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General dynamic‐stiffness matrix of a timoshenko beam for transverse vibrations
Author(s) -
Chen YungHsiang
Publication year - 1987
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290150308
Subject(s) - vibration , timoshenko beam theory , deflection (physics) , rotary inertia , stiffness , structural engineering , beam (structure) , direct stiffness method , stiffness matrix , transverse plane , damping matrix , spring (device) , inertia , bending stiffness , physics , classical mechanics , engineering , acoustics
The general dynamic‐stiffness matrix of a Timoshenko beam for transverse vibrations is presented in this paper. All the effects of rotary inertia of the mass, shear distortion, structural damping, axial force, elastic‐spring and dashpot foundation are taken into account in the formulation. As a consequence, the deflection function of the beam vibration is in complex form, and the nature of the beam vibration and the corresponding dynamic stiffnesses of the beam are characterized by general complex wave numbers. The dynamic‐stiffness matrix for any special case can be derived easily from the general formula, which may be used directly in standard structural analysis.