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.

In this article, the authors presented a unified solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. Regardless of the shapes of the plates and the types of boundary conditions, each displacement and rotation component of the elements is expanded as an improved Fourier series expansion which is composed of a double Fourier cosine series and several auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations. Since the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the plates. The accuracy, reliability, and versatility of the current solution is fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. Some new results of free vibration analysis for composite laminated annular sector plate, circular sector plate, annular plate, and circular plate are presented, which may be served as benchmark solution for future computational methods. The effects of the sector angles, layer numbers, and boundary spring stiffness on vibration characteristics of the plates are reported. In addition, the force vibration analysis of the plates is also studied. The influence of the boundary spring stiffness, layer number, orthotropic stiffness ration, and fiber orientation angle on dynamic characteristics of the plates is investigated.

A formulation for static and dynamic vibration analysis of composite laminated curved beams is presented by using an efficient domain decomposition method. Multi-segment partitioning strategy is used to accommodate the accurate requirements of responses. The system potential functional is introduced to satisfy the continuity constraints on the segment interfaces. The Chebyshev orthogonal polynomials are used as displacement admissible functions. The theoretical results are verified by comparing with those previously published in literature, and the ones obtained by using the program ABAQUS. Based on the verification, the parametric study of composite laminated curved beam is carried out.