Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections

Chen, Xianfeng; Chen, Lunting; Huang, Shilin; Li, Ming; Li, Xiao

doi:10.1016/j.apm.2020.12.033

Cited by 34 publications

(4 citation statements)

References 80 publications

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“…Zhou et al [ 11 ] proposed a unified solution considering both classical and non-classical boundary conditions to analyze the vibration and flutter behavior of supersonic porous functionally graded material plates. Chen et al [ 12 ] studied the nonlinear vibration of a bidirectional functionally graded material plate with geometric defects under transverse harmonic excitation and found that changes in gradient parameters and the presence of geometric defects did indeed alter the nonlinearity of the resonance response. Yin et al [ 13 ] combined three-dimensional elastic theory with the finite element method to study the bending and free vibration of porous functionally graded material plates.…”

Section: Introductionmentioning

confidence: 99%

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

Han

Huang

et al. 2023

Materials

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This paper investigates the thermal mechanical bending response of symmetric functionally graded material (FGM) plates. This article proposes a thermodynamic analysis model of both the FGM plate and FGM sandwich plate, and the model only involves four control equations and four unknown variables. The control equation is based on the refined shear deformation theory and the principle of minimum potential energy. The Navier method is used to solve the control equation. According to the method, numerical examples are provided for the thermo-mechanical bending of the symmetric FGM plate and FGM sandwich plate under a simply supported boundary condition, and the accuracy of the model is verified. Finally, parameter analysis is conducted to investigate the effects of the volume fraction index, side-to-thickness ratio, thermal load, and changes in core thickness on the thermal mechanical bending behavior of the symmetric FGM plate and FGM sandwich plate in detail. It was found that the deflection of the FGM plate is greater than that of the FGM sandwich plate, while the normal stress of the FGM plate is smaller than that of the FGM sandwich plate. Moreover, the FGM plate and FGM sandwich plate are sensitive to nonlinear temperature changes.

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Section: Introductionmentioning

confidence: 99%

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

Han

Huang

et al. 2023

Materials

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“…Further, numerous investigations were performed to analyze the BDFGM plate structures in the framework of three-dimensional elasticity equations, analytical methods, finite element methods, iso-geometric approach, and several shear deformation theories. 7,[33][34][35][36][37][38][39] Many studies on BDFGM plates have been carried out to examine the flexural, 3,5,32,37,[40][41][42][43][44] vibrational, [45][46][47][48][49][50][51][52] and stability 7,40,53,54 behavior of the BDFGM and MDFGM plates. Besides, Lezgy-Nazargah 55 employed the NURBS-dependent isogeometric finite element (FE) approach to examine the thermo-mechanical behavior of BDFGM beams.…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials

Shivaramaiah

Kattimani

Shariati

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This article investigates the influence of porosity distributions on the nonlinear behavior of two-directional functionally graded porous plates (TDFGPP) made from four distinct materials for the first time. A simple and effectual approach is established based on the improved generalized shear deformation plate theory (GSDPT) and von Karman’s assumptions. The GSDPT incorporates transverse shear strains with a higher order polynomial to avoid shear locking. The TDFGPP constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both transverse and longitudinal directions. The governing equations are obtained using a nonlinear finite element approach in conjunction with Hamilton’s principle. Then, the direct iterative and Newmark’s methods are incorporated to accomplish the numerical results. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, thickness ratio, and aspect ratio for different support conditions provides a thorough insight into the linear and nonlinear responses of the porous plate. In addition, this study emphasizes the influence of the volume fraction gradation profiles with four different materials on the linear frequency, nonlinear frequency, and deflections of the TDFGPP. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in specified directions with appropriate materials. Hence, two-directional functionally graded materials panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

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“…In recent years, the vibration behaviors of composite laminated beams [20], plates [21,22], and shells [23,24] have been of much interest to many engineers and researchers. Among them, composite laminated conical shells with spinning motion are normally paid much interest, especially in the following papers.…”

Section: Introductionmentioning

confidence: 99%

“…21 ), and Q 66 = G 12 , in which E 1 , E 2 are elastic moduli in principal orientation, G 12 shear modulus, and v 12 , v 21 Poisson ratios.…”

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confidence: 99%

Free Vibration Analysis of a Spinning Composite Laminated Truncated Conical Shell under Hygrothermal Environment

Zhang

Zhou

2022

Symmetry

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This paper is concerned with free vibration characteristics of a spinning composite laminated truncated conical shell subjected to hygrothermal environment. Hygrothermal strains are introduced into the constitutive law of single-layer material, and fiber orientation lies symmetrically with respect to the midplane of the composite shell. Considering the spin-induced Coriolis and centrifugal forces, as well as initial hoop tension, the governing equations of free vibration of the composite conical shell with hygrothermal effects are derived on the basis of Love’s thin-shell theory and Hamilton’s principle. The solution of the equations is derived using the Galerkin approach. Then, a detailed parametric study on natural frequencies and critical spinning speeds is numerically performed. Results indicate that the Coriolis force induces an asymmetric influence on natural frequencies of forward and backward traveling waves, while the centrifugal force enhances the frequencies of both traveling waves symmetrically. Initial hoop tension plays a major role in the increase of critical spinning angular speed. Temperature, moisture concentration, and design parameters show the significant influence on the free vibration characteristics of the conical shell, and thermal expansion deformation is nonnegligible in the free vibration analysis.

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Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections

Cited by 34 publications

References 80 publications

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials

Free Vibration Analysis of a Spinning Composite Laminated Truncated Conical Shell under Hygrothermal Environment

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