By R.V. Dukkipati
Vibration research is a multidisciplinary topic and provides a approach dynamics method in keeping with mathematical basics and stresses actual procedure modeling. The classical tools of vibration research engineering are lined: matrix research, Laplace transforms and move services. the various labored examples and unsolved workout difficulties are meant to supply the reader with an understanding of the final applicability of vibration research difficulties utilizing MATLAB. an intensive bibliography to steer the coed to additional assets of knowledge on vibration research utilizing MATLAB is supplied on the finish of the booklet. All end-of bankruptcy difficulties are totally solved within the answer handbook to be had in simple terms to teachers.
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6 BASE EXCITATION In many mechanical systems such as vehicles mounted on a moving support or base, the forced vibration of the system is due to the moving support or base. The motion of the support or base causes the forces being transmitted to the mounted equipment. Fig. 22 shows a damped single degree of freedom mass-spring system with a moving support or base. y =Y0 sin wt k c m x Fig. 22 Harmonically excited base. 8 RESPONSE UNDER HYSTERESIS DAMPING The steady-state motion of a single degree of freedom forced harmonically with hysteresis damping is also harmonic.
Depending on the values of A and B, many forms of motion are possible, but each form is characterized by amplitude which decays without oscillations, such as is shown in Fig. 12. x(t) z=1 t Fig. 12 Amplitude decaying without oscillations. In this case ζ > 1, and the system is said to be overdamped. The solution is given by: x(t) = C1e ( − ζ + ζ 2 − 1) ω n t + C2 e ( − ζ − ζ 2 − 1) ω n t The motion will be non-oscillatory and will be similar to that shown in Fig. 13. x(t) z>1 t Fig. 13 Non-oscillatory motion.
9 TWO DEGREE OF FREEDOM SYSTEMS Systems that require two independent coordinates to describe their motion are called two degrees of freedom systems. Some examples of two degree of freedom models of vibrating systems are shown in Fig. 25(a) and (b). k1 l1 q1 m1 y1 m1 x1 y2 x1 q2 k2 l2 m2 m2 x2 (a) x2 (b) Fig. 25 Two degree of freedom systems. 1 EQUATIONS OF MOTION Consider the viscously damped two-degree of freedom spring mass system shown in Fig. 26. F1(t) x1(t) k1 F2(t) x2(t) k2 m1 k3 m2 c1 c2 c3 Fig.