| Abstrakt: |
The article is devoted to the analysis of the wave field, which is excited when the first normal propagating wave is reflected from the end of the elastic hemisphere, part of which is rigidly clamped, and part is free from stresses. The boundary value problem belongs to the class of mixed boundary value problems, the characteristic feature of which is the presence of a local feature of stresses at the point of change of the type of boundary conditions. In order to solve this boundary value problem, it was proposed in the article a method of superposition, which allows taking into account the peculiarity of stresses due to the asymptotic properties of the unknowns. Asymptotic dependences for unknowns are determined by the nature of the feature, which is known from the solution of the static problem. The criterion for the correctness of the results was the control of the accuracy of the law of conservation of energy. The error of the law of conservation of energy did not exceed 2 % of the energy of the incident wave for the entire frequency range in which the research was conducted, provided that 30 members in the series through which the voltages are represented are taken into account. The analysis of the wave field was performed for antisymmetric oscillations. It is shown in the article that starting from the locking frequency for the second normal wave, the energy transferred by the first and second reflected waves depends significantly on the frequency. While there may be cases when there is no wave of the same order as the incident wave in the reflected field. In addition to the frequency, the energy transferred by the normal waves reflected from the end depends on the value of the ratio to the length at which the end of the hemisphere is rigidly clamped, to the length of the free end. The article shows that for a specific frequency the dependence of energy on h is very complex and the same energy in the far field corresponds to different values h . Since the dependence of energy on h for various frequencies is different, the criterion for estimating the value of h related to the amount of energy (when calculating the amount of displacement) can be the distinction in energy at different frequencies. [ABSTRACT FROM AUTHOR] |
