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Vibration of Mechanical Systems by Alok Sinha

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3 Responses of an SDOF Spring–Mass–Damper System to Periodic and Arbitrary Forces

In Chapter 2, the response has been calculated when the excitation is either constant or sinusoidal. Here, a general form of periodic excitation, which repeats itself after a finite period of time, is considered. The periodic function is expanded in a Fourier series, and it is shown how the response can be calculated from the responses to many sinusoidal excitations. Next, a unit impulse function is described and the response of the single-degree-of-freedom (SDOF) system to a unit impulse forcing function is derived. Then, the concept of the convolution integral, which is based on the superposition of responses to many impulses, is developed to compute the response ...

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