Dynamic equations governing the free vibration of laminated composite beams are developed using Hamilton's principle. The effects of transverse shear and rotary inertia are included in the energy formulation. Analytical solutions are obtained by the method of Lagrange multipliers wherein the free vibration problem is posed as a constrained variational problem, the constraints being imposed through Lagrange multipliers. Natural frequencies and mode shapes of clamped-clamped and clamped-supported composite beams are presented to demonstrate the efficiency of the methodology.
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