TY - JOUR
T1 - Exact solutions for free vibration of shear-type structures with arbitrary distribution of mass or stiffness
AU - Li, Q. S.
PY - 2001
Y1 - 2001
N2 - In this paper, shear-type structures such as frame buildings, etc., are treated as nonuniform shear beams (one-dimensional systems) in free-vibration analysis. The expression for describing the distribution of shear stiffness of a shear beam is arbitrary, and the distribution of mass is expressed as a functional relation with the distribution of shear stiffness, and vice versa, Using appropriate functional transformation, the governing differential equations for free vibration of nonuniform shear beams are reduced to Bessel's equations or ordinary differential equations with constant coefficients for several functional relations. Thus, classes of exact solutions for free vibrations of the shear beam with arbitrary distribution of stiffness or mass are obtained. The effect of taper on natural frequencies of nonuniform beams is investigated. Numerical examples show that the calculated natural frequencies and mode shapes of shear-type structures are in good agreement with the field measured data and those determined by the finite-element method and Ritz method. © 2001 Acoustical Society of America.
AB - In this paper, shear-type structures such as frame buildings, etc., are treated as nonuniform shear beams (one-dimensional systems) in free-vibration analysis. The expression for describing the distribution of shear stiffness of a shear beam is arbitrary, and the distribution of mass is expressed as a functional relation with the distribution of shear stiffness, and vice versa, Using appropriate functional transformation, the governing differential equations for free vibration of nonuniform shear beams are reduced to Bessel's equations or ordinary differential equations with constant coefficients for several functional relations. Thus, classes of exact solutions for free vibrations of the shear beam with arbitrary distribution of stiffness or mass are obtained. The effect of taper on natural frequencies of nonuniform beams is investigated. Numerical examples show that the calculated natural frequencies and mode shapes of shear-type structures are in good agreement with the field measured data and those determined by the finite-element method and Ritz method. © 2001 Acoustical Society of America.
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U2 - 10.1121/1.1372225
DO - 10.1121/1.1372225
M3 - 21_Publication in refereed journal
C2 - 11681376
VL - 110
SP - 1958
EP - 1966
JO - Journal of the Acoustical Society of America
JF - Journal of the Acoustical Society of America
SN - 0001-4966
IS - 4
ER -