Non-linear vibration characteristics of clamped laminated shallow shells

This paper examines non-linear free vibration characteristics of first and second vibration modes of laminated shallow shells with rigidly clamped edg es. Non-linear equations of motion for the shells based on the first order shear deformation and classical shell theories are derived by means of Hami lton's principle. We apply Galerkin's procedure to the equations of motion in which eigenvectors for first and second modes of linear vibration obtain ed by the Ritz method are employed as trial functions. Then simultaneous no n-linear ordinary differential equations are derived in terms of amplitudes of the first and second vibration modes. Backbone curves for the first and second vibration modes are solved numerically by the Gauss-Legendre integr ation method and the shooting method respectively. The effects of laminatio n sequences and transverse shear deformation on the behavior are discussed. It is also shown that the motion of the first vibration mode affects the r esponse for the second vibration mode. (C) 2000 Academic Press.