Premium
Solution of quadratic matrix equations for free vibration analysis of structures
Author(s) -
Gupta K. K.
Publication year - 1973
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620060113
Subject(s) - discretization , cantilever , stiffness matrix , vibration , algorithm , fortran , matrix (chemical analysis) , quadratic equation , numerical analysis , computer program , mass matrix , computer science , stiffness , mathematics , mathematical analysis , structural engineering , engineering , geometry , acoustics , physics , materials science , neutrino , nuclear physics , composite material , operating system
An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures: a cantilever beam and a semicircular arch.