CONTINUOUS AND DISCRETE MODELS OF BOUNDED ONE-DIMENSIONAL MEDIA IN THE THEORY OF VISCOELASTICITY

The relation between the discrete and continuous models of a one-dimen sional viscoelastic medium is discussed. Beginning with the discrete m odel, for the linear case it is shown how to construct a series of par tial differential equations which might be thought of as intermediate between the differential-difference equation for a chain of discrete m asses and the equation for a continuous medium. For these intermediate equations (one of which will be, in particular, the equation of a vib rating continuous medium) we give the conditions under which one is ju stified in replacing the initial continuous model by a discrete chain. For the non-linear case, the analogue of the Fermi-Pasta-Ulam (FPU) p roblem with strongly non-linear constraints is considered. This versio n of the FPU problem can be applied to a chain with non-linear viscoel asticity. (C) 1997 Elsevier Science Ltd. All rights reserved.