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A boundary perturbation method is developed to determine the fundamental frequency of vibrating plates.
A boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem.
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The perturbation method is employed.
A perturbation method is presented to analytically calculate eigensolutions of the two dimensional wave equation when asymmetric perturbations are present in the boundary conditions.
A perturbation method is then employed to determine the nonlinear vibration behavior and the nonlinear natural frequencies of the beams with simply supported and clamped boundary conditions.
The perturbation method is applied in two different ways.
The perturbation method is used for solving the problem.
Perturbation method is a well-known and highly efficient method for the linearization of nonlinear systems.
Also homotopy perturbation method was successfully applied to Voltra's integrodifferential equation [14], boundary value problem [8], nonlinear wave equations [15], and so forth; see [16 20].
Results of perturbation method are agreement with numerical simulations.
More details of the perturbation methods are discussed below.
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