Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions

The Carrera Unified Formulation (CUF) is used in this paper to develop higher-order beam theories for composite laminates. In the framework of the CUF, the three-dimensional displacement field is approximated as a truncated Taylor-type expansion series of the generalized displacements, which lie on the beam axis. The truncation of the series determines the theory order N, which is a free parameter of the formulation. The strong form of the principle of virtual displacements is used to obtain the equations of motion and the natural boundary conditions for the laminated beam in free vibration. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The Wittrick–Williams algorithm is applied to solve the transcendental eigenvalue problem resulting from the present approach. Composite beams with arbitrary boundary conditions, geometries and lamination schemes can be analysed with the proposed method. Numerical investigations are carried out and the results are compared with reference solutions from the literature and with solutions from commercial finite elements codes.