A spectral element model for thermal effect on vibration and buckling of laminated beams based on trigonometric shear deformation theory

A spectral element model is presented for analyzing thermal effect on free vibration and buckling behaviors of generally laminated composite beams subjected to uniform temperature distribution. Coupled differential equations of motion for the generally layered composite beams are derived on the basis of trigonometric shear deformation theory, in which temperature-dependent material properties, temperature change and Poisson effect are incorporated in the mathematical formulation. A spectral element matrix is formulated from the exact analytical solutions of the governing differential equations of the composite beams in free vibration. The spectral element method together with the Wittrick-Williams algorithm is employed to obtain the natural frequencies and buckling temperature change of the generally layered composite beams with various boundary conditions. Comparison of the natural frequencies and/or buckling temperature changes with the ANSYS solutions and/or corresponding results in literature validates the derived spectral element formulation. The effects of temperature change, Poisson effect, boundary condition, material anisotropy and thermal expansion coefficient on the natural frequencies and/or buckling temperature changes of the composite beams are investigated.