Досліджено термомеханічні властивості в"язкопружного матеріалу. Розглянуто задачу про гармонічні коливання гумоподібного стержня при кінематичному навантаженні, прикладеному на одному з його кінців. Для розв"язання задачі використано концепцію комплексних модулів. Отримані амплітудно-частотні характеристики для напруження та деформації. Введено дисипативну функцію, за допомогою якої досягнуто дисипативний розігрів стержня. На основі скінченно-елементної моделі побудовано розв"язок задачі з врахуванням в"язкопружних властивостей матеріалу. Проаналізовано результати згідно з термомеханічними властивостями матеріалу. Зроблені відповідні висновки щодо поведінки гумоподібного матеріалу при термомеханічному навантаженні. Перевірено достовірність значень частот для перших резонансів.
The Thermomechanical coupling problems are common phenomena in the field of Solid Mechanics. In the area of structural mechanics and materials engineering the primary motivation for studying damping is its importance as an engineering property in the analysis of structural response and performance. There are a number of interesting applications where modeling viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection &and ultrasonic imaging. Nowadays, in structural design, the analysis of all but simple structures is carried out using the finite element method. This investigation deals with the notions of stress-strain and strain-displacements relation, which are &fundamental in understanding mechanics. The problem on harmonic vibration of a viscoelastic rubber-like rod under kinematic load at one of its ends is considered. The thermomechanical properties of a viscoelastic material is investigated. The externa&l loading has a significant 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 rubber-like material should exhi&bit the same dependence on frequency. The properties of a rubber-like 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 de&formations. 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 anal&ysis 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 fo&r the first resonances was checked. The numerical results of the problem on vibration of a viscoelastic cylindrical rod under kinematic load at one of its end by the general thermomechanical laws on vibration in damped mechanical systems were obtaine&d and investigated. The numerical understanding of the thermomechanical coupling of rubber-like materials is a prerequisite to predict the temperature rise in viscoelastic components. Distribution of the temperature of dissipative heating along the r&od axis is built and analyzed.
