Approximate solution to standing water waves of finite amplitude in material description

An analysis is given of standing water waves of finite amplitude growing in time. In the model considered, a piston-type wave maker generates the waves in a rectangular fluid domain. The frequency of the generation corresponds to water waves of lengths equal to double length of the fluid domain. In this way the case of resonance the obtained and the amplitude of the generated standing wave grew in time. The analysis has been confined to the second order approximation expressed in the material variables. Theoretical results have been compared with experimental data.