Nonlinear vibration analysis of a circular plate–cavity system

  • Fatemeh Sadat Anvariyeh
  • Mohammad Mahdi JaliliEmail author
  • Ali Reza Fotuhi
Technical Paper


Vibration of plate with air cavity has been one of the interesting research fields by many researchers. This topic has many applications in vehicles, airplanes, aircraft, fuselage panels and buildings. In this study, nonlinear vibroacoustic of circular plate with air cavity under harmonic excitation is investigated. The von Karman theory is used to obtain plate equation and solved together with the air pressure equation. First, the nonlinear equation of the plate is converted to ordinary differential equations by using the Galerkin method. Then the method of multiple scales is employed to solve the corresponding nonlinear equations. Frequency response for primary, subharmonic and superharmonic resonances is studied analytically. Using this method, a parametric study is carried out and the effects of different parameters on the frequency response of the plate are investigated. According to the results, jump phenomena are observed for primary and superharmonic resonance cases. Also, with an increase in damping coefficient, the amplitude of the steady-state response increases in the subharmonic resonance case.


Vibroacoustic Nonlinear oscillation Circular plate Harmonic excitation Multiple scales method 



Depth of acoustic enclosure


Sound speed


Structural damping coefficient


Bending stiffness


Young’s modulus of elasticity




Acoustic pressure


External excitation


Airy stress function




Poisson’s ratio


Detuning parameter


Excitation frequency


Natural frequency


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringYazd UniversityYazdIran

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