Flexural Free Vibration of a Straight Vertical Cantilever Beam
DOI:
https://doi.org/10.21063/jtm.2018.v8.i1.11-21Kata Kunci:
flexural free vibrations, a straight vertical cantilever beam, Partial Differential Equations, deflection shapes, amplitude of vibrations, Fourier series, natural frequenciesAbstrak
In this paper, flexural free vibration of a straight vertical cantilever beam has 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 within time. This technique yields the motion equation of a modeled-cantilever beam contains two functions; one defines deflection shapes and another defines amplitude of vibration within time. The deflection shapes of a modeled-cantilever beam are described in first five natural frequencies. 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 first five natural frequencies respectively 16.29, 102.11, 285.95, 560.36, and 926.22 rad/s.
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