| 1. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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A hierarchy of dynamic equations for solid isotropic circular cylinders
- 2014
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Ingår i: Wave Motion. - : Elsevier BV. - 0165-2125. ; 51:2, s. 206-221
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Tidskriftsartikel (refereegranskat)abstract
- This work considers homogeneous isotropic circular cylinders adopting a power series expansion method in the radial coordinate. Equations of motion together with consistent sets of end boundary conditions are derived in a systematic fashion up to arbitrary order using a generalized Hamilton’s principle. Time domain partial differential equations are obtained for longitudinal, torsional, and flexural modes, where these equations are asymptotically correct to all studied orders. Numerical examples are presented for different sorts of problems, using exact theory, the present series expansion theories of different order, and various classical theories. These results cover dispersion curves, eigenfrequencies and the corresponding displacement and stress distributions, as well as fix frequency motion due to prescribed end displacement or lateral distributed forces. The results illustrate that the present approach may render benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.
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| 2. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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Dynamic Higher Order Functionally Graded Micropolar Plate Equations
- 2014
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Ingår i: Civil-Comp Proceedings. - Stirlingshire, UK : Civil-Comp Press. - 1759-3433. ; 106
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Tidskriftsartikel (refereegranskat)abstract
- The work, described in this paper, considers the analysis and derivation of dynamical equations on rectangular functionally graded plates governed by micropolar continuum theory. The proposed method is based on a power series expansion of the displacement field, micro-rotation field and material parameters in the thickness coordinates of the plate. This assumption results in sets of equations of motion together with consistent sets of boundary conditions. These derived equations are hyperbolic and can be constructed in a systematic fashion to any order desired. It is believed that these sets of equations are asymptotically correct. The construction of the equation is systematized by the introduction of recursion relations which relates higher order displacement and micro-rotation terms with the lower order terms. The fundamental eigenfrequency is obtained for the plate using different truncations orders of the present theory. Also various plots of mode shapes and stress distributions are compared for the fundamental eigenfrequency.
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| 3. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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Dynamic higher order micropolar plate equations
- 2013
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Ingår i: Proceedings of the 11th International Conference on Vibration Problems (ICOVP-2013)”, Lisbon, Portugal, 9-12 September, 2013. - 9789899626447 ; , s. p.133-
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Konferensbidrag (refereegranskat)abstract
- This work considers the analysis and derivation of dynamical equations on rectangular plates governed by micropolar continuum theory. The proposed method is based on a power series expansion of the displacement field and micro-rotation field in the thickness coordinate of the plate. This assumption results in sets of equations of motion together with consistent sets of boundary conditions. These derived equations are hyperbolic and can be constructed in systematic fashion to any order desired. Hence it is believed that these sets of equations are asymptotically correct. The construction of the equation is systematized by the introduction of recursion relations which relates higher order displacement and micro-rotation terms with the lower order terms. Furthermore the equations can be divided into two categories of motions, namely extensional and flexural motion.Results are only obtained for the flexural motion of the plate using different truncations orders of the present theory, comparisons are performed with the plate theory developed by Eringen and the exact theory for micropolar continuum. Numerical examples are presented for dispersion curves on an infinite plate for the three lowest flexural modes. The three lowest eigenfrequencies for a simply supported plate are presented for different truncation orders, Eringen's plate theory and the exact theory. Also various plots on mode shapes stress distributions are compared for a infinite plate vibrating with a fix frequency.
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| 4. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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Higher order beam equations
- 2012
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Ingår i: Civil-Comp Proceedings. - Stirlingshire, UK : Civil-Comp Press. - 1759-3433. ; 99
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers the dynamic equations of circular cylindrical beams. The method is based on the three dimensional theory, adopting the generalized Hamilton's principle. By adopting a power series expansion method in the radial coordinate, together with a Fourier series expansion in the circumferential direction, this procedure results in sets of equations of motion together with consistent sets of end boundary conditions. These are derived in a systematic fashion up to arbitrary order, and are believed to be asymptotically correct. As such, the equations of motion are hyperbolic. Among the derived equation set are recursion relations, from which it is possible to express higher order displacement and stress fields in terms of lower order displacement fields. Results are obtained for all Fourier modes, among which axisymmetric, torsional and flexural modes are special cases. Special attention is paid towards the flexural mode. Using different truncation orders of the present theory, comparisons may be performed with classical theories such as the Euler-Bernoulli and the Timoshenko theories, besides the exact theory. Numerical examples are presented for dispersion curves of an infinite beam for the three lowest modes. Here various truncation orders are presented, as well as the exact theory. It is clear that higher accuracy is obtained as more terms are used. The lowest mode curve is accurately captured in the lower frequency range for all theories. Higher order truncations are indistinguishable from the exact curves in the presented range. Concerning eigenfrequencies, the three lowest frequencies for two different beams are presented for different truncation orders, classical theories as well as the exact theory for simply supported ends. As for the dispersion curves, the series expansion results converge to the exact results as the power series orders are increased. It is clear that more accurate results are obtained for lower frequencies and slender beams as expected. The Timoshenko theory is astonishingly accurate while the Euler-Bernoulli theory confirms the well known fact that this theory renders reasonably accurate results for slender beams in the low frequency spectra. Various plots on mode shapes and stress distributions are compared for the fundamental frequency for a simply supported beam. Here the curves using the lowest series expansion theory are very close to the exact results. There are more pronounced differences between theories for the mode shapes and the stress distributions, compared to the eigenfrequency calculations and the dispersion curves. The differences are most prominent for the stress distributions.
