A unified Jacobi–Ritz approach for the FGP annular plate with arbitrary boundary conditions based on a higher-order shear deformation theory

Zhao, Yiming; Qin, Bin; Wang, Qingshan; Liang, Xifeng

doi:10.1177/10775463211072677

Cited by 3 publications

(1 citation statement)

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“…However, in the majority of practical applications, these boundary conditions are not accurate. It is essential to study the dynamic characteristics of bi-stable structures under elastic support boundary conditions [18][19][20][21][22][23][24][25][26][27]. Also, both asymmetric and antisymmetric stacking sequences are the most common laminates; they should receive more attention and research.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Trapezoidal Bi-Stable Laminates Supported at the Elastic Midpoint of the Median Line

Xu,

Hao,

Zhang

et al. 2023

Mathematics

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This study investigates the natural vibration of trapezoidal bi-stable laminates (TBL) with elastic supports at the midpoints of the median lines. Configuration of the midplane of the TBL is expressed by a polynomial with 17 parameters. Then, the first order shear deformation theory, curing temperature, and nonlinear strain displacement relations combining energy principles are applied to obtain the bi-stable shapes numerically. Three translational springs and two rotational springs are added at the midpoint of the median line in the trapezoidal bi-stable laminate to acquire elastic point supports. And, by varying the stiffness of the springs, arbitrary elastic point support boundary conditions can be achieved. Chebyshev polynomials are applied to characterize the mode shape function of the TBL. The vibration mode functions of the TBL are mapped to a square area under the new coordinate system by using the coordinate mapping method. Furthermore, the effects of geometry, layup sequence, and spring stiffness on the natural vibrations of the TBL are analyzed, which provides a reference for research in this field. The innovation and highlights lie in the following: (1) the natural frequencies and modes of trapezoidal bi-stable plates are solved; (2) arbitrary elastic support is achieved by a set of artificial springs; (3) the influences of spring stiffness, layer sequence, and trapezoidal base angle on the natural vibration of a trapezoidal bi-stable plate are studied.

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