Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates

Autor: S. H. Huang, Chiung-Shiann Huang
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Materials; Volume 13; Issue 17; Pages: 3820
Materials, Vol 13, Iss 3820, p 3820 (2020)
Materials
ISSN: 1996-1944
DOI: 10.3390/ma13173820
Popis: This study aimed to develop series analytical solutions based on the Mindlin plate theory for the free vibrations of functionally graded material (FGM) rectangular plates. The material properties of FGM rectangular plates are assumed to vary along their thickness, and the volume fractions of the plate constituents are defined by a simple power-law function. The series solutions consist of the Fourier cosine series and auxiliary functions of polynomials. The series solutions were established by satisfying governing equations and boundary conditions in the expanded space of the Fourier cosine series. The proposed solutions were validated through comprehensive convergence studies on the first six vibration frequencies of square plates under four combinations of boundary conditions and through comparison of the obtained convergent results with those in the literature. The convergence studies indicated that the solutions obtained for different modes could converge from the upper or lower bounds to the exact values or in an oscillatory manner. The present solutions were further employed to determine the first six vibration frequencies of FGM rectangular plates with various aspect ratios, thickness-to-width ratios, distributions of material properties and combinations of boundary conditions.
Databáze: OpenAIRE
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje