Numerical solution of quadratic matrix equations for free vibration analysis of structuresThis paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.
Document ID
19760048897
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Gupta, K. K. (California Institute of Technology, Jet Propulsion Laboratory, Structures and Dynamics Section, Pasadena Calif., United States)