Geometrically nonlinear analysis of thin circular plates on Winkler elastic foundations has been studied in this paper. The nonlinear partial differential equations obtained from von Karman’s large deflection plate theory have been solved by using the discrete singular convolution (DSC) in the space domain and the harmonic differential quadrature (HDQ) method in the time domain.

The current work focuses on predicting the buckling and free vibration frequencies (fn) of cenosphere reinforced epoxy based syntactic foam beam under varying loads. Critical loads (Ncr) fn are predicted using differential quadrature method (DQM). Ncr have been calculated for beams volume fractions subjected to axial load clamped-clamped (CC), clamped-simply (CS), simply-simply (SS), clamped-fr...

V-shaped and triangular cantilevers are widely employed in atomic force microscope (AFM) imaging techniques due to their stability. For the design of vibration control systems of AFM cantilevers which utilize patched piezo actuators, obtaining an accurate system model is indispensable prior to acquiring the information related to natural modes. A general differential quadrature element method (...