University of Cambridge > > Isaac Newton Institute Seminar Series > Dissipation at a shock wave in an elastic bar

Dissipation at a shock wave in an elastic bar

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact nobody.

HY2W05 - Physical applications

Propagating discontinuities in continua, such as, shocks and phase transition fronts often cause dissipation. The dissipated energy is said to manifest in high frequency oscillations behind the propagating front, yet there is no quantitative accounting of it. In this talk we relate the energy dissipated at a shock wave in a non-linearly elastic bar to the energy in the oscillations in two related dissipationless, dispersive systems. We study three one-dimensional dynamic impact problems. Problem 1 concerns a nonlinearlu elastic bar. Problem 2 a discrete chain of particles, and Problem 3 a continuum with a strain-gradient term in the constitutive relation. In the impact problem considered the free boundary of each initially quiescent body is subjected to a sudden velocity, that is then held constant for all subsequent time. There is energy dissipation at the shock in Problem 1, but Problems 2 and 3 are conservative. Problem 1 is solved analytically, Problem 2 numerically and an approximate solution to Problem 3 based on dispersive shock waves is constructed analytically. The rate of increase in the oscillatory energy in Problems 2 and 3 are calculated and compared with the dissipation rate at the shock in Problem 1. The results indicate that the former is a good qualitative measure of the latter. The quantitative agreement is satisfactory at larger impact speeds but less so at smaller speeds, some reasons for which are discussed. Joint work with Rohan Abeyaratne, Massachusetts Institute of Technology, Cambridge, USA .

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2023, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity