Non-linear parametric vibration responses of composite plates on Pasternak foundations using extended dynamic stiffness method. Issue 3 (1st September 2020) - Huynh, Hung Quoc; Nguyen, Hien Luong Thi; Nguyen, Hai
ABSTRACT: In this work, the non-linear parametric vibration responses of rectangular laminated composite plates subjected on Pasternak foundation, under in-plane periodic compressive load applied along two opposite edges, are theoretically studied using the extended dynamic stiffness method. The authors present the new method to establish the exact dynamic stiffness matrices of rectangular laminated composite plates subjected to in-plane periodic forces based on general Von-Kármán large deflection plate theory. A set of second-order ordinary differential non-linear equations of extended Mathieu–Hill type with periodic coefficients is formed to determine the regions of dynamic instability and non-linear parametric vibration responses based on Bolotin method. The effects of various parameters such as static load, dynamic load, aspect ratio, boundary conditions, orthotropy and foundation stiffness factor on the dynamic instability regions and non-linear parametric vibration characteristics are investigated and discussed. For linear theory, the present results are found to be in agreement with available conclusions in the literature which was obtained based on the linear analysis.