Free vibration analysis of laminated composite and functionally graded sector plates with general boundary conditions

Su, Zhu; Jin, Guoyong; Wang, Xueren

doi:10.1016/j.compstruct.2015.06.008

Cited by 36 publications

(19 citation statements)

References 32 publications

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“…Results were found to be the same for both Love's and Donnell's theories. By increasing sector angle, natural frequencies of FGM sector plates tend to decrease (Su et al [156]). Li and Zhang [157] examined free vibration of rotary FGM plates by means of dynamic model considering the dynamic stiffening effect.…”

Section: Fgm Platesmentioning

confidence: 99%

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Zhang

Khan

Guo

et al. 2019

Advances in Materials Science and Engineering

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Functionally graded materials (FGMs) are novel materials whose properties change gradually with respect to their dimensions. It is the advanced development of formerly used composite materials and consists of two or more materials in order to achieve the desired properties according to the application where an FGM is used. FGMs have obtained a great attention of researchers in the past decade due to their graded properties at every single point in various dimensions. The properties of an FGM are not identical to the materials that constitute it. This paper aims to present an overview of the existing literature on stability, buckling, and free vibration analysis of FGM carried out by numerous authors in the past decade. Moreover, the analyses of mathematical models adopted for the aforementioned analyses are not the core purpose of this paper. At the end, future work is also suggested in this review paper.

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Section: Fgm Platesmentioning

confidence: 99%

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Zhang

Khan

Guo

et al. 2019

Advances in Materials Science and Engineering

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“…Akbari et al [9] took account of the effects of parameters on natural frequencies and utilized generalized differential quadrature method to study free vibration of Levy type of FGM conical panels. Su et al [10,11] examined free vibration of FGM cylindrical, conical shells and annular plates by the Rayleigh-Ritz method. Xie et al [12] explored a simple efficient solution for the free vibration analysis of functionally graded conical shells and annular plates.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of Imperfect FGM Conical Panel

Niu

Hao

Yao

et al. 2018

Shock and Vibration

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Structures composed of functionally graded materials (FGM) can satisfy many rigorous requisitions in engineering application. In this paper, the nonlinear dynamics of a simply supported FGM conical panel with different forms of initial imperfections are investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers of the imperfection, amplitudes of the imperfection, and damping on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories, phase portraits, and Poincare maps are obtained to show the dynamic responses of the system.

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“…However, the aim of this paper is to study the vibration analysis of moderately thick functionally graded sector plates resting on two-parameter elastic foundation with general boundary conditions. Thus, in order to simplify this study and based on existing literature [5,71], the shear Shock and Vibration 5 correction factor is selected as a generic parameter = 5/6 in the next calculation.…”

Section: Energy Expressionsmentioning

confidence: 99%

“…It is worthwhile to note that the interest of researches in this procedure is increasing due to its great simplicity and versatility. Therefore, this simple and direct procedure can be applied to a large number of structures, that is, beams [60][61][62][63], plates [5,[64][65][66][67][68][69][70][71][72][73][74][75][76], shells [77][78][79][80][81][82][83], coupled structures [84][85][86][87][88], and so on. In addition, compared with other methods, the present method can obtain accurate results and circumvent the difficulties of programming complex algorithms for the computer as well as the excessive use of storage and computer time.…”

Section: Introductionmentioning

confidence: 99%

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Pang

Wang

et al. 2017

Shock and Vibration

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The free vibration analysis of moderately thick functionally graded (FG) sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the powerlaw distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT) is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.

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Free vibration analysis of laminated composite and functionally graded sector plates with general boundary conditions

Cited by 36 publications

References 32 publications

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Nonlinear Dynamics of Imperfect FGM Conical Panel

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

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