| 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
(författare)
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Dynamic higher order equations for structural elements
- 2014
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The subject of this thesis is to derive and evaluate governing equations and corresponding boundary conditions for solid isotropic cylinders and isotropic micropolar rectangular plates. This is achieved by a systematic power series expansion approach, by either adopting a generalized Hamilton's principle or a direct approach.For the solid cylinders a power series expansion in the radial coordinate is adopted. 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. Governing equations are obtained for longitudinal, torsional, and flexural modes. In the case of the isotropic micropolar plate a power series expansion of the displacements and micro-rotations are adopted in the thickness coordinate. Governing equations of motion, for extensional and flexural case, together with consistent sets of edge boundary conditions are derived in a systematic fashion up to arbitrary order with use of the direct approach.Both the governing equations for the solid cylinder and the micropolar plate 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, various classical theories and other newly developed approximate theories. These results cover dispersion curves, eigenfrequencies, various curves of cross sectional quantities such as displacements, stresses and micro-rotations, as well as fixed 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 equations using low order truncation.
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| 3. |
- 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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