A General Approach for the Analysis of Transverse Vibration Characteristics of a Rectangular Plate with Arbitrary-shaped Openings

Abstract Based on the Rayleigh-Ritz method, transverse vibration characteristics of a rectangular plate with an arbitrarily shaped inner opening are investigated. A modified two-dimensional Fourier series was chosen as trial function and springs different stiffnesses were used to equate arbitrary boundary conditions plate. The Lagrange generalization open is obtained by equating area special film physical properties zero according energy superposition principle. variational method derive characteristic equations thin find intrinsic frequencies corresponding modes. convergence this theoretical analyzed means example, accuracy verified comparison results finite element software calculations, which provides reference for practical engineering problems.