Free vibration analysis of laminated composite shallow curved beam with various boundary conditions

This study introduces a novel Ritz approximation function to analyze the free vibrations of laminated compositeshallow curved beams. The methodology utilizes polynomial functions-based Fibonacci series to develop theRitz’s approximation function. The displacement field aligns with the high-order shear deformation theorydesigned explicitly for shallow curved beams. The problem’s governing equation is established by applying theLagrange equation, providing a comprehensive framework for the subsequent analysis. The study meticulouslyexamines the convergence rate and accuracy of the proposed approximation function. Numerical investigationsare conducted to determine the natural frequencies of curved beams. Factors such as curvature-to-length ratio,length-to-thickness ratio, boundary conditions, and material anisotropy are carefully considered. Furthermore,extensive survey results concerning the natural frequencies of curved beams are presented. These results serveas valuable reference data for future investigations in this area, thereby contributing to the academic discourseon this subject matter.