Measurement of Mechanical Impedance and Its Applications

The impedance concept for mechanical elements is briefly developed through the analogy to electric circuits. This concept then makes the whole field of circuit analysis with its highly developed set of rules, theorems, and mathematics available for the solution of mechanical problems. Many devices are available for the application of forces and the measurement of motion and force. Some of these are combined in several devices designed specifically to measure the driving-point impedance of soils. An analog computer is presented that takes force and velocity information from the impedance devices, computes their complex ratio and plots impedance as the measurement is being made. Examples of the impedance of soils, sponge rubber, and a simple beam are presented. Impedance information is used to predict the motion of the bar to a sinusoidal driving force and Norton's equivalent circuit is used to predict the motion of a mass attached to the bar. Finally, the transient response of a mass dropped on sponge rubber is predicted from the equivalent circuit as determined from impedance measurements. Each of these cases is verified experimentally.