A Simple and Quick Technique for the Determination of Transfer Functions of Linear Mechanical Systems

Abstract

Usual methods for the determination of the transfer functions of mechanical systems consisting of linear elements (i.e. mass, spring and damper), are practical only for simple cases. In a complicated system with many elements, the process is tedious and error-prone. In this work, with the aid of a simple model which easily transfers the system from time domain into the Laplace domain, the general forms of the transfer functions of the system have been derived. In this report, three general forms of such systems are discussed and examples are considered. The advantages of this method in addition to its simplicity are that the transfer functions provide numerators and denominators (characteristic equations) separately; the formulae are easily applicable in digital computer programs; and finally, the method can be used for academic purposes (for example, for quick problem-checking by the instructor).