The notion of quadratic pencils, λ 2M + λC + K, where M, C, and K are n × n real matrices with or without some additional properties such as symmetry or positive definiteness, plays critical roles in many important applications. It has been long desirable, yet with very limited success, to reduce a complicated high-degree-of-freedom system to some simpler low-degree-of-freedom subsystems. Recently Garvey et al. [J. Sound Vibration, 258(2002), pp. 885-909] proposed a promising approach by which, under some mild assumptions, a general quadratic pencils can be converted by real-valued isospectral transformations into a totally decoupled system. This approach, if numerically feasible, would reduce the original n-degree-of-freedom second order system to n totally independent single-degreeof-freedom second order subsystems. Such a claim would be a striking breakthrough in the common knowledge that generally no three matrices M, C, and K can be simultaneously diagonalized. This paper intends to serve three purposes: to clarify some of the ambiguities in the original proposition, to simplify some of the computational details and, most importantly, to complete the theory of existence by matrix polynomial factorization tactics.
Total decoupling of general quadratic pencils, Part I: Theory
DEL BUONO, Nicoletta
2008-01-01
Abstract
The notion of quadratic pencils, λ 2M + λC + K, where M, C, and K are n × n real matrices with or without some additional properties such as symmetry or positive definiteness, plays critical roles in many important applications. It has been long desirable, yet with very limited success, to reduce a complicated high-degree-of-freedom system to some simpler low-degree-of-freedom subsystems. Recently Garvey et al. [J. Sound Vibration, 258(2002), pp. 885-909] proposed a promising approach by which, under some mild assumptions, a general quadratic pencils can be converted by real-valued isospectral transformations into a totally decoupled system. This approach, if numerically feasible, would reduce the original n-degree-of-freedom second order system to n totally independent single-degreeof-freedom second order subsystems. Such a claim would be a striking breakthrough in the common knowledge that generally no three matrices M, C, and K can be simultaneously diagonalized. This paper intends to serve three purposes: to clarify some of the ambiguities in the original proposition, to simplify some of the computational details and, most importantly, to complete the theory of existence by matrix polynomial factorization tactics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
