A Power Series Solution for Free Vibration of Variable Thickness Mindlin Circular Plates with Two-Directional Material Heterogeneity and Elastic Foundations
Publish place: Journal of Solid Mechanics، Vol: 3، Issue: 2
Publish Year: 1390
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JSMA-3-2_007
تاریخ نمایه سازی: 28 مرداد 1402
Abstract:
In the present paper, a semi-analytical solution is presented for free vibration analysis of circular plates with complex combinations of the geometric parameters, edge-conditions, material heterogeneity, and elastic foundation coefficients. The presented solution covers many engineering applications. The plate is assumed to have a variable thickness and made of a heterogeneous material whose properties vary in both radial and transverse directions. While the edge is simply-supported, clamped, or free; the bottom surface of the plate is resting on a two-parameter (Winkler-Pasternak) elastic foundation. A comprehensive sensitivity analysis including evaluating effects of various parameters is carries out. Mindlin theory is employed for derivation of the governing equations whereas the differential transform method is used to solve the resulted equations. In this regard, both the in-plane and rotary inertia are considered. Results show that degradations caused by a group of the factors (e.g., the geometric parameters) in the global behavior of the structure may be compensated by another group of factors of different nature (e.g, the material heterogeneity parameters). Moreover, employing the elastic foundation leads to higher natural frequencies and postponing the resonances.
Keywords:
Free vibration , Circular plate , Elastic foundation , Two-directional functionally graded material , Variable thickness , Differential transform
Authors
M.M Alipour
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
M Shariyat
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
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