Instability analysis for Faraday waves under arbitrarily periodic vibration

In the framework of linear theory of instability the pattern instability is studied for a layer of a viscous fluid in a large aspect ratio container s ubject to vertically arbitrarily periodic excitation. As some applications, first the instabilities for Faraday water-wave system under excitations of the triangle and square waves are analyzed. Then, the relations between re lative amplitudes and phase of the excitation, and the response modes of th e patterns are investigated in the double-frequency Faraday experiment. The results are satisfactory.