# Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity

J. Awrejcewicz, V. A. Krysko, M. V. Zhigalov, A. V. Krysko

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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.

Original language English 1-21 21 Nonlinear Dynamics 91 2 https://doi.org/10.1007/s11071-017-3939-6 Accepted/In press - 23 Nov 2017

### Fingerprint

Rectangular Plate
Power spectrum
Ordinary differential equations
Contacts (fluid mechanics)
Partial differential equations
Elasticity
Stiffness
Nonlinearity
Contact
Mathematical models
Interaction
Contact Problem
Power Spectrum
Convergence Theorem
Modulus
Ordinary differential equation
Partial differential equation
Vibration
Mathematical Model
Iteration

### Keywords

• Contact interaction
• Iteration
• Physical nonlinearity
• Plate
• Stiffness variable parameters
• Variation

### ASJC Scopus subject areas

• Control and Systems Engineering
• Aerospace Engineering
• Ocean Engineering
• Mechanical Engineering
• Applied Mathematics
• Electrical and Electronic Engineering

### Cite this

Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity. / Awrejcewicz, J.; Krysko, V. A.; Zhigalov, M. V.; Krysko, A. V.

In: Nonlinear Dynamics, Vol. 91, No. 2, 23.11.2017, p. 1-21.

Research output: Contribution to journalArticle

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