Deterministic behavior of elevated water tanks under vertical motion

The dynamic response of 3n elsstic structure carrying 3 rigid cylindrical tank partially filled with a liquid subjected to vertical sinusoidal harmonic excitation Is considered.

The nonlinear response is determined by using an asymptotic expansion technique developed by Struble. Secular terms which give rise to parametric resonance conditions are identified. Four parametric resonance conditions are found to take place when the excitation frequency is in the neighborhood of twice the natural frequency of one of the normal modes, or close to the sum or difference of the normal mode frequencies of the system. The steady-state responses of the system are obtained for the first three parsmetric resonance conditions and show the occurrence of the jumps phenomenon at a certain critical excitation frequency. Under combination parametric resonance of difference type the method does not provide any steady state response.