Mathematical Formulation for Bending Moment Wave in Non-Dispersive Finite Rod

M. A. Salim(1), A. Putra(2*), M. A. Abdullah(3)

(1) Green Technology Vehicle, Centre for Advanced Research on Energy, Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
(2) Sustainable Maintenance Engineering, Centre for Advanced Research on Energy, Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
(3) Advanced Vehicle Technology, Centre for Advanced Research on Energy, Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
(*) Corresponding author


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Abstract


Natural rubber (NR) is an incompressible material and has potential to become vibration isolator for many engineering applications. In this study, mathematical formulation for bending moment wave is derived by using wave propagation method for non-dispersive finite rod. This finite rod is developed by NR material. Impedance matrix is developed in order to determine at which of four different locations the highest internal resonance wave occurred. Bending moment is used as an excitation force to create unstable energy for finite rod and to produce internal resonance wave. This wave is propagating from free boundary to fixed boundary and finally returns back to free boundary. This happens because of the nature of science where wave cannot pass the fixed boundary. The bending moment wave slowly changed to bending moment displacement at the free boundary. This phenomenon is recorded at plotted into frequency domain graph.
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Keywords


Bending Moment; Wave Propagation; Internal Resonance; Natural Rubber

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References


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