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A receptance formula for general second‐degree square lambda matrices
Author(s) -
Palazzolo Alan B.,
Wang Bo Ping,
Pilkey Walter D.
Publication year - 1982
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.1620180603
Subject(s) - mathematics , matrix (chemical analysis) , subspace topology , square (algebra) , stiffness , vibration , mathematical analysis , harmonic , structural engineering , geometry , physics , engineering , materials science , quantum mechanics , composite material
A computational algorithm utilizing the free vibration modes of a structure is presented for calculating receptances. The usual eigensystem computed for large structural models is incomplete; hence the receptances are approximate. The formulae developed here increased receptance accuracy compared to classical spectral representations. Receptances are used extensively in eigensolution reanalysis, design and synthesis and also for forced harmonic response studies. In these areas receptance approaches offer a popular alternative to Rayleigh–Ritz subspace type methods. Structural models represented by nonsymmetric mass, damping and stiffness matrices, which occur frequently in rotating structures, may be treated using the receptance formulae presented. The receptance matrix derived is applicable to general, second‐degree, square lambda matrices. This generalizes the receptance matrix commonly associated with matrix pencils.