Electric Analog Computer Techniques Applied to Certain Mechanical Vibration Problems

Solutions are given for two distinct types of vibration problems of importance in the field of applied mechanics. These solutions are of themselves useful, and in addition they represent the development of basic electric analog computer techniques which may be applied to the solution of a vast number of hitherto unsolved engineering problems. Part One treats the problem of a linear system excited by one or more forces of varying frequency. An analytical solution is given for the case in which the exciting force is of constant amplitude and of a frequency which varies linearly with time. A device which generates electric forces of varying frequency is discussed, and the results of its application to the solution of time-varying frequency problems are shown. A detailed study is made of a low loss two degree of freedom system excited by a force of constant amplitude and a frequency varying linearly with time. This study demonstrates the tremendous saving in time which may be effected by electric analog computation methods. It is demonstrated how forces of time-varying frequency may be used to rapidly obtain a qualitative measure of a system's steady state frequency response. The transient draft gear forces existing during the braking of a long train are treated in Part Two. An analytical solution and an Electric Analog Computer solution are given for a train of identical cars and draft gears assumed to behave as perfect springs. The electric analog for a nonlinear draft gear is developed. A computer solution is presented for a train containing nonlinear draft gears and, in addition, for certain distributions of cars of unequal weights. This problem, involving a system of fifty nonlinear elements and fifty separate excitation forces would be completely impracticable by even the best available digital computation methods.