Resonant vibrations of FG viscoelastic imperfect Timoshenko beams

An investigation is performed on the viscoelastic nonlinear vibrations of functionally graded imperfect Timoshenko beams. The internal viscosity is incorporated using the Kelvin-Voigt scheme. Beam's centerline stretching is the cause of geometric nonlinearities. Material property distributions follow the Mori-Tanaka model. Shear deformation and rotary inertia are incorporated using the Timoshenko theory. A slight curvature is included to account for a geometric imperfection. The coupled axial/transverse/rotational motion model is developed using Hamilton's energy/work/energy loss. Galerkin's method is used, without neglecting the longitudinal inertia/displacement, and a large dimensional discretized/truncated model is obtained. Numerical integrations, using a continuation-based technique, are employed for force/frequency diagrams. Viscosity, material gradient index, and imperfection effects on the system vibrations are investigated.