| 11. |
- 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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| 12. |
- 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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| 13. |
- 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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| 14. |
- 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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