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2D Free Vibration Solution of the Hybrid Piezoelectric Laminated Beams Using Extended Kantorovich Method
https://orcid.org/http://orcid.org/0000-0002-0984-5347
Analytical two-dimensional (2D) piezoelasticity free vibration solution is presented for the beams under different combinations of support conditions, using the multi-term multi-field extended Kantorovich method (MMEKM). Piezoelasticity-based extended Hamilton principle with the mixed variational field is applied to derive the governing equations in terms of stresses, displacements along with electric displacements and electric potential. Therefore, boundary conditions, both natural and essential, are satisfied in an exact manner at all points. By employing MMEKM, the first-order differential–algebraic system of 8n equations is obtained along the z-direction (thickness) for each layer and another set along the x-direction (in-plane). The final solution of these first-order ODEs is obtained in closed form. The numerical results are verified by comparing against the exact 2D solution available in the literature for the simply supported boundary condition case and with 2D finite element results for other support conditions. New benchmark results for free vibration are presented for piezoelectric beams subjected to arbitrary boundary conditions.
2D Free Vibration Solution of the Hybrid Piezoelectric Laminated Beams Using Extended Kantorovich Method
https://orcid.org/http://orcid.org/0000-0002-0984-5347
Analytical two-dimensional (2D) piezoelasticity free vibration solution is presented for the beams under different combinations of support conditions, using the multi-term multi-field extended Kantorovich method (MMEKM). Piezoelasticity-based extended Hamilton principle with the mixed variational field is applied to derive the governing equations in terms of stresses, displacements along with electric displacements and electric potential. Therefore, boundary conditions, both natural and essential, are satisfied in an exact manner at all points. By employing MMEKM, the first-order differential–algebraic system of 8n equations is obtained along the z-direction (thickness) for each layer and another set along the x-direction (in-plane). The final solution of these first-order ODEs is obtained in closed form. The numerical results are verified by comparing against the exact 2D solution available in the literature for the simply supported boundary condition case and with 2D finite element results for other support conditions. New benchmark results for free vibration are presented for piezoelectric beams subjected to arbitrary boundary conditions.
2D Free Vibration Solution of the Hybrid Piezoelectric Laminated Beams Using Extended Kantorovich Method
https://orcid.org/http://orcid.org/0000-0002-0984-5347
Analytical two-dimensional (2D) piezoelasticity free vibration solution is presented for the beams under different combinations of support conditions, using the multi-term multi-field extended Kantorovich method (MMEKM). Piezoelasticity-based extended Hamilton principle with the mixed variational field is applied to derive the governing equations in terms of stresses, displacements along with electric displacements and electric potential. Therefore, boundary conditions, both natural and essential, are satisfied in an exact manner at all points. By employing MMEKM, the first-order differential–algebraic system of 8n equations is obtained along the z-direction (thickness) for each layer and another set along the x-direction (in-plane). The final solution of these first-order ODEs is obtained in closed form. The numerical results are verified by comparing against the exact 2D solution available in the literature for the simply supported boundary condition case and with 2D finite element results for other support conditions. New benchmark results for free vibration are presented for piezoelectric beams subjected to arbitrary boundary conditions.
2D Free Vibration Solution of the Hybrid Piezoelectric Laminated Beams Using Extended Kantorovich Method
J. Inst. Eng. India Ser. C
Singh, Agyapal (Autor:in) / Kumari, Poonam (Autor:in) / Bind, Prabhakar (Autor:in)
01.02.2020
12 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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