Flexural Free Vibration of a Straight Vertical Cantilever Beam - Asmara Yanto (Jurnal Teknik Mesin (JTM), 2018)
In this paper, flexural free vibrations of a straight vertical cantilever beam have been modeled and simulated. Here, a modeled cantilever beam has modulus of elasticity, moment of inertia, cross-section and density are constant. Motion equation of a modeled cantilever beam are separated become two Partial Differential Equations; one depends on position and another on time. This technique yields the motion equation of a modeled cantilever beam contains two functions; one defines deflection shapes and another defines amplitude of vibrations within time. The deflection shapes are described for first five natural frequencies of a modeled cantilever beam. Furthermore, the motion equation of a modeled cantilever beam is solved by using Fourier series. From simulation of a modeled cantilever beam with 2 GPa modulus of elasticity, 2.67x10-8 m4 moment of inertia, 8x10-4 m2 cross-section, 7862.30 kg/m3 density, 1 m length, and 100 N initial load obtained 16.29, 102.11, 285.95, 560.36, and 926.22 rad/s first five natural frequencies respectively.