Parametric excitation of nonlinear elastic systems involving hydrodynamic sloshing impact

The parametric excitation of an elevated water tower experiencing sloshing hydro-dynamic impact is studied using the multiple scales method. The liqui d sloshing mass is replaced by a mechanical model in the form of a simple p endulum experiencing impacts with the tank walls. The impact loads are mode led based on a phenomenological representation in the form of a power funct ion with a higher exponent. In this case the system equations of motion inc lude impact nonlinearities (selected to be of fifth power) and cubic struct ural geometric nonlinearities. When the first mode is parametrically excite d the system exhibits hard nonlinear behavior and the impact loading reduce d the response amplitude. On the other hand, when the second mode is parame trically excited, the impact loading results in complex response behavior c haracterized by multiple steady state solutions, where the response switche s from soft to hard nonlinear characteristics. Under combined parametric re sonance, the system possesses a single steady-state response in the absence and in the presence of impact. However, the system behaves like a soft sys tem in the absence of impact and like a hard system in the presence of impa ct.