A NOTE ON “THE FINITE RESIDUAL MOTION OF A DAMPED THREE-DEGREE-OF-FREEDOM VIBRATING SYSTEM”

✍ Scribed by P. HAGEDORN

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 67 KB
• Volume: 232
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2765

✦ Synopsis

Recently, in a letter to the editor of this journal Wilms and Pinkney discussed a damped linear three-degree-of-freedom system with two di!erent types of damping matrices (see reference [1]). They examined the question whether or not undamped motions are possible in their systems. Similar two-degree-of-freedom examples had been examined earlier in this journal, the references being given in reference [1].

It seems to have escaped the authors' attention that the question examined in these publications is the one of pervasiveness of damping in a linear system. This is an important albeit rather elementary concept which is not new but unfortunately not always discussed in textbooks. It is, for example, introduced by Meirovitch in his now classical book [2] and also presented in many other vibration texts, for example in references [3}5]. Since it does not seem to be su$ciently well known, here is a short discussion of this property.

Consider the n-degree-of-freedom system