| 1. |
- Boström, Anders E, 1951, et al.
(author)
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Dynamic equations for an orthotropic plate
- 2010
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In: Proceedings of the International Conference Days on Diffraction, DD 2010. St. Petersburg, 8-11 June 2010. - 9785965105298 ; , s. 35-39
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Conference paper (peer-reviewed)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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| 2. |
- Folkow, Peter, 1968, et al.
(author)
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Dynamic higher-order equations for finite rods
- 2010
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In: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 63:1, s. 1-21
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Journal article (peer-reviewed)abstract
- This work considers longitudinal wave propagation in circular cylindrical rods adopting Bostrom's power series expansion method in the radial coordinate. Equations of motion together with consistent sets of general lateral and end boundary conditions are derived in a systematic fashion up to arbitrary order using a generalized Hamilton's principle. Analytical comparisons are made between the present theory to low order and several classic theories. Numerical examples for eigenfrequencies, displacement and stress distributions are given for a number of finite rod structures. The results are presented for series expansion theories of different order and various classical theories, from which one may conclude that the present method generally models the rod accurately.
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| 3. |
- Mauritsson, Karl, 1980
(author)
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Dynamic Anisotropic and Piezoelectric Plate Equations - A Power Series Approach with Recursion Relations among the Expansion Functions
- 2010
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Doctoral thesis (other academic/artistic)abstract
- The subject of this thesis is dynamics of plates. Both anisotropic elastic plates, piezoelectric plates, thin piezoelectric layers on elastic plates and elastic laminates are considered. Piezoelectric materials are often used in sensors and actuators and common applications for these are vibration control and ultrasonic transducers. Composite laminates are used in a variety of industrial applications, due to their high strength and light weight. Throughout this thesis a systematic power series expansion approach is used to derive plate equations and the corresponding edge boundary conditions. The displacements, and for piezoelectric materials also the electric potential, are expanded in power series in the thickness coordinate, which are inserted into the three-dimensional equations of motion. Identifying equal powers of the thickness coordinate leads to recursion relations among the expansion functions. These are used in the surface boundary conditions as well as the possible interface conditions, which gives a system of plate equations for some of the lowest-order expansion functions. The equations can be truncated to any order and it is believed that they are asymptotically correct. Numerical comparisons with exact three-dimensional theory and also some other approximate theories illustrate the accuracy.
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| 4. |
- Mauritsson, Karl, 1980, et al.
(author)
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Dynamic equations for a fully anisotropic elastic plate
- 2011
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In: Journal of Sound and Vibration. - : Elsevier BV. - 1095-8568 .- 0022-460X. ; 330:11, s. 2640-2654
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Journal article (peer-reviewed)abstract
- A hierarchy of dynamic plate equations is derived for a fully anisotropic elastic plate. Using power series expansions in the thickness coordinate for the displacement components, recursion relations are obtained among the expansion functions. Adopting these in the boundary conditions on the plate surfaces and along the edges, a set of dynamic equations with pertinent edge boundary conditions are derived on implicit form. These can be truncated to any order and are believed to be asymptotically correct. For the special case of an orthotropic plate, explicit plate equations are presented and compared analytically and numerically to other approximate theories given in the literature. These results show that the present theory capture the plate behavior accurately concerning dispersion curves, eigenfrequencies as well as stress and displacement distributions.
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| 5. |
- Mauritsson, Karl, 1980, et al.
(author)
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Dynamic equations for a fully anisotropic piezoelectric rectangular plate
- 2015
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In: Computers and Structures. - : Elsevier BV. - 0045-7949. ; 153, s. 112-125
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Journal article (peer-reviewed)abstract
- A hierarchy of dynamic plate equations based on the three dimensional piezoelectric theory is derived fora fully anisotropic piezoelectric rectangular plate. Using power series expansions results in sets ofequations that may be truncated to arbitrary order, where each order set is hyperbolic, variationally consistentand asymptotically correct (to all studied orders). Numerical examples for eigenfrequencies andplots on mode shapes, electric potential and stress distributions curves are presented for orthotropicplate structures. The results illustrate that the present approach renders benchmark solutions providedhigher order truncations are used, and act as engineering plate equations using low order truncation.
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| 6. |
- Mauritsson, Karl, 1980, et al.
(author)
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Dynamic equations for a homogenous, fully anisotropic, elastic plate
- 2008
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In: Proceedings of the 6th International Conference on Computation of Shell & Spatial Structures. ; , s. 18-21
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Conference paper (peer-reviewed)abstract
- The derivation of plate equations for a homogenous, fully anisotropic, elastic plate is considered. Power series expansionsin the thickness coordinate for the displacements lead to recursion relations among the expansion functions.Using these in the boundary conditions a set of plate equations, which can be truncated to any order in the thickness,are obtained and it is believed that these equations are asymptotically correct. Numerical investigations for guidedwaves along the plate illustrate the accuracy.
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| 7. |
- Mauritsson, Karl, 1980, et al.
