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The coupling effect of axial motion and joint mass on the lateral vibrations of a rigid‐jointed triangular frame
Author(s) -
Kounadis A. N.,
Meskouris K.
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.4290150404
Subject(s) - kinematics , inertia , joint (building) , vibration , boundary value problem , stiffness , rigid body , equations of motion , mechanics , structural engineering , mathematics , classical mechanics , physics , mathematical analysis , engineering , quantum mechanics
In this investigation, the coupling effects of the axial motion and other parameters on the bending eigenfrequencies and eigenmodes of laterally vibrating frames are re‐examined. To this end an energy variational approach is performed on a rigid‐jointed triangular frame, whose joint mass is eccentrically located with respect to its theoretical position. The governing partial differential equations subject to the appropriate boundary conditions are very conveniently formulated and successfully solved in a closed form by using generalized functions and Laplace transforms. Contrary to the usual assumptions of the standard dynamic analysis of continuous systems, herein the effect of axial contraction and extension is accounted for when establishing the translational kinematic boundary conditions. This may lead to considerable discrepancies that reveal the decisive role of the axial motion effect on the dynamic response of framed structures. Such discrepancies are clearly confirmed through a thorough numerical discussion of the governing parameters: joint mass and its rotatory inertia, joint angle, positioning of the mass, slenderness ratios, stiffness and length ratios.