Stability and Free Vibration Analyses of Cantilever Shear Buildings with Semi-Rigid Support Conditions and Multiple Masses

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Journal of Sound and Vibration

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The stability and free vibration analyses of a cantilever shear building with generalized support conditions and with multiple masses (rotational and translational) rigidly attached at both ends and along its height are presented. The proposed model includes the simultaneous effects of: (1) lateral and rotational elastic restraints at the base support; (2) a uniform distributed mass and rotary inertia plus lumped rotary and translational masses rigidly attached at both extremes and along its height; (3) linearly distributed axial load plus the concentrated vertical axial loads caused by the lumped masses; and (4) shear deformations and shear forces induced by the applied axial forces. A parametric study is carried out that shows the importance of all variables included in this work on the stability and dynamic behavior of cantilever shear buildings, particularly the effects of the attached lumped masses and the rotational and translational constraints at the base support. A comparison with results presented by other researchers in previous studies shows that the proposed method and corresponding equations can be very useful in the assessment design of cantilever shear buildings. The main objective is to present readily solutions on the static stability and free vibration of cantilever shear buildings with generalized support conditions and multiple masses rigidly attached. The proposed method and corresponding expressions for the natural frequencies and modal shapes, buckling modes and axial critical loads are extensions of those presented recently by the senior author.


Journal of Sound and Vibration, Vol. 333, No. 5 (February 28, 2014): 1390-1407. DOI.

J.A. Hernandez-Urrea was afilliated with University of Illinois at Champaign-Urbana at the time of publication.