LATERAL VIBRATION OF A NONLINEAR VISCOELASTIC BEAM UNDER INITIAL AXIAL TENSION.
Engineering sciences rept.,
STATE UNIV OF NEW YORK BUFFALO FACULTY OF ENGINEERING AND APPLIED SCIENCES
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The free lateral vibration of a simply-supported metallic beam under axial creep deformation is considered. The constitutive law is formulated with stress power functions in the primary and secondary creep terms the instantaneous linear elastic deformation is also included. For better physical visualization, a nonlinear Maxwell-Kelvin model is used to represent the constitutive law. A reduction to various special models is also obtained. It is assumed that the initial stress is much greater than the increments of stress caused by the oscillation, and a perturbation technique is employed. In the present study, the perturbation essentially results in replacing a nonlinear viscoelastic problem by an equivalent linear viscoelastic problem. Analytical solutions for the Maxwell-Kelvin model and for the special models are obtained. Numerical results for a stainless steel and an aluminum alloy are also presented and discussed. Author