RMVT-and PVD-based finite layer methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates

Chih-Ping Wu, Hao Yuan Li

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The Reissner mixed variational theorem (RMVT)-and principle of virtual displacements (PVD)-based finite layer methods (FLMs) are developed for the quasi-three-dimensional (3D) free vibration analysis of simply-supported, multilayered composite and functionally graded material (FGM) plates. The material properties of the FGM layers are assumed to obey either an exponent-law exponentially varied with the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In these formulations, the plate is divided into a number of finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in-and out-of-plane variations of the field variables of each individual layer, respectively. Because an h-rather than p-refinement process is adopted to yield the convergent solutions in this analysis, a layerwise linear or parabolic function distribution through the thickness coordinate is assumed for the related field variables. The unified formulations of these two kinds of FLMs with freely-chosen orders are presented, which are used for expansion of in-and out-of-plane field variables through the thickness coordinate. The natural frequencies and their corresponding modal field variable distributions through the thickness coordinate of the multilayered composite and FGM plates are studied using the various RMVT-and PVD-based FLMs developed in this paper, and the accuracy and convergence rate of these are assessed by comparing their solutions with the exact 3D solutions available in the literature.

Original languageEnglish
Pages (from-to)155-198
Number of pages44
JournalComputers, Materials and Continua
Volume19
Issue number2
Publication statusPublished - 2010 Dec 1

Fingerprint

Functionally graded materials
Vibration Analysis
Free Vibration
Vibration analysis
Composite
Composite materials
Theorem
Distribution functions
Natural frequencies
Volume fraction
Materials properties
Polynomials
Lagrange's polynomial
Formulation
Circular function
Power-law Distribution
Natural Frequency
Volume Fraction
Material Properties
Distribution Function

All Science Journal Classification (ASJC) codes

  • Biomaterials
  • Modelling and Simulation
  • Mechanics of Materials
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

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abstract = "The Reissner mixed variational theorem (RMVT)-and principle of virtual displacements (PVD)-based finite layer methods (FLMs) are developed for the quasi-three-dimensional (3D) free vibration analysis of simply-supported, multilayered composite and functionally graded material (FGM) plates. The material properties of the FGM layers are assumed to obey either an exponent-law exponentially varied with the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In these formulations, the plate is divided into a number of finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in-and out-of-plane variations of the field variables of each individual layer, respectively. Because an h-rather than p-refinement process is adopted to yield the convergent solutions in this analysis, a layerwise linear or parabolic function distribution through the thickness coordinate is assumed for the related field variables. The unified formulations of these two kinds of FLMs with freely-chosen orders are presented, which are used for expansion of in-and out-of-plane field variables through the thickness coordinate. The natural frequencies and their corresponding modal field variable distributions through the thickness coordinate of the multilayered composite and FGM plates are studied using the various RMVT-and PVD-based FLMs developed in this paper, and the accuracy and convergence rate of these are assessed by comparing their solutions with the exact 3D solutions available in the literature.",
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RMVT-and PVD-based finite layer methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates. / Wu, Chih-Ping; Li, Hao Yuan.

In: Computers, Materials and Continua, Vol. 19, No. 2, 01.12.2010, p. 155-198.

Research output: Contribution to journalArticle

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