Dynamic Response and Vibration Power Flow Analysis of Rectangular Isotropic Plate Using Fourier Series Approximation and Mobility Approach

  • Kavikant Mahapatra
  • S. K. PanigrahiEmail author
Original Paper



In this paper, a unified and numerically efficient method is proposed to analyse the dynamic response and vibration power flow characteristics of flat isotropic rectangular plate subjected to a harmonic loading.


The boundary of the plate system has been assumed to be elastic boundary and expressed as a combination of translational and rotational spring stiffness, making the system near to real system. The plate displacement function has been derived using combination of trial beam functions, expressed as modified Fourier cosine series, in x and y direction. Finally, Rayleigh-Ritz method is employed to the Lagrangian function to derive the frequency matrix.


The derived frequency matrix can be universally applied to analyse the dynamic response of the plate system and power flow distribution on the plate surface for any condition of boundary condition and force application.


The method is numerically superior to other method because of omission of complex hyperbolic trigonometric functions and appreciable reduction of the size of the frequency matrix, which has been established through comparison of results with the existing literature


Elastic boundary Fourier cosine series Harmonic loading Isotropic rectangular plate Spring stiffness Modified dynamic response Vibration power flow 


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Authors and Affiliations

  1. 1.Department of Mechanical EngineeringDefence Institute of Advanced Technology (Deemed University)PuneIndia

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