our results are consistent with and complement thoses of Baik and Thompson who introduced the distributed spring model in this and a number of other contexts. Our analysis provides a systematic assessment of the range of validity of the model and suggests ways in which the present estimates may be improved.
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| 37. |
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| 38. |
- Boström, Anders E, 1951
(författare)
-
On wave equations for elastic rods
- 2000
-
Ingår i: Zeitschrift für Angewandte Mathematik und Mechanik. ; 80, s. 245-251
-
Tidskriftsartikel (refereegranskat)abstract
- The derivation of one-dimensional wave equtions for axially symmetric waves in elastic rods is discussed. By series expansions in the radial coordinate a hierarchy of wave equations are derived. As the lowest reasonable approximation the usual simple wave equation for the rod is recovered. At the next level a fourth order wave equation is obtained. The dispersion relation and the displacements for these approximations and for Love's equation are compared with the lowest branch of the exact Pochhammer-Chree equation. An excitation with a shear force is also solved and compared among the theories.
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| 39. |
- Boström, Anders E, 1951
(författare)
-
Passbands and stopbands for an electromagnetic waveguide with a periodically varying cross section
- 1983
-
Ingår i: IEEE Transactions on Microwave Theory and Techniques. - 0018-9480 .- 1557-9670. ; 31, s. 752-756
-
Tidskriftsartikel (refereegranskat)abstract
- Electromagnetic waves in a rotationally symmetric and perfectly conducting waveguide with a periodically varying cross section are considered. Using the null field (the T matrix) approach, a rahter complicated determinantal condition for computing the axial wavenumber is derived. For a waveguide where the radius varies sinusoidally with the axial coordinate, the passbands and stopbands for the TE11, TM11, and TE12 modes are numerically computed. When the axial wavenumbers of two modes differ by a multiple of the wavenumber of the wall corrugations, the result is a stopband in the following cases: for two TE modes propagating in opposite directions, for a TE and a TM mode in the same direction, and sometimes for two TM modes in opposite directions.
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| 40. |
- Boström, Anders E, 1951
(författare)
-
Propagating, damped, and leaky surface waves on the corrugated traction-free boundary of an elastic half-space
- 1989
-
Ingår i: Journal of the Acoustical Society of America. - 1520-8524 .- 0001-4966. ; 85, s. 1549-1555
-
Tidskriftsartikel (refereegranskat)abstract
- The dispersion relation for surface waves on the corrugated boundary (periodic in one direction and constant in the other) of an elastic half-space is derived using a modal approach, and the result is shown to be equivalent to that derived by the null-field approach. The dispersion relation is solved numerically for roots on all Riemann sheets for varying corrugation heights, frequencies, and angles of propagation. Many of the roots move on several sheets, and this leads to zero, one, or two roots residing on the physical sheets.
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| 41. |
- Boström, Anders E, 1951, et al.
(författare)
-
Propagation of elastic surface waves along a cylindrical cavity and their excitation by a point force
- 1982
-
Ingår i: Journal of the Acoustical Society of America. - 1520-8524 .- 0001-4966. ; 72, s. 998-1004
-
Tidskriftsartikel (refereegranskat)abstract
- The existence of surface wave modes, propagating along on infinite cylindrical cavity in an elastic medium, is established for every integer m, where m is the azimuthal mode number. These waves are analogous to the Rayleigh wave on a half-space, being confined to the immediate vicinity of the cavity. The modes exhibit dispersion and have a cutoff frequency that increases with m, except for the flexural (m=1) mode which exists at all frequencies. At cutoff the phase velocity is equal to that of the shear waves and decreases, with increasing frequency, to that of the Rayleigh wave. We present results for the group velocities and displacement and stress fields of the modes and also exhibit the effect of various point forces acting near the cavity. In the vicinity of the cavity, not too near the point force, the surface wave contribution dominates the total displacement field.
