Simple human-structure interaction model of walking on a flexible surface

We present a new human-structure interaction (HSI) model of walking on a flexible surface. A human is considered as a mass point, located at the body’s center of mass (COM). The mass moves along a predefined trajectory, which deforms together with the surface on which the human walks. The forces of motion, equal to the sum of inertial and gravitational forces acting on the mass, are transfered to the surface at prescribed foot positions. The motion of the surface is described using a few selected mode shapes, corresponding damping ratios, and natural frequencies. The equations of motion of the system are time-dependent and discontinuous. They can be written in the form of the second order differential equations of structural dynamics, but with the right-hand forcing dependent on the deformation of the surface. We present a numerical example of a human walking on a long beam structure. The motion of the beam is described by three mode shapes, representing its vertical, lateral, and torsional deflections.