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A Non-uniform Equivalent Model for Free Vibration Analysis of Sandwich Composite Panels with Trapezoidal Lattice Core

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Abstract

Objective

Free vibration characteristics of the trapezoidal lattice sandwich composite panels are investigated based on a novel equivalent plate model.

Methods

The equivalent shear modulus and the relative density of the graded lattice core are assumed to be thickness-dependent and these material properties are calculated based on the single-cell equivalence theory and the continuity assumption. Under the framework of the higher-order shear deformation theory (HSDT), the unknown displacement functions are expressed in terms of standard Fourier series and auxiliary functions to avoid discontinuities on the edges of lattice sandwich plate. Artificial spring technique is utilized to simulate arbitrary boundary conditions and the unknown coefficients in the displacement functions are obtained by Rayleigh–Ritz variational method.

Results

The accuracy of the present method can be verified by comparing the obtained results with FEM results and those from literature. On this basis, a detailed parametric study concerning the effect of boundary conditions, aspect ratio a/b, tilt angle θ, and lamination schemes on the vibration frequencies of the trapezoidal lattice sandwich plate is also performed.

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Data availability

Data sharing is not applicable to this paper as no data sets were created or analyzed during the current investigation.

Abbreviations

C,S,E,F:

Clamped, Simply support, Elastic, Free boundary conditions

x,y,z :

Coordinates axes

K u, K v, K w, K x, K y :

Spring stiffness coefficients

a, b :

Short and long bases of the trapezoidal core, (m)

c :

Distance between adjacent lattice core, (M)

t 0 :

Thickness of lattice core, (M)

θ :

Tilt angle of the core, (°)

l1, l2:

Length and width of a single cell, (m)

h f, h c :

Thickness of panel and core, (m)

L a, L b :

Length and width of sandwich panels, (m)

H :

Total thickness of sandwich panels, (M)

E 1 :

Modulus of elasticity of the face sheets, (GPa)

G :

Equivalent shear modulus, (GPa)

ρ, ρ c, ρ 0 :

Relative density, core density, the density of face sheets, (kg/m3)

M, N :

Truncation numbers

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (Grant Numbers: 12202324).

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Authors and Affiliations

  1. State Key Laboratory of Maritime Technology and Safety, Wuhan University of Technology, Wuhan, China

    Haoran Wang, Mengzhen Li & Xiaolong Liu

  2. School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan, China

    Haoran Wang, Mengzhen Li & Xiaolong Liu

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  1. Haoran Wang
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  2. Mengzhen Li
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Correspondence to Mengzhen Li.

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Wang, H., Li, M. & Liu, X. A Non-uniform Equivalent Model for Free Vibration Analysis of Sandwich Composite Panels with Trapezoidal Lattice Core. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01295-2

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  • DOI: https://doi.org/10.1007/s42417-024-01295-2

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