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

Abstract

This study introduces a novel Ritz approximation function to analyze the free vibrations of laminated composite
shallow curved beams. The methodology utilizes polynomial functions-based Fibonacci series to develop the
Ritz’s approximation function. The displacement field aligns with the high-order shear deformation theory
designed explicitly for shallow curved beams. The problem’s governing equation is established by applying the
Lagrange equation, providing a comprehensive framework for the subsequent analysis. The study meticulously
examines the convergence rate and accuracy of the proposed approximation function. Numerical investigations
are 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 serve
as valuable reference data for future investigations in this area, thereby contributing to the academic discourse
on this subject matter.