Dynamics of Multiple-Degree-of-Freedom Oscillators With Colliding Components

✍ Scribed by S. Natsiavas

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 468 KB
• Volume: 165
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1993.1269

✦ Synopsis

An analysis is presented for determining exact steady state response for a class of strongly non-linear multiple-degree-of-freedom oscillators. These oscillators consist of a linear component, with an arbitrary number of degrees of freedom and configuration, incorporating a component with a geometric non-linearity. Their behavior is analyzed by generalizing previous work on single- and two-degree-of-freedom piecewise linear systems under harmonic excitation. First, a methodology is developed for locating harmonic and subharmonic response characterized by one abrupt change of the parameters of the nonlinear element per response cycle. Then, a stability analysis is presented, which is appropriate for general piecewise linear systems. The present analysis is applicable to a variety of engineering areas. Here, its validity and effectiveness is demonstrated by applying it to two classes of problems with large practical significance and rich dynamics. Performance of vibration absorbers with elastic stops is investigated first, while in the second category of examples the oscillators exhibit (2: 1) and (3: 1) internal resonance. Regular and irregular motions are encountered and analyzed. The response characteristics are compared with those of systems with continuous non-linearities.