DYNAMICS OF THICK VISCOELASTIC BEAMS

A viscoelastic higher-order thick beam finite element formulation is e xtended to include elastodynamic deformations. The material constituti ve law is a special differential form of the Maxwell solid, which empl oys viscous strains as internal variables to determine the viscous str esses. The total time-dependent stress is the superposition of its ela stic and viscous components. In the constitutive model, the elastic st rains and the conjugate viscous strains are coupled through a system o f first-order ordinary differential equations. The use of the internal strain variables allows for a convenient finite element formulation. The elastodynamic equations of motion are derived from the virtual wor k principle. Computational examples are carried out for a thick orthot ropic cantilevered beam. Relaxation, creep, relaxation followed by fre e damped vibrations, and damping related modal interactions are discus sed.