Free vibration of FGM plates with in-plane material inhomogeneity

Liu, D.Y.; Wang, C.Y.; Chen, Weiqiu

doi:10.1016/j.compstruct.2009.10.001

Cited by 87 publications

(32 citation statements)

References 25 publications

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“…The Poisson's ratio is considered constant. This power law distribution is one of the most appropriate and also simplest models for a two phase mixture, which is established by VoightType estimate (Liu et al 2010;Markworth et al 2012). The constitutive equation of the FGM beam is given by the Hooke's law:…”

Section: Introductionmentioning

confidence: 99%

“…Simsek et al (2012) studied the dynamic behavior of an axially FGM beam under action of a moving harmonic load. Liu et al (2010) and Uymaz et al (2012) have considered the case of FGMs plates frequencies. Liu et al (2010) used a semi analytic Levy-integration, while the vibrations solutions are obtained using the Ritz method and the Chebyshev polynomials in Uymaz et al (2012).…”

Section: Introductionmentioning

confidence: 99%

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Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Bruant

Proslier

2015

Int J Mech Mater Des

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Up to now, optimal location for active control studies concern principally multilayers or homogeneous structures. In the case of functionally graded materials, very few papers exist and they only concern cross section variations. In this way, this paper deals with the optimization of piezoelectric actuators locations on axially functionally graded beams for active vibration control. For this kind of structures, the free vibration problem is more complicated as the governing equations have variable coefficients. Here, the eigenproblem is solved using Fredholm integral equations. The optimal locations of actuators are determined using an optimization criterion, ensuring good controllability of each eigenmode of the structure. The linear quadratic regulator, including a state observer, is used for active control simulations. Two numerical examples are presented for two kinds of boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Bruant

Proslier

2015

Int J Mech Mater Des

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“…Direct problems concerned with finding stresses and displacements in a structure of known shape and composed of inhomogeneous materials, such as fiber-reinforced composites and functionally graded materials (FGMs), have been studied extensively [1][2][3][4][5][6][7][8][9][10]. Generally an inhomogeneous material has material moduli varying in one or more spatial directions.…”

Section: Introductionmentioning

confidence: 99%

Material tailoring for orthotropic elastic rotating disks

Nie

Zhong

Batra

2011

Composites Science and Technology

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“…However, information about rectangular plates with in-plane inhomogeneity is very limited. Fundamental frequencies of FGM rectangular plates with in-plane material inhomogeneity was studied by Liu et al [14] using the Fourier series expansion and an integration technique. Uymaz et al [15] presented natural frequencies for classical and higher order plates by the Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

Boreyri

Ketabdari

Mohtat³

et al. 2016

IJPR

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In this research, free vibration of rectangular functionally graded (FG) plates with in-plane exponentially non-homogeneous material is investigated. Young's modulus and mass density are assumed to vary between a metal-rich and a ceramic-rich zone along one in-plane direction of the plate. The governing differential equation is derived for the case, and a truncated Taylor series expansion technique is utilized to calculate natural frequencies. A Levy-type solution is obtained for plates having two simply supported edges parallel with the material gradient direction. Results for normalized natural frequency are compared with the 4th order Runge-Kutta method, and when possible with exact solution, showing an accurate agreement. Furthermore, a comprehensive parametric study is carried out to determine the effects of different boundary conditions, aspect ratios, and material variations on the free vibration of FGM plates. Nomenclature

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Free vibration of FGM plates with in-plane material inhomogeneity

Cited by 87 publications

References 25 publications

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Material tailoring for orthotropic elastic rotating disks

Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

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