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| 5. |
- Ander, Mats, 1964, et al.
(författare)
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Studenterna lyfter sig själva i Studion för Mekanik och Hållfasthetslära
- 2014
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Ingår i: KUL2014.
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Konferensbidrag (refereegranskat)abstract
- För att inom mekanik och hållfasthetslära öka studentens förståelse, väcka nyfikenhet, konkretisera fenomen och för att möjliggöra för studenten att erövra en handgriplig känsla har en Studio i Mekanik och hållfasthetslära med demonstrationsexperiment inrättats av studenter för studenter. Resultatet av en pilotstudie där studion för första gången använts presenteras.
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| 6. |
- Boström, Anders E, 1951, et al.
(författare)
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Dynamic equations for an orthotropic plate
- 2010
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Ingår i: Proceedings of the International Conference Days on Diffraction, DD 2010. St. Petersburg, 8-11 June 2010. - 9785965105298 ; , s. 35-39
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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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| 7. |
- Folkow, Peter, 1968, et al.
(författare)
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Dynamic higher-order equations for finite rods
- 2010
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Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 63:1, s. 1-21
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Tidskriftsartikel (refereegranskat)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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| 8. |
- Folkow, Peter, 1968
(författare)
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How master theses can promote new research constellations
- 2014
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Ingår i: KUL2014.
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Konferensbidrag (refereegranskat)abstract
- In order to better meet broader engineering problems, collaborations among various fields are needed. At Applied mechanics, such cooperation is promoted through financially supporting cross divisional master thesis projects. Since 2008 13 such projects have run, which has resulted in new research constellations involving several PhD students.
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| 9. |
- Folkow, Peter, 1968
(författare)
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”Utbildning i världsklass” – Vad kan man göra på institutionsnivå?
- 2013
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Ingår i: KUL2013.
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Konferensbidrag (refereegranskat)abstract
- Institutionen för tillämpad mekanik (TM) har sedan drygt ett år tillbaka utvecklat institutionsspecifika delmål kopplat till Chalmers PVU. Presentationen beskriver detta arbetet, samt andra kvalitetshöjande grundutbildningsaktiviteter som löpande introducerats de senaste åren på TM. Förhoppningen är att ge utrymme för inspel från auditoriet kring de aktiviteter TM och övriga institutioner gör eller skulle kunna göra, samt att bidra till att samla goda idéer som kan komma alla till gagn.
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| 10. |
- Golub, Mikhail, 1982, et al.
(författare)
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Wave propagation of functionally graded layers treated by recursion relations and effective boundary conditions
- 2013
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683. ; 50:5, s. 766-772
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Tidskriftsartikel (refereegranskat)abstract
- Wave propagation through a layer of a material that is inhomogeneous in the thickness direction, typically a functionally graded material (FGM), is investigated. The material parameters and the displacement components are expanded in power series in the thickness coordinate, leading to recursion relations among the displacement expansion functions. These can be used directly in a numerical scheme as a means to get good field representations when applying boundary conditions, and this can be done even if the layer is not thin. This gives a schema that is much more efficient than the approach of subdividing the layer into many sublayers with constant material properties. For thin layers for which the material parameters do not depend on the layer thickness the recursion relations can be used to eliminate all but the lowest order expansion functions. Employing the boundary conditions this leads to a set of effective boundary conditions relating the displacements and stresses on the two sides of the layer, thus completely replacing the layer by these effective boundary conditions. Numerical examples illustrate the convergence properties of the scheme for FG layers and the influence of different variations of the material parameters in the FG layer.
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