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The Transcendental Eigenvalue Problem of the Exact Dynamic Stiffness Matrix of Linearly Elastic Plane Frames
Author(s) -
Sotiropoulos George H.
Publication year - 1982
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19820620705
Subject(s) - eigenvalues and eigenvectors , transcendental equation , mathematics , transcendental number , mathematical analysis , algebraic number , matrix (chemical analysis) , plane (geometry) , stiffness matrix , stiffness , geometry , physics , numerical analysis , materials science , quantum mechanics , composite material , thermodynamics
A new iteratives procedure is proposed to solve the transcendental eigenvalue problem of the “exact” dynamic stiffness matrix of linearly elastic plane frames. According to the presented algorithm the exact solution, i.e. natural frequencies and mode shapes of the structure, is found in a number of cycles with an algebraic eigenvalue problem to be solved within each cycle.