Transverse vibration of viscoelastic Timoshenko beam-columns

Abstract

Transverse vibration of viscoelastic Timoshenko beam-columns is investigated. The normal and the shear stress-strains are constituted by the Kelvin model with different viscosity parameters. The governing equations and the boundary conditions are derived from the generalized Hamilton principle. The exact frequency equations and the modal functions are proposed. The orthogonality conditions are established in the state space. The transverse response to arbitrary external excitation and initial conditions is determined via decoupling the governing equations based on the orthogonality. The natural frequencies and the decrement coefficients of various beam and beam-column models are numerically contrasted. The effects of the length-to-depth ratio, the axial tension, and the viscosity coefficients on the natural frequencies and the decrement coefficients are numerically demonstrated.

Vibration Analysis of Viscoelastic Timoshenko Cracked Beams with Massless Viscoelastic Rotational Spring Models

“…By using the complex modal method and Laplace transform, Huang and Huang [3] studied the free vibration of Timoshenko viscoelastic beams satisfying the standard linear solid constitutive equations. Considering the axial forces, Chen et al [4] studied the vibration characteristics of clamped-clamped Timoshenko viscoelastic beams constituted by the Kelvin-Voigt model. Peng [5] applied the complex modal method and differential quadrature method to analyze the transverse vibration characteristics of the elastic Euler-Bernoulli and Timoshenko beams resting on the viscoelastic foundation.…”

Vibration of rectangle plate with variable density and Poisson’s ratio

“…Forced vibration of orthotropic circular plate with linear variation in thickness, resting on elastic foundation is discussed in [12]. The effect of axial tension, viscosity coefficients and ratio of length-to-depth is studied on transverse vibration of viscoelastic Timoshenko beam columns [13]. Vibration of square and skew plate [14,15] is discussed with variation in thickness, density and temperature using Classical plate theory.…”