Analytic and experimental determination impulse response of single degree of freedom system

Abstract

The paper presents an experimental and analytical way of determining the impulse response of a linear time-invariant damped system with one degree of freedom. An experiment was conducted where the mass was excited by an impact load. Both the mass acceleration and impact force values were recorded. The magnitude of the system's frequency response was determined based on the recorded values, ensuring the relatively simple identification of the system's basic parameters. Those parameters were used to define a suitable mathematical model of the system, transfer function, and frequency response function in an analytical form. The impulse response of the system based on the recorded values of mass acceleration and impact load is expressed as a discrete function. This function is determined by applying the inverse discrete Fourier transform of the corresponding frequency response function. The impulse response of the system, based on the mathematical model, is expressed as a continuous function. This function is determined by applying the inverse Fourier transform of the corresponding frequency response. Finally, it was shown that the response of a system to arbitrary load could be determined by convolving the impulse response of the system with the load function. Convolution of continuous functions is difficult to perform, and it can be used only for the simplest problem and for understanding the physical phenomenon. Discrete convolution has a practical utility because it is easy to perform in some program languages like Matlab. However, discrete impulse response has limitations depending on the test conditions.