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On Transverse Vibrations of Rectangular Plates of Unidirectional Parabolic Thickness Variation

[+] Author Affiliations
Dumitru I. Caruntu

University of Toledo

Paper No. IMECE2005-80903, pp. 1009-1012; 4 pages
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Design Engineering, Parts A and B
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Design Engineering Division
  • ISBN: 0-7918-4215-0 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME


This paper presents an approach for finding the solution of partial differential equation describing the motion of transverse vibrations of rectangular plates of unidirectional convex parabolic varying thickness. The partial differential equation consists of three operators: fourth-order spatial-dependent, second-order spatial-dependent, and second-order time-dependent. Using the method of multiple scales, the partial differential equation has been reduced to two simpler partial differential equations which can be analytically solved and which represent two levels of approximation. The first partial differential equation was a homogeneous equation and consisted of two operators, the fourth-order spatial-dependent and second-order time-dependent. Using the factorization method, so-called zero-order approximation of the exact solution has been found. The second partial differential equation was an inhomogeneous equation. Its solution, so-called first-order approximation of the exact solution has been found. This way the first-order approximations of the natural frequencies and mode shapes are found. Various boundary conditions can be considered. The influence of Poisson’s ratio on the natural frequencies and mode shapes could be further studied using the approximations reported here. This approach can be extended to nonlinear, and/or forced vibrations.

Copyright © 2005 by ASME



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