Abstract

Nonlinear Dynamics of Grains in a Liquid-Saturated Soil

C.M.Hedberg (Blekinge Institute of Technology, Karlskrona, Sweden)

e-mail: claes.hedberg@bth.se

Known models with huge nonlinear response of grainy media are based on nonlinear stress-strain relationships typical for solids containing mesoscopic inhomogeneities or defects in their structure. Such nonlinear behaviour is well-defined at significant local deformation caused by high applied load, even if the load does not vary in time. However, there exist a different type of nonlinearity which manifests itself due to inertial forces between grains. Such forces appear in a moving noninertial frame of reference, in particular, if a small system of interacting particles is placed into a vibrating fluid. High spatial gradients of internal forces are determined by the non-uniform distribution of mass. These gradients varying in time can excite the internal degrees of freedom. So, even at harmonic vibration of the fluid caused by sound, the nonlinear internal dynamics can be responsible for generation of higher harmonics. A model of grainy medium is developed as an example of nonlinearity of inertial type. The model deals with an ensemble of grains immersed into vibrating fluid. The inertial attractive forces have hydrodynamic origin, and the repulsive forces are caused by deformation of colliding grains. Dynamic and stochastic motion is studied, resonances are discovered and nonlinear response is evaluated.

Section : 3