By Jong-Shyong Wu
''This e-book illustrates theories and linked mathematical expressions with numerical examples utilizing a variety of tools, resulting in designated recommendations, extra actual effects, and extra computationally effective suggestions. It provides the derivations of the equations of movement for all constitution foundations utilizing both the continual version or the discrete version. It discusses purposes for college students taking classes together with vibration mechanics, dynamics of constructions, and finite point analyses of buildings, the move matrix process, and Jacobi method''
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Extra resources for Analytical and numerical methods for vibration analyses
5(c) one sees that the three points A, B and C vibrate synchronously. This means that the dynamic responses of the beam is near the resonant condition. 5(a) and (b), and the purpose of forced vibration analysis in the time domain is obvious. 6. 0 rad/s. 6 The frequency-response amplitude curves for vertical displacements of the three points A, B and C on the 2D P-P beam subjected to a harmonic exciting force FðtÞ ¼ 1:0 sin ve t (newtons) applied at point A (cf. 4) obtained from the time-history method.
Since all equations of motion in this chapter are derived from non-uniform structures, they are available for the subsequent chapters, in spite of the fact that only uniform systems are illustrated in the examples. In the forced vibration analysis of structures, the mode superposition method is one of the efficient approaches, where all mode shapes considered must be orthonormal. Thus, some attention is paid to the determinations of normal mode shapes and the associated orthonormality conditions of the above-mentioned structural systems except for membranes and plates.
2001) Torsional vibration analysis of gear-branched systems by finite element method. Journal of Sound and Vibration, 240 (1), 159–182. J. (1965) Axial shaft vibration in large turbine-powered merchant ships. Transactions of the Institute of Marine Engineers, 77, 53–113. R. T. (1949) Longitudinal vibrations of marine propulsion shafting systems. Transactions of the Society of Naval Architects and Marine Engineers (SNAME), 57, 193–252. Panagopulos, E. (1950) Design-stage calculation of torsional, axial and lateral vibrations of marine shafting.