Abstract
The dynamical behavior of an viscoelastic body is known to be well described by fractional derivatives of the amount of deformation. The physical reason of this fact is the underlying fractal nature of the molecular structure of such materials. By using the Schiessel-Blumen ladder of mechanical system, it has been shown that the fractal structure would produce the asymptotic power law decay of the deformation, which is the most distinguished characteristics of fractional derivatives. So far, this has been shown by asymptotic behavior of the Laplace transform of the impulse response of the relaxation. Here, we generalize this result, and show that the exact solution of the impulse response function is obtained for a large class of parameter values in terms of confluent hypergeometric functions. The asymptotic expression is then readily obtained which shows the power law decay.
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 callMore From: The Proceedings of the Dynamics & Design Conference
Disclaimer: 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.
