A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports

Yeqing Jin,Haiwei Xu,Hailong Chen,Hengxu Liu,Ruiping Yang

doi:10.3390/app11199141

Yeqing Jin, Haiwei Xu + Show 3 more

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https://doi.org/10.3390/app11199141

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Abstract

Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed method is to convert the three truss cores of lattice sandwich beams into an equivalent homogeneous layer and introduce two different types of constraint springs to simulate the general elastic support boundary at both ends of lattice sandwich beams. By changing the rigidity of the boundary restraint spring, various boundary conditions can be easily obtained without modifying the solving algorithm and solving process. In order to overcome all the discontinuities or jumps associated with the elastic boundary support conditions, the displacement function of lattice sandwich beams is usually obtained as an improved Fourier cosine series along with four sine terms. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh–Ritz method. The correctness of the present method is verified through comparison with existing literature. The calculation results of the present method are highly accurate, indicating that the present method is suitable for analyzing the vibration characteristics of lattice sandwich beams with general elastic supports. In addition, the effects of beam length, panel thickness, core height, radius and truss inclination on the natural frequencies of lattice sandwich beams with arbitrary boundary conditions have been discussed in this paper.

Highlights

Consisting of two thin panels attached to each side of a thick core, the sandwich structure is a special structure of composite materials
The calculation results will be compared to the data of existing literature, which were calculated by Hwu et al [19], Lou et al [21] and Xu et al [27] under typical boundary conditions
The material properties and geometric dimensions of the pyramidal lattice sandwich beam involved in the calculation are listed as: L = 0.6364 m, B = 0.06364 m, t = 0.0005 m, c = 0.015 m, r = 0.001 m, α = 45, Es = Ex = 210 GPa, υ = 0.3 and ρf = ρ = 7930 kg/m3

Summary

Introduction

Consisting of two thin panels attached to each side of a thick core, the sandwich structure is a special structure of composite materials. When the sandwich structure is subjected to a bending load, its panel will bear plane compression and tensile loads, and the core material will bear shear loads. The mechanical properties of the sandwich structure can be obtained by selecting different panel and core material configurations simultaneously. Sandwich structures of foam [10,11] and honeycomb materials [12,13] have been widely used as traditional sandwich structures due to their high rigidity and weight ratio, which can significantly reduce weight while maintaining mechanical properties. The conventional sandwich structure cannot be universally used, as it is not compatible with closed-cell foam or a honeycomb core

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