NONLINEAR VIBRATIONS OF AXIALLY ACCELERATING VISCOELASTIC TIMOSHENKO BEAMS

Nonlinear parametric vibrations are investigated for axially accelerating viscoelastic Timoshenko beams subject to parametric excitations resulting from longitudinally varying tensions and axial accelerations. The dependence of the tension on the finite axial support rigidity is also considered. The governing equations of coupled planar vibration of the Timoshenko beam and the associated boundary conditions are established from the generalized Hamilton principle and the Kelvin viscoelastic constitutive relation. The governing equation of transverse vibration is simplified into a nonlinear integro-partial-differential equation with time-dependent and space-dependent coefficients. The method of multiple scales is employed to investigate parametric resonances with the focus on steady-state responses. Some numerical examples are presented to demonstrate the effects of the viscosity coefficient, the mean axial speed, the axial speed fluctuation amplitude, the large rotary inertia, the rotary inertia, and the small nonlinear coefficient on the amplitudes of the steady-state oscillating response.