A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams

Zhao, Jing; Wang, Qingshan; Deng, Xiaowei; Choe, Kwangnam; Xie, Fei; Shuai, Cijun

doi:10.1016/j.compositesb.2018.11.080

Cited by 66 publications

(15 citation statements)

References 33 publications

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“…We can get by the solving equation of L-shaped plate and cuboid cavity coupling system by using the equations (15) and (49) based on the Rayleigh-Ritz energy method. 48 The specific method is as follows…”

Section: Solution Process Of the Structural-acoustic Coupling Systemmentioning

confidence: 99%

“…We can get by the solving equation of L-shaped plate and cuboid cavity coupling system by using the equations (15) and (49) based on the Rayleigh–Ritz energy method. 48 The specific method is as follows where Hmn=true[boldW1mnboldU1mnboldV1mnboldW2mnboldU2mnboldV2mntrue]T. Through taking equations (16) to (43) and (45) to (49) into equations (50) and (51), the equation can be written as the following formula in which the stiffness matrix of L-shaped plate and cuboid cavity is noted as K plate and K cavity .…”

Section: Theoretical Knowledgementioning

confidence: 99%

See 1 more Smart Citation

Vibro-acoustic coupling characteristics of orthotropic L-shaped plate–cavity coupling system

Shi

Ren

Zhang

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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The research object of this paper is the L-shaped plate-cavity coupling system established by a cuboid acoustic cavity with rigid-wall or impedance-wall and L-shaped plate with numerous elastic boundary conditions in view of the Fourier series method. The main research content of this paper is the vibro-acoustic coupling characteristics. In this paper, the displacements admissible functions of the L-shaped plate are generally set as the sum of two cosines' product and two polynomials. Sound pressure admissible functions of the cuboid acoustic cavity can be considered as the sum of three cosines' product and six polynomials. The discontinuity of coupling system at all boundaries in the overall solution domain is overcome in this way. Through the energy principle and the Rayleigh-Ritz technology, it can be got that the solving matrix equation of the L-shaped plate-cavity coupling system. Based on verifying the great numerical characteristics of the L-shaped plate-cavity coupling model, they obtained both the frequency analysis and the displacement or sound pressure response analysis under the excitation, including a unit simple harmonic force or a unit monopole source. The advantages of this method are parameterization and versatility. In addition, some new achievements have been shown, based on various materials, boundary conditions, thicknesses, and orthotropic degrees, which may become the foundation for the future research.

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Section: Solution Process Of the Structural-acoustic Coupling Systemmentioning

confidence: 99%

Section: Theoretical Knowledgementioning

confidence: 99%

Vibro-acoustic coupling characteristics of orthotropic L-shaped plate–cavity coupling system

Shi

Ren

Zhang

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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“…The relationship between coefficients of porosity and mass density is determined based on the Gibson and Ashby approach considering open-cell unidirectional porosity where the porosity is distributed through the thickness of the beam. Same concept for porosity modeling has been used by Gao et al [39], Baghlani et al [40], Wu et al [41], Zhao et al [42] and Xie et al [43] to study dynamic responses of porous beams and shells with various boundary conditions. Most of the researches in the literature are focusing on the unidirectional porous structures, where Young's modulus and mass density are varying only through the thickness.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of bidirectional porous beams

Keleshteri

Jelovica

2021

Engineering with Computers

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This paper presents nonlinear vibration behavior of shear deformable bidirectional porous beams with non-uniform porosity distribution. A new porosity distributions are proposed to maximize natural frequencies of the porous beam. It is assumed that closed-cell voids are distributed along the thickness and length of the beam. Hamilton principle is used to derive nonlinear governing equations using Reddy beam theory considering von Karman geometrical nonlinearity. Generalized differential quadrature method, harmonic balance approach along with the Picard iterative approach are used to discretize and solve the nonlinear dynamic equations. The variation of nonlinear frequency versus the vibration amplitude is highlighted considering various influential factors such as geometrical parameters, porosity distributions, beam theories and boundary conditions. It is shown that the newly defined porosity distribution can increase the frequencies in comparison to the conventional porosity distribution. Comparing beams of the same weight shows that porosities near the center of the beam further increases frequencies in comparison to the other porosity distributions. Moreover, bidirectional porosity increases the frequencies in comparison to the unidirectional porosity. Frequencies of the bidirectional porous Reddy beam depend not only on the bending stiffness, as in the case of unidirectional porous beam, but also on the first derivative of the bending stiffness.

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“…The size effect was included using the modified couple stress theory. A modified series solution for free vibration analyses of moderately thick functionally graded porous deep curved and straight beams with general boundary conditions were proposed by Zhao et al [36]. Their results showed that the highest frequencies were obtained by the FGP beams with symmetric porosity distribution, but the lowest frequencies were resulted by the FGP beams with uniform porosity distribution.…”

Section: Introductionmentioning

confidence: 99%

Bending, Free Vibration, and Buckling Analysis of Functionally Graded Porous Micro-Plates Using a General Third-Order Plate Theory

2019

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Static bending, free vibration and buckling of functionally graded porous micro-plates are investigated using a general third order plate theory. In addition, analytical solutions are obtained using the Navier method. The effect of the material length scale factor and the variation of material property through the thickness direction of plates are considered as well as porosity effects. Three different porosity distributions are considered and the effects of porosity variations are examined in the framework of a general third order plate theory. Numerical results show that the effect of each distribution of porosity is distinguished due to coupling between the heterogeneity of the material properties and the variation of porosity.

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A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams

Cited by 66 publications

References 33 publications

Vibro-acoustic coupling characteristics of orthotropic L-shaped plate–cavity coupling system

Vibro-acoustic coupling characteristics of orthotropic L-shaped plate–cavity coupling system

Nonlinear vibration analysis of bidirectional porous beams

Bending, Free Vibration, and Buckling Analysis of Functionally Graded Porous Micro-Plates Using a General Third-Order Plate Theory

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