In the preceding chapter, we have shown that the free motion of a dynamic system may be expressed in terms of free modal vibrations. Our present interest is to demonstrate that the forced motion of such a system may also be expressed in terms of the normal modes of vibration and that the total response may be obtained as the superposition of the solution of independent modal equations. In other words, our aim in this chapter is to show that the normal modes may be used to transform the system of coupled differential equations into a set of uncoupled differential equations in which each equation contains only one dependent variable. Thus the modal superposition method reduces the problem of finding the response of a multidegree-of-freedom system to the determination of the response of single degree-of-freedom systems.
KeywordsExcitation Function Couple Differential Equation Modal Contribution Free Body Diagram Participation Factor
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