Modal interactions of a geometrically nonlinear sandwich beam with transversely compressible core

Modal interactions of a geometrically nonlinear sandwich beam with transversely compressible core in the presence of combination internal resonance are investigated. At first, a geometrically nonlinear, {2,1}-order theory is used to derived the equations of motion and the compatible boundary conditions of the beam. Then, Galerkinʹs weighted residual method and the multiscale approach are used to address the governing system. Next, modal interactions in the presence of combination internal resonance and subjected to primary-resonance excitation are investigated. Finally, the commercial code ABAQUS is used to validate the theoretical results we have obtained.