Dynamic analysis of sandwich beam and frame systems

The dynamic analysis of a general class of sandwich beam and frame systems is presented. The beam element employed in the analysis has three degrees of freedom per node, corresponding to the deflection p, the rotation of the beam [straight phi] and the slope Rp/R x . The stiffness and consistent mass matrices of the sandwich beam and frame systems are derived by using the inhomogeneous solution to the fourth order differential equation as the interpolating function between the degrees of freedom of each node in the element. The consistent mass matrix of the sandwich beam element is developed by means of a special shape function consistent with the displacement functions used in the derivation of the stiffness matrix. Superposing the element matrices of the individual elements, the total stiffness and mass matrices of the entire structure can be constructed by a method known as the direct stiffness method which presents the results in a format ideally suited for computer implementation. Static and dynamic problems are included for demonstration of the consistency of the theory; the results are comparable with results published in the literature and the effects of certain important parameters on the frequency results are evaluated. With the introduction of the uniform axial displacement, the element is applicable to frame analysis