GENERAL ANALYTICAL METHOD FOR FREE VIBRATION OF RECTANGULAR PLATES ELASTICALLY RESTRAINED AGAINST ROTATION

Different from simple supports and clamped supports, the supports with elastic restrains against rotation restrain not only the vertical translation, but the moment at the supported edge, which linearly related to the slope of the edge. Using the differential equation for transverse displacement function of rectangular thin plates in free vibration, a general analytical solution is established. This general solution includes both trigonometric function solutions and hyperbolic function solutions, and can satisfy arbitrary boundary conditions. The unknown constants can be determined by applying boundary conditions of four edges. Each natural frequency and vibration mode can be exactly solved by the condition that the determinate of coefficient matrix from the homogeneous linear algebraic equations equals to zero. As the rectangular plate is symmetric in plane, it can facilitate the analysis to take advantages of symmetric and anti-symmetric conditions. Finally, a square plate with four edges elastically restrained against rotation is analyzed and discussed.