Термомеханічна задача про коливання в'язкопружного гумоподібного стержня при динамічному навантаженні

Abstract

The problem on vibration of a viscoelastic rod under dynamic load at one of its ends is considered. The external loading has a signfficant influence on the dynamic characteristics of the material. By using the complex moduli, the problem on vibration of the viscoelastic rod was solved. The complex shear and Young's moduli of a rubberlike material should exhibit the same dependence on frequency. The properties of a rubberlike material was applied. The temperature influence is associated both with the Newton boundary conditions and dissipative heating. The dissipative function is expressed in terms of deformations. The frequencies of high-damping materials occur at or near frequencies that are normally of interest in vibration problems at room temperature. For solving the problem a finite element model was applied. Using this model, qualitative analysis of the influence of dynamic load and dissipative heating on the resonant vibrations of viscoelastic rod is performed. According to the theory of viscoelasticity an analysis of the results was done. The reliability of the values of frequencies for the first resonances was checked. The numerical results qf the problem on vibration of a viscoelastic cylindrical rod under dynamic load at one of its end by the general thermomechanical laws on vibration in damped mechanical systems were obtained and investigated. Distribution of the temperature of dissipative heating along the rod axis is analyzed.