Vibration analysis of thin circular plates with multiple openings by the assumed mode method

Abstract

Circular plates with openings are used in many engineering structures, especially as swash bulkheads in cargo tanks of liquefied gas carriers. In this article, an approximate procedure is worked out for the vibration analysis of circular plates with different boundary conditions and a different number and size of openings with an arbitrary arrangement within the plate area. The assumed mode method, recently used in the vibration analysis of rectangular plates, is applied in this case. Following the basic idea, the effect of the openings is accounted for by subtracting the potential and kinetic energy of the cutout plate parts corresponding to the total plate energies without openings. The procedure is illustrated with numerical examples related to the vibration analysis of annular plates and circular plates with openings. The results are evaluated through their comparison with an analytical and finite element method solution.

Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution

“…Comparison with the classic motion equation of the circular plate without a complex pre-stress will be considered, and the coupling item Cðw; r 0;r ; r 0;h Þ is added, which is the function of coordinates h and r. Comparison with the motion equation of the circular thin plate with uniform pre-stress distribution, the varying factor of the pre-stress amplitude is considered. Thus, a new approach is required to gain the analytic solution of equation (11). The analytical solution can be applied to the circular plate structure with arbitrarily distributed stress and has a wide range of applications than previous analytical methods.…”

“…In the numerical analysis, the energy method based on Hamiltonian dual equations or Rayleigh-Ritz method becomes a hot issue in dynamic response analysis of the circular plate structure. [9][10][11] The Rayleigh-Ritz method has extensively gained the attention of researchers because the assumed deflection functions are required to satisfy the geometrical boundary conditions only. 12,13 On the other hand, the various form stress usually exists in the continuous structure before it undertakes the work loading, and it is named as pre-stress or initial stress.…”