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Free Vibration Analysis Of Linear Vibrating Deficient Systems With Arbitrary Damping

✍ Scribed by Q.K. Liu; J.E. Sneckenberger

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
329 KB
Volume
177
Category
Article
ISSN
0022-460X

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✦ Synopsis

The "deficient" system that exists when the geometric multiplicity of an eigenvalue of a linear vibrating system is less than its algebraic multiplicity is defined and constructed. A complex mode theory is developed for the deficient system. The normal complex modes and generalized complex modes are defined. The free vibration characteristics of the deficient system are discussed. It is shown that the state equations of motion of the deficient system cannot be decoupled completely, and that the free vibration of the deficient system will decay more slowly than a damped normal system with the same damping ratio. A three-degree-of-freedom deficient system of springs and masses is used to illustrate the utility and correctness of the results.

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