Large Amplitude Free Vibration of thick Laminated Composite Plates with Magnetorheological Core Via a New Sinusoidal Shear Deformation Theory

Large amplitude free vibrations have nonlinear behavior that may be detrimental to structures . As a result, they need to be effectively regulated .A composite sandwich panel with a magnetorheological (MR) core's nonlinear vibration was examined, and the softening and hardening behaviors were investigated utilizing the New Sinusoidal Shear Deformation Theory. The extraction of the governing equations and boundary conditions was made possible by Hamilton's principle. Using the harmonic balancing approach, the equation was solved analytically with cubic and quadratic nonlinearities, followed by comparing the data with the proven findings. The utilization of Galerkin's approximation approach led to the development of ordinary differential equations from the governing PDEs. When aspect ratio, damping parameter and sandwich panel thickness values increase, the vibration amplitude reduces. It is used to describe a rise in amplitude that causes a rise in nonlinear frequency. The structure's inherent frequency increased as the MR layer's thickness increased. Sandwich panels that are thick and orthotropic were found to exhibit a more significant hardening behavior. As the magnetic field grows, the structure substantially hardens in the nonlinear state, improving the stability of the system. For controlling the vibration behavior, raising the magnetic field declines the structure frequency and elevates the aspect ratio of panel raises the frequency.