Abstract
A mathematical model of a contact interaction between two plates made from materials with different elasticity modulus is derived taking into account physical and design nonlinearities. In order to study the stress–strain state of this complex mechanical structure, the method of variational iteration has been employed allowing for reduction of partial differential equations to ordinary differential equations (ODEs). The theorem regarding convergence of this method is formulated for the class of similar-like problems. The convergence of the proposed iterational procedure used for obtaining a solution to contact problems of two plates is proved. In the studied case, the physical nonlinearity is introduced with the help of variable parameters associated with plate stiffness. The work is supplemented with a few numerical examples. Both Fourier and Morlet power spectra are employed to detect and analyse regular and chaotic vibrations of two interacting plates.
Highlights
Many researchers have indicated that several structural materials may exhibit different tensile and compression response under flexural testing
The so far discussed method of variational iterations (MVI) coincides with the first term of the series of the method developed by Arganovskiy and Baglay [36], Baglay and Smirnov [37]
The following general conclusions can be formulated as a result of the carried out research
Summary
Many researchers have indicated that several structural materials may exhibit different tensile and compression response under flexural testing. Composites fabricated from carbon fibres pre-impregnated by epoxy polymer usually present different elastic responses under tension and compression in the principal material directions This phenomenon has been observed for the first time by Jones [1], who introduced the name of multi-modulus materials. Patel et al [5] carried out both theoretical and experimental investigations of material properties of a calendared ply of numerous composites widely used in the body and belt of radial tires They detected bi-modulus behaviour under tension and compression. The second widely accepted model was proposed by Amburtsmian [17] and was validated for isotropic materials It allows for estimation of different tension and compression moduli based on the positive/negative sign of the fundamental stresses, which play an important role in engineering application.
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