Nonlinear vibrations of laminated shells with layers of variable thickness

Kurpa, Lidiya; Shmatko, Tatiyana

doi:10.1201/b15684-75

Cited by 3 publications

(2 citation statements)

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“…where � i , i ¼ 1, 5 are undetermined components of the solution structure. 23,[30][31][32][33][34][35][36][37] They are expanded in a power series. In formula (27), !…”

Section: Investigation Of Laminated Fgm Shallow Shells With Complex Planformmentioning

confidence: 99%

“…[26][27][28] The problems of free vibration of laminated shallow shells with complex planform by RFM were considered in Kurpa et al 28 The algorithms of solving geometrically nonlinear vibrations of plates and shallow shells were proposed in various studies. [29][30][31][32][33][34] In the papers, [35][36][37] the method of the R-functions was extended to the problems of vibration of functionally graded shallow shells of arbitrary planforms.…”

Section: Introductionmentioning

confidence: 99%

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Buckling and free vibration analysis of functionally graded sandwich plates and shallow shells by the Ritz method and the R-functions theory

Kurpa

Shmatko

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The purpose of the paper is to study stability and free vibrations of laminated plates and shallow shells composed of functionally graded materials. The approach proposed incorporates the Ritz method and the R-functions theory. It is assumed that the shell consists of three layers and is loaded in the middle plane. The both cases of uniform as well as non-uniform load are possible. The power-law distribution in terms of volume fractions is applied to get effective material properties for the layers. These properties are calculated for different arrangements and thicknesses of the layers by the analytical formulae obtained in the paper. The mathematical formulation is carried out in framework of the first-order shear deformation theory. The proposed approach consists of two steps. The first step is to define the pre-buckling state by solving the respective elasticity problem. The critical buckling load and frequencies of functionally graded material shallow shells are determined in the second step. The highlight of the method proposed is that it can be used for vibration and buckling analysis of plates and shallow shells of complex shape. The numerical results for frequencies and buckling load of plates and shallow shells of complex shape and different curvatures are presented to demonstrate the potential of the method developed. Different functionally graded material plates and shallow shells composed of a mixture of metal and ceramics are studied. The effects of the power law index, boundary conditions, thickness of the core, and face sheet layers on the fundamental frequencies and critical loads are discussed in this paper. The main advantage of the method is that it provides an analytical representation of the unknown solution, which is important when solving nonlinear problems.

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“…where � i , i ¼ 1, 5 are undetermined components of the solution structure. 23,[30][31][32][33][34][35][36][37] They are expanded in a power series. In formula (27), !…”

Section: Investigation Of Laminated Fgm Shallow Shells With Complex Planformmentioning

confidence: 99%