Akademik Veri Yönetim Sistemi
Archive of Applied Mechanics, cilt.95, sa.9, 2025 (SCI-Expanded)
This study presents an enhanced matrix collocation method based on Fibonacci polynomials for free vibration problems of Euler–Bernoulli, Rayleigh, and Timoshenko beams. Firstly, governing equations of the beams are reduced to fourth-order ordinary differential equations in spatial coordinates. Then, these equations are transformed into a fundamental matrix equation through the equally spaced collocation points and operational matrices. Thereby, using the Fibonacci matrix collocation method along with the eigenvalue problem, the approximate solutions are obtained in terms of the truncated Fibonacci series. These solutions correspond to the natural frequencies and modal shape functions. Also, some examples, together with relative error, are performed to illustrate the validity and applicability of the presented method. Solving the eigenvalue problem, the natural frequencies are obtained for simple–simple and clamped-free support conditions for each beam model. In addition, normalized modal shape functions corresponding to the natural frequencies are plotted. The obtained results are compared with the existing results in the literature. Moreover, the obtained numerical results are scrutinized by using tables and figures.