Free Vibration Analysis of Cross-Ply Laminated Conical Shell, Cylindrical Shell, and Annular Plate with Variable Thickness Using the Haar Wavelet Discretization Method

Kim, Jangsu; Kim, Kwanghun; Kim, Kwang Il; Hong, Kwonryong; Paek, Chonghyok

doi:10.1155/2022/6399675

Cited by 6 publications

(1 citation statement)

References 76 publications

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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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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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Dynamics of a three-phase polymer/fiber/CNT laminated nanocomposite conical shell with nonuniform thickness

Darakhsh,

Rahmani,

Amirabadi

et al. 2023

J Braz. Soc. Mech. Sci. Eng.

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In the presented paper, the free vibration of a polymer/fiber/CNT laminated nanocomposite conical shell with nonuniform thickness and surrounded by an elastic two-parameter foundation are analyzed. The shell is made of a polymeric matrix enriched simultaneously with randomly oriented carbon nanotubes (CNTs) and aligned glass fibers. CNTs agglomeration is included and the density and elastic constants of such a three-phase nanocomposite are calculated using the rule of mixture and the Eshelby-Mori-Tanaka approach alongside Hanh's homogenization method. The conical shell and the elastic foundation are modeled using the first-order shear deformation theory (FSDT) and the Pasternak foundation model, consecutively. The governing equations are derived using Hamilton's principle and are solved numerically via the differential quadrature method (DQM). The impacts of several parameters on the natural frequencies of such a structure are discussed such as thickness variation parameters, mass fraction and chirality of the CNTs, mass fraction of the fibers, and boundary conditions. It is observed that by considering the specific value for the average thickness of the shell, the thickness variation parameters associated with the highest natural frequency are different in various vibrational modes. It is discovered that, the natural frequencies grow by increasing mass fraction of the CNTs, but the influences of mass fraction of the fibers on the natural frequencies are strongly dependent on the vibration mode.

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Localized stochastic dynamic solution for laminated coupled open conical-cylindrical cabin system based on the condensation method

Guo,

Wang,

Liu

et al. 2025

Thin-Walled Structures

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Free Vibration Analysis of Cross-Ply Laminated Conical Shell, Cylindrical Shell, and Annular Plate with Variable Thickness Using the Haar Wavelet Discretization Method

Cited by 6 publications

References 76 publications

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

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

Dynamics of a three-phase polymer/fiber/CNT laminated nanocomposite conical shell with nonuniform thickness

Localized stochastic dynamic solution for laminated coupled open conical-cylindrical cabin system based on the condensation method

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