الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
The parametric excitation of an elevated water tower experiencing liquid sloshing hydrodynamic impact is studied in the absence and presence of the internal resonance. The Multiple Time Scales method is used