A Solution to the Response of a Single Degree of Freedom System to Swept Sine Inputs

This paper presents a solution of the response of a single-degree-of-freedom system to swept sine input. Including the derivations for how this solution was obtained. This solution includes the time-domain response to a linearly varying swept sine input. The time-domain response includes the transient response of the system. The solution is simplified, so it can easily be computed by software packages. The Pearson correlation coefficient is measured between the solution presented in this paper and the Runge-Kutta simulation to measure the accuracy of the solution presented. Comparison of the time-domain response to similar results obtained from Runge-Kutta simulation of various systems shows excellent agreement. Results from a physical beam are also compared and shows good agreement. From the time-domain response, the frequency response functions are generated by taking the Fourier transform of the response. The frequency response functions of the response also show excellent agreement with those obtained via theoretical singledegree frequency results. The agreement of the time domain results is maintained even when non-ideal swept sine parameters are chosen. This paper also presents a method for ensuring the transient responses of the system have died out for when swept sines are used to measure the frequency response of a system.