Abstract
In this paper, higher-order shear deformation theories for a thorough analysis of the in-plane and out-of-plane vibrational characteristics of laminated composite beams have been presented. Through the introduction of new displacement fields and the consideration of rotary inertia and Poisson's effect, the kinetic and potential energies of the beams have been derived. This formulation, displaying significant generality, accommodates arbitrary stacking sequences. Utilizing the finite element method, a new element has been presented for calculating the beam's vibrational characteristics. Featuring three nodes, each with seven degrees of freedom, this higher-order element provides a detailed representation of complex behaviors. Mass and stiffness matrices have been derived using the energy method and apply boundary conditions through the penalty approach. The results exhibit a high degree of consistency and alignment with those obtained from the 3D commercial software ANSYS, validating the accuracy and reliability of the proposed methodology for structural analysis. This comprehensive approach contributes to advancing the understanding and modeling of laminated composite beams in diverse engineering applications. The effects of different parameters on the in-plane and out-of-plane vibration analysis of laminated composite beams have been investigated in detail.
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