Vibration analysis of point and column supported mindlin plates.

Abstract

Free vibration characteristic of an isotropic, homogeneous point supported square plate with no initial deflection and no initial stresses have been critically examined by a method based on the application of variation principle to the energy expressions in conjuction with Finite Difference methods with interlacing grids. Using the symmetry of the geometry of the plate and the symmetry in the distribution of the point supports, only one quarter of the plate was examined. Three mode types were developed to account for the full plate. The effect of transverse shear deformation and rotary inertia have been considered and the effect of finite area of the point support has also been analyzed. The produced mode shapes and nodal patterns were presented. Experiments were conducted to give an insight to the theoretical predictions. The natural frequencies were obtained from the frequency response of the real and imaginary part. Nyquist (Argand) plots of the corner supported case were also presented. The convergence of the present method to the theoretical exact value of the frequency parameter were found to be either from above or below. It has been shown by the theoretical investigation that the effect of transverse shear deformation and rotary inertia were more pronounced in the higher modes. It was observed that the fundamental frequency parameter increases as the point support moves towards the center and the maximum occurs at a = 0.23. The radian natural frequency obtained from the frequency response showed that the theoretical predictions were considerably accurate with maximum discrepancy of 2.48 percentage. The result of the studies could be applied in many practical applications such as the design of large shakers capable of supplying yaw as well as thrust motion to the test specimens.