ON VIBRATION ISOLATION OF MECHANICAL SYSTEMS WITH NON-LINEAR FOUNDATIONS

✍ Scribed by S. Natsiavas; P. Tratskas

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 457 KB
• Volume: 194
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0351

✦ Synopsis

An analysis is presented on the dynamics of a two-degree-of-freedom non-linear mechanical oscillator. The model consists of a rigid body which is supported by non-linear springs and can exhibit both vertical translation and rocking motions. Attention is focused on the response of the system under external excitation of the translation only, close to conditions of subharmonic resonance of order three. For the cases where the two linear natural frequencies of the system are almost identical, approximate periodic motions are determined by applying the method of multiple time scales. It is shown that besides linear and non-linear single-mode response, two-mode response is also possible, due to the 1:1 internal resonance. Some important aspects of the dynamics when no internal resonance is activated are also investigated. Next, the analytical findings are verified and complemented by numerical results. The primary interest lies in identifying the effect of the system parameters on the existence and stability of the predicted motions. The results reveal patterns of appearance of the periodic motions, providing valuable help in the efforts to eliminate them and achieve proper vibration isolation. Finally, direct integration of the original equations of motion shows that complex responses of the system can coexist with the analytically predicted motions, within the frequency ranges of interest.