Nonlinear free and forced vibration analysis of thin circular functionally graded plates

2008 ◽  
Vol 310 (4-5) ◽  
pp. 966-984 ◽  
Author(s):  
A. Allahverdizadeh ◽  
M.H. Naei ◽  
M. Nikkhah Bahrami
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Forced Vibration Analysis

Forced Vibration Analysis of Functionally Graded Plates With Geometric Nonlinearity

2015 ◽  
Author(s):  
Saurabh Kumar ◽  
Anirban Mitra ◽  
Haraprasad Roy
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Geometric Nonlinearity ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Functionally Graded ◽  
Static Case ◽  
Functionally Graded Plates ◽  
Governing Equations ◽  
Forced Vibration Analysis

Forced vibration analysis has been carried out on functionally graded plates where the material properties vary along axial direction. The geometric nonlinearity is incorporated in the system using nonlinear strain displacement relations. An indirect methodology is adopted in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude, thus reducing the problem to an equivalent static case. The computational points are selected and start functions are generated at those points by satisfying the flexural and membrane boundary conditions of the plate. The start functions are later used for generating higher order functions using Gram-Schmidt orthogonalisation procedure. The mathematical formulation is based on the variational form of energy principles and the governing equations are derived using Hamilton’s principle. The set of nonlinear governing equations is solved using an iterative direct substitution method employing an appropriate relaxation technique. The results are generated for combinations of clamped and simply supported boundary conditions and presented in amplitude-frequency plane. Three dimensional operational deflection shape plots along with contour plots are also provided for some cases. Results are validated with the works available in the literature.

scholarly journals Forced Vibration Analysis for a FGPM Cylindrical Shell

2013 ◽  
Vol 20 (3) ◽  
pp. 531-550 ◽  
Author(s):  
Hong-Liang Dai ◽  
Hao-Jie Jiang
Keyword(s):  
Cylindrical Shell ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Mechanical Load ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Constituent Material ◽  
Present Solution ◽  
Functionally Graded Piezoelectric ◽  
Forced Vibration Analysis

This article presents an analytical study for forced vibration of a cylindrical shell which is composed of a functionally graded piezoelectric material (FGPM). The cylindrical shell is assumed to have two-constituent material distributions through the thickness of the structure, and material properties of the cylindrical shell are assumed to vary according to a power-law distribution in terms of the volume fractions for constituent materials, the exact solution for the forced vibration problem is presented. Numerical results are presented to show the effect of electric excitation, thermal load, mechanical load and volume exponent on the static and force vibration of the FGPM cylindrical shell. The goal of this investigation is to optimize the FGPM cylindrical shell in engineering, also the present solution can be used in the forced vibration analysis of cylindrical smart elements.

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