Transverse vibration of viscoelastic Timoshenko beam-columns

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.