Free vibration of thin rectangular steel plates with geometrically-nonlinear load-displacement behavior

This paper provides means for obtaining the first three significant vibration modes for rectangular plates based on mass participation ratios. A non-dimensional frequency parameter is presented which results into the vibration frequency of rectangular plates at each of these three significant modes. Various aspect ratios and four combinations of boundary conditions at the plate edges are studied. A correlation between the nonlinear load deformation behavior of the plate and its vibrational behavior is also presented accordingly. It is demonstrated that the vibration frequency of the studied rectangular plates increases significantly upon increasing the applied lateral pressure if the large deformation effects are considered in the analysis. The easy-to-follow method of frequency calculation presented in this paper is useful for assessing the dynamic characteristics of rectangular plates with or without lateral pressure that are subject to vibration.