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| 42. |
- Boström, Anders E, 1951
(författare)
-
Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation
- 2003
-
Ingår i: Applied Mechanics Reviews. - : ASME International. - 1088-8535 .- 0003-6900 .- 2379-0407. ; 56:4, s. 383-405
-
Tidskriftsartikel (refereegranskat)abstract
- The scattering of elastic waves by cracks in isotropic and anisotropic solids has important applications in various areas of mechanical engineering and geophysics, in particular in ultrasonic nondestructive testing and evaluation. The scattering by cracks can be investigated by integral equation methods, eg, boundary elements methods, but here we are particularly concerned with more analytically oriented hypersingular integral equation methods. In these methods, which are only applicable to very simple crack shapes, the unknown crack opening displacement in the integral equation is expanded in a set of Chebyshev functions, or the like, and the integral equation is projected onto the same set of functions. This procedure automatically takes care of the hypersingularity in the integral equation. The methods can be applied to cracks in 2D and 3D, and to isotropic or anisotropic media. The crack can be situated in an unbounded space or in a layered structure, including the case with an interface crack. Also, problems with more than one crack can be treated. We show how the crack scattering procedures can be combined with models for transmitting and receiving ultrasonic probes to yield a complete model of ultrasonic nondestructive testing. We give a few numerical examples showing typical results that can be obtained, also comparing with some experimental results. This review article cites 78 references.
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| 43. |
- Boström, Anders E, 1951
(författare)
-
Scattering by a smooth elastic obstacle
- 1980
-
Ingår i: Journal of the Acoustical Society of America. - 1520-8524 .- 0001-4966. ; 67, s. 1904-1913
-
Tidskriftsartikel (refereegranskat)abstract
- In the present paper we adapt the transition matrix method to the case of a smooth elastic obstacle. The boundary conditions employed are discussed in some detail and are seen to be responsible for the fact that the rather complicated formal solution in many respects resembles that of an elastic obstacle in a fluid. Comparisons are made between the smooth and the usually employed welded obstacles, and for spheres approximate expressions are given for the transition matrices in the long wavelength limit. Numerical results (cross sections and surface stresses) are given for spheres and spheroids, and it is then seen that often the smooth and welded obstacles, at least qualitatively, show similar features.
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| 44. |
- Boström, Anders E, 1951
(författare)
-
Scattering by an anisotropic circle
- 2015
-
Ingår i: Wave Motion. - : Elsevier BV. - 0165-2125. ; 57, s. 239-244
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Tidskriftsartikel (refereegranskat)abstract
- The scattering by a circle is considered when the outside medium is isotropic and the inside medium is anisotropic (orthotropic). The problem is a scalar one and is phrased as a scattering problem for elastic waves with polarization out of the plane of the circle (SH wave), but the solution is with minor modifications valid also for scattering of electromagnetic waves. The equation inside the circle is first transformed to polar coordinates and it then explicitly contains the azimuthal angle through trigonometric functions. Making an expansion in a trigonometric series in the azimuthal coordinate then gives a coupled system of ordinary differential equations in the radial coordinate that is solved by power series expansions. With the solution inside the circle complete the scattering problem is solved essentially as in the classical case. Some numerical examples are given showing the influence of anisotropy, and it is noted that the effects of anisotropy are generally strong except at low frequencies where the dominating scattering only depends on the mean stiffness and not on the degree of anisotropy.
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| 45. |
- Boström, Anders E, 1951, et al.
(författare)
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Scattering by two penny-shaped cracks with spring boundary conditions
- 1993
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Ingår i: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. - 1471-2946 .- 1364-5021. ; 443, s. 183-201
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Tidskriftsartikel (refereegranskat)abstract
- The elastodynamic scattering by a penny-shaped crack with spring boundary conditions is investigated. The transition (T) matrix of the crack is determined and the usefulness of this is illustrated by considering also the scattering by two cracks. The T matrix of a single crack is first determined by a direct integral equation method which gives the crack-opening displacement and the integral representation which subsequently gives the scattered field expanded in spherical waves. Two cracks are considered by a multi-centred T matrix approach where matrix inverses are expanded in Neuman series. Rotation matrices are employed so that the cracks may have an arbitrary rotation. The back-scattered longitudinal far field amplitude is computed both in the frequency and time domain in a few cases and the effects due to multiple scattering are in particular explored.
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| 46. |
- Boström, Anders E, 1951, et al.
(författare)
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Scattering of a pulsed Rayleigh wave by a spherical cavity in an elastic half space
- 1983
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Ingår i: Wave Motion. - 0165-2125. ; 5, s. 137-143
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Tidskriftsartikel (refereegranskat)abstract
- The time-dependant scattering by a spherical cavity in an elastic half space is considered. The incoming wave is a pulsed Rayleigh wave. The stationary part of the problem is solved by the T-matrix method, and an integration in frequency is perforemd with a modified gaussian weight function. The displcsement components at some points on the surface of the half space are computed and shown in a number of plots.
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| 47. |
- Boström, Anders E, 1951, et al.
(författare)
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Scattering of acoustic waves by a circular disc in the interface between two fluids
- 1991
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Ingår i: Journal of the Acoustical Society of America. - 1520-8524 .- 0001-4966. ; 90, s. 3338-3343
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Tidskriftsartikel (refereegranskat)abstract
- The scattering of acoustic waves by a sound-hard circular disc situated in the planar interface between two different fluids is considered. The incident wave is taken as a plane wave and a Hankel transform representation of the scattered field is used. After some manipulations using the boundary conditions, this leads to an integral equation over the disc for the potential jump across the disc. This jump is expanded in a series of Legendre functions which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre functions. The far fields are calculated and the implications of energy conservation are explored and used as a numerical check. A few numerical computations showing the disc-scattered far field amplitude and the total scattering cross section are given and are shown to compare favorably with the expectations from simple ray theory at higher frequencies.
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| 48. |
- Boström, Anders E, 1951
(författare)
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Scattering of acoustic waves by a layered elastic obstacle in a fluid - an improved null field appraoch
- 1984
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Ingår i: Journal of the Acoustical Society of America. - 1520-8524 .- 0001-4966. ; 76, s. 588-593
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Tidskriftsartikel (refereegranskat)abstract
- Scattering by a layered elastic obstacle submerged in a fluid is considered. The null field approach (T-matrix method) is used, but the method is modified so that all surface fields can be expanded in spherical harmonics. The resulting method is then compared with the conventional null field approach (which uses expansions in regular wavefunctions), and it is concluded that the present method is better in general. It is, however, doubtful if the null field approach is applicable to cases where there is no sphere that circumscribes the core and inscribes the outer surface. Some numerical results are given for a layered spheroid and superspheroid.
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| 49. |
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| 50. |
- Boström, Anders E, 1951, et al.
(författare)
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Scattering of elastic waves by a rectangular crack in an anisotropic half-space
- 2003
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Ingår i: Wave Motion. - 0165-2125. ; 38, s. 91-107
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Tidskriftsartikel (refereegranskat)abstract
- The scattering of elastic waves by a rectangular crack in a half-space of arbitrary anisotropy is considered. The application in mind is ultrasonic testing of thick-walled anisotropic components where the crack is close to a planar back surface. The orientation of the crack and the back surface may be arbitrary relative the anisotropy. The scattering problem is formulated as hypersingular integral equation for the crack-opening-displacement (COD) by means of a half-spce Green's tensor. The integral equation is solved by expanding the COD in a double series of Chebyshev functions with the correct behavior along the crack's edges. Insertion inte the integral equation and projection onto the same set of functions result in a linear system of equations for the expansion coefficients appearing in the representation of the COD. The transmitting transducer is modeled by the traction beneath it on the scanning surface and the incident field may then be calculated. An electromechanical reciprocity relation is used to model the receiving transducer. Numerical examples are included which show the influence of the anisotropy and espcially the prexence of a nearby planar back surface.
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