In this study, the new refine trigonometric shear deformation plate theory is used to study theout of plane vibration of rectangular isotropic plates with different boundary conditions. The novelty of the paper is that the analytical precision closed-form solution is developed without any use of approximation for a combination of six different boundary conditions; specifically, two opposite edges are hard simply supported and any of the other two edges can be hard simply supported, clamped or free. The equations of motion and natural boundary conditions, using Hamilton’s principle are derived. The present analytical Precision closed-form solution can be obtained with any required accuracy and can be used as benchmark. Based on comparison with previously published results, the accuracy of the results is shown. Finally, the effect of boundary conditions, variations of aspect ratios and thickness ratios on natural frequency parameters and relation between natural frequencies for different plates examined and discussed in detail.
