Low-frequency vibrations of a thin-walled functionally graded cylinder (plane strain problem)
Ege N. Erbaş B. Kaplunov J. Noori N.
2023Taylor and Francis Ltd.
Mechanics of Advanced Materials and Structures
2023#30Issue 61172 - 1180 pp.
Low frequency vibrations of a thin walled functionally graded cylinder are considered within the plane strain framework. The dynamic relations in elasticity are subject to asymptotic analysis over cylinder cross section resulting in a consistent approximate equation of motion on the mid-surface. A simple explicit formula for natural frequencies emerging from the derived equation is validated by comparison with previous numerical predictions. The formula demonstrates that the ratio of the natural frequencies for functionally graded and homogeneous cylinders does not depend upon the mode number. Useful expressions for the variation of all stress components across the thickness are also obtained.
asymptotic , cylinder , elasticity , functionally graded , low-frequency , Thin-walled
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Eskişehir Technical University, Eskişehir, Turkey
School of Computing and Mathematics, Keele University, Keele, United Kingdom
Department of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Eskişehir Technical University
School of Computing and Mathematics
Department of Mechanics and Mathematics
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