(author)
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Dynamic equations for an orthotropic piezoelectric plate
- 2010
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In: Proceedings of the tenth international comference on computational structures technology, Valencia 14-17 September 2010. - 9781905088386
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Conference paper (peer-reviewed)abstract
- Piezoelectric materials have been used widely in applications for sensing and actuation purposes in recent years. As piezoelectric sensors and actuators usually are thin in comparison to the relevant wavelengths, the analysis of thin piezoelectric layers has attracted considerable research interest. The present work considers the derivation of new plate equations and the corresponding edge boundary conditions for an orthotropic piezoelectric plate. Here, power series expansions in the thickness coordinate for the displacements and the electric potential are stated, that lead to recursion relations among the expansion functions. These recursion relations are important as all fields hereby can be expressed in a finite number of expansions functions without performing any truncations. Moreover, the recursion formulas involve no approximations since they stem from the definition of the series expansions and are as such exact. Using the recursion relations in the boundary conditions on the surfaces and along the edges, a set of plate equations and the corresponding edge boundary conditions are obtained in a systematic fashion. Hence the surface boundary conditions constitute the plate equations of motion, and as such the lateral boundary conditions are exactly fulfilled. These plate equations can be truncated to any order in the thickness and it is believed that they are asymptotically correct, based on experience for other structures. Contrary to most traditional theories, there is no need to assume kinematical simplifications based on various engineering assumptions; neither for the equations of motion nor for the corresponding edge boundary conditions. Note that various sorts of series expansion procedure have been developed by others, but there are several differences in the derivation procedure among these works, such as in the series expansion formulation, the development of recursion relations or in the truncation process. The plate theory developed is given explicitly for flexural motion using a low order truncation. These equations of motion resemble the Mindlin type plate equations, albeit the present theory involves some further terms as well as no correction factors. The accuracy of the plate theory is displayed for the displacement, electric and stress fields, where comparisons are made with exact and traditional approximate theories. These results show that the present asymptotic plate theory renders considerably more accurate results than the Kirchhoff and the Mindlin theories.
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| 8. |
- Mauritsson, Karl, 1980
(author)
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Dynamics of Plates with Thin Piezoelectric Layers
- 2007
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Licentiate thesis (other academic/artistic)abstract
- The subject of this thesis is dynamics of plates with thin piezoelectric layers. Piezoelectric materials are often used in sensors and actuators and common applications for these are vibration control and ultrasonic transducers. In the first part of the thesis plate equations for a plate consisting of one anisotropic elastic layer and one piezoelectric layer with an applied electric voltage are derived. The displacements and the electric potential are expanded in power series in the thickness coordinate, which leads to recursion relations among the expansion functions. Using these in the boundary and interface conditions, a set of equations is obtained for some of the lowest-order expansion functions. This set is reduced to a system of six plate equations, where three of them are given to linear order in the thickness and correspond to the symmetric (in plane) motion, while the other three are given to quadratic order in the thickness and correspond to the antisymmetric (bending) motion. In principle it is possible to go to any order and it is believed that the equations are asymptotically correct. Some numerical comparisons are made with exact theory for infinite plates and very good agreement is obtained for low frequencies. In the second part of the thesis the plate equations are evaluated by investigating a vibration problem with a finite elastic layer and a shorter piezoelectric layer on top of it. The boundary conditions to combine with the plate equations are derived by inserting the power series expansions into the physical boundary conditions at the sides of the elastic layer and identifying equal powers of the thickness coordinate. Numerical comparisons of the displacement field are made with two other theories. The first one is another approximate theory based on the same type of power series expansions, where the piezoelectric layer is modeled as equivalent boundary conditions. The other one is exact three-dimensional theory. Both approximate theories yield accurate results for thin plates and low frequencies as long as the piezoelectric layer is thin in comparison to the total plate thickness.
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| 9. |
- Mauritsson, Karl, 1980
(author)
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Modelling of finite piezoelectric patches: comparing an approximate power series expansion theory with exact theory
- 2009
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In: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 46:5, s. 1053-1065
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Journal article (peer-reviewed)abstract
- Plate equations for a plate consisting of one elastic layer and one piezoelectric layer with an applied electric voltage have previously been derived by use of power series expansions of the field variables in the thickness coordinate. These plate equations are here evaluated by the consideration of a time harmonic 2D vibration problem with finite layers. The boundary conditions at the sides of the layers then have to be considered. Numerical comparisons of the displacement field are made with solutions from two other theories; a solution with equivalent boundary conditions for a thin piezoelectric layer applied on an elastic plate and an exact solution based on Fourier series expansions. The two approximate theories are shown to be equally good and they both yield accurate results for low frequencies and thin plates.
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| 10. |
- Mauritsson, Karl, 1980, et al.
(author)
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Modelling of thin piezoelectric layers on plates
- 2008
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In: Wave Motion. - : Elsevier BV. - 0165-2125. ; 45:5, s. 616-628
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Journal article (peer-reviewed)abstract
- The derivation of plate equations for a plate consisting of twolayers, one anisotropic elastic and one piezoelectric, isconsidered. Power series expansions in the thickness coordinate forthe displacement components and the electric potential lead torecursion relations among the expansion functions. Using these inthe boundary and interface conditions, a set of equations areobtained for some of the lowest-order expansion functions. This setis reduced to six equations corresponding to the symmetric(in-plane) and antisymmetric (bending) motions of the elastic layer.These equations are given to linear (for the symmetric equations) orquadratic (for the antisymmetric equations) order in the thickness.It is noted that it is, in principle, possible to go to any order,and that it is believed that the corresponding equations areasymptotically correct. A few numerical results for guided wavesalong the plate and a 1D actuator case illustrate the accuracy.
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