Influence of Gravity-Induced Axial Force on the Natural Frequencies of an Inclined Cantilever Beam - Ananta Kusuma Yoga Pratama; Sunarko Sunarko (Department of Mathematics and Science Education, Faculty of Teacher Training and Education, University of Mataram. Jurnal Pijar MIPA colaborates with Perkumpulan Pendidik IPA Indonesia Wilayah Nusa Tenggara Barat, 2026)
The limitations of conventional horizontal cantilever models in capturing gravity-induced axial effects in inclined structures that influence stiffness and natural frequencies. This study investigates the influence of gravity on the dynamic behavior of an inclined cantilever beam, with particular emphasis on a 10-m steel beam configuration. Unlike conventional horizontal cantilever models, structural inclination generates a spatially varying axial compressive force that increases from zero at the free end to a maximum value at the fixed support. The objective of this study is to analyze how this gravity-induced axial force distribution affects the natural frequencies and effective stiffness of the beam. To achieve this, a high-fidelity numerical model was developed in MATLAB, where the beam was discretized into 100 Euler–Bernoulli elements to capture the gradual variation of axial load and the resulting geometric softening effect. The analytical formulation is based on the Rayleigh–Ritz method, in which the spatial axial force distribution is incorporated into the potential energy expression. The predicted natural frequencies were validated through frequency-domain analysis of the transient response obtained from numerical simulation. Both analytical and numerical results indicate that, for an inclination angle of 60°, the first and second natural frequencies are approximately 1.84 Hz and 11.61 Hz, respectively. These results demonstrate that beam inclination significantly reduces the effective structural stiffness due to gravity-induced geometric softening. The findings highlight the importance of incorporating spatially varying geometric stiffness in the dynamic analysis, stability assessment, and vibration-sensitive design of large-scale inclined cantilever structures.