Exact dynamic stiffness matrix for flexural vibration of three-layered sandwich beams

An exact dynamic member stiffness matrix (exact finite element), which defines the flexural motion of a three-layered sandwich beam with unequal faceplates, is developed from the closed form solution of the governing differential equation. This enables the powerful modelling features associated with the finite element technique to be utilised, including the ability to account for nodal masses, spring support stiffnesses and non-classical boundary conditions. However, such a formulation necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm, which enables the required natural frequencies to be converged upon to any required accuracy with the certain knowledge that none have been missed. The accuracy of the method is confirmed by comparison with three sets of published results and a final example indicates its range of application.