Free vibration analysis of axially loaded laminated composite beams with general boundary conditions by using a modified Fourier-Ritz approach

In this paper, a modified Fourier-Ritz approach has been adopted to analyze the free vibration of axially loaded laminated composite beams with arbitrary layup and general boundary conditions, which include classical boundaries, elastic boundaries, and their combination. The influences of Poisson effect, axial deformation, couplings among extensional, bending and torsional deformations, shear deformation, and rotary inertia are incorporated in the formulation. In this present method, regardless of boundary conditions, the displacements and rotation components of the beam are invariantly expressed as a standard Fourier cosine series and several auxiliary closed-form functions. These auxiliary functions are introduced to eliminate any potential discontinuities of the original displacement function and its derivatives, throughout the whole beam including its ends, and to effectively enhance the convergence of the results. Since the displacement field is constructed to be adequately smooth in the whole solution domain, an accurate solution can be obtained by using Ritz procedure based on the energy functions of the beam. Numerical examples are presented for several different boundary conditions, geometric properties, and material parameters. The results show that the present method enables rapid convergence, high reliability, and accuracy. Numerous new free vibration results for axially loaded laminated composite beams with different lamination schemes and elastic restraints are presented.