ALTERNATIVE SOLUTION TO “THE FINITE RESIDUAL MOTION OF A DAMPED FOUR-DEGREE-OF-FREEDOM VIBRATING SYSTEM”

✍ Scribed by M. GÜRGÖZE

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 57 KB
• Volume: 255
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.4174

✦ Synopsis

Very recently in a Letter to the Editor of this journal, Wilms and Cohen [1] introduced a damped four-degree-of-freedom system with two di!erent types of damping matrices. The reader was required to decide which of the systems in Figure 1 oscillates inde"nitely, while all oscillations are eventually damped out for the other one. They derived the equations of motion of both systems via Lagrange's procedure by making use of the special nature of the symmetric and asymmetric generalized co-ordinates. They showed that the vibrations of the system (b) damp out totally, whereas those of (a) do not.

As was also done in reference [2] and suggested in reference [3], we would like to give the answer of the posed question in a relatively short and straightforward way. The problem is identical to the task of "nding which system is asymptotically stable. It is known that a system with n degrees-of-freedom MqK #Dq #Kq"0

(1)