Assessing the Reliability of some Classical Mechanical Vibration Designs via Simulation Software

This work is part of a series on problems which aid students in achieving a better understanding of underlying engineering principles and a better appreciation for the limitations of linear physical modeling in dynamics. Another issue worthy of attention is how robust some designs are based on linear modeling. The problems treated here (3 in all) do not have analytical solutions and have only become tractable due to the widespread availability and early exposure in introductory mathematics classes to simulation software such as MAPLE (R), MATLAB (R) etc. MAPLE (R) is employed here. The first problem is meant to enhance students understanding of stability. It concerns a spring-mass system vibrating in a slot in a horizontal disk rotating with a prescribed motion. It is shown that for certain spin-up speeds, instabilities can develop if the system parameters are not chosen properly. Effects of spring non-linearity on these instabilities are explored. An area that students should be aware of is the reliability of designs based on linear models. A passive vibration absorber is revisited and it is shown that the classical choice of system parameters may not work if spring non-linearities are included. Choices that do work are given. Finally a problem involving "vibration cancellation" is studied. The response of a linear single degree of freedom spring-mass system to a pulse can be made identically zero for all times greater than a certain one by the application of a second pulse with a suitable phase difference. Some effects of spring non-linearities on the linear model predictions are given. Assessment was achieved by noting students better and fuller understanding of the basics.