Background Free vibrations with high amplitude behave mainly nonlinearly, which can be dangerous to structures. Thus, they must be controlled effectively. We used an improved higher-order shear deformation theory for analyzing the nonlinear versus linear vibration of a composite sandwich panel with an Electrorheological (ER) Core and examined the hardening and softening behaviors. Methods The boundary conditions and governing equations were extracted by Hamilton’s principle. Via the harmonic balance method, we solved the equation analytically with quadratic and cubic nonlinearities and the data were compared with the established results. Ordinary differential equations were yielded by applying Galerkin’s approximation technique to the governing partial differential equations. Results As each of the parameters of the aspect ratio and the sandwich panel thickness and damping increases, the vibration amplitude decreases. This means the increase of non-linear frequency by the increased amplitude. By increasing the thickness of the ER layer, the natural frequency of the structure increased. An increase was found in hardening behavior for the orthotropic and thick sandwich panel. Conclusions By increasing the electric field in the nonlinear state, the structure hardens significantly, which improves the system’s stability. To control the vibration behavior, increasing the electric field decreases the structure’s frequency while increasing the panel’s aspect ratio increases the frequency.
