Free vibrations of a laminated composite curved beam with arbitrary layups

Abstract In this article, a new mathematical modeling is introduced for analyzing the free vibrations of a laminated composite curved beam (LCCB) with arbitrary layups. To achieve this, in‐plane and out‐of‐plane deformations, shear deformations, rotary inertia, warping effect, Poisson's effect, and coupling of tension‐bending‐torsion are considered. Using the analytical and finite element methods, the system's discrete equations are derived in matrix form. By solving these equations, the free vibration characteristics of the beam are calculated. The computed results are compared with those of specific cases presented by other researchers, as well as with results obtained from a three‐dimensional ANSYS software, showing very good agreement. Furthermore, the effects of various parameters on the vibrational behavior of the curved beam are investigated in detail.

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