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Extra resources for Physics Reports vol.297
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M1 F k1 Pivot m2 z c1 (a) L 3 δz L 3 L 3 k1 1 z 2 ( ) m2z˙˙ (b) _ F c1 1 z˙ 2 ( ) m1 1 z˙˙ 2 ( ) (c) 1 δz 2 1 δz 2 Fig. 1. δz 32 Structural dynamics and vibration in practice Possible candidates are the angle of rotation about the pivot, or the vertical displacement of one of the masses. Let us choose to use the displacement, z, of the mass m2 , which is defined as positive in the downward direction. It follows that the velocity, _ and the acceleration, z€, will also be positive downwards at that point.
34 Structural dynamics and vibration in practice mz˙˙ z Free body diagram Mass m y k c ky cy x Base Fig. 3 Single-DOF system with base motion input in schematic form. 4) is seen to be of the same form as Eq. 1a), but with the term Àm€ x replacing the force F. If Eq. 2 Free response of single-DOF systems by direct solution of the equation of motion If the system shown in Fig. 1, and represented by Eq. 6) This is a linear, second-order, homogeneous (because all terms are of the same kind), differential equation, and it can be solved by trial.
Thus, one newton-meter (N m) of energy is equal to one joule (J), and one J/s is a power of one watt. All other systems require special factors to relate, say, mechanical energy to heat or electrical energy. 1 Scanlan, RH and Rosenbaum, R (1951). Introduction to the Study of Aircraft Vibration and Flutter. Macmillan. Reprinted 1968 Dover Publications. 2 Meriam, JL (1966). Dynamics. Wiley. 3 Setting up the differential equation of motion . . . . . . . . . . . . . . . Free response of single-DOF systems by direct solution of the equation of motion .