Abstract
A mathematical model for elastic oscillations of a longitudinal rod has been developed on the basis of relaxation terms in the Newton’s second law. An exact analytical solution of the corresponding boundary value problem has been obtained using the method of separation of variables. The analysis of the obtained solution showed that taking into account the medium relaxation properties has a significant effect on the oscillatory process: the amplitude of the oscillations and the shape of the wave profile. Taking into account relaxation coefficients leads to the smoothing of the wave, eliminating jumps in the unknown displacement function. The author estimated for the first time, the influence of high-order derivatives in a modified equation of motion on an oscillatory process. It is shown that high-order derivatives, at a sufficiently large value of the relaxation coefficients, reduce the intensity of the oscillatory process. In this case, the delay of the displacement function in time occurs (compared to the case when the relaxation properties are not taken into account). The theoretical and experimental studies performed made it possible to determine the values of the relaxation and resistance coefficients.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
