Nonlinear Free Vibration of Sandwich Beam with Electrorheological Core Via Third Order Shear Deformation Theory

Background: Free vibrations with large amplitudes exhibit nonlinear behavior, which is potentially harmful to structures. They need to be effectively regulated as a result. We used the Third-Order Shear Deformation Theory to analyze the nonlinear vibration of a sandwich beam with an Electrorheological (ER) core.Methods: Hamilton's principle allowed for the extraction of the governing equations and boundary conditions. By using the Galerkin's approximation method on the governing partial differential equations, ordinary differential equations were produced. We analytically solved the equation using differential quadrature method (DQM) method, and the data were compared with the established results.Results: The vibration amplitude reduces as each of the aspect ratio, sandwich beam thickness, and damping parameter values rises. This refers to a rise in amplitude leading to an increase in nonlinear frequency. The inherent frequency of the structure grew as the ER layer's thickness rose.Conclusions: The structure hardens dramatically in the nonlinear state as the Electric field increases, which enhances the stability of the system. Raising the electric field lowers the structure's frequency while increasing the aspect ratio of the beam raises the frequency to manage the vibration behavior

Keywords:

Electrorheological core , Large amplitude , Nonlinear vibration , Sandwich beam , Third-Order Shear Deformation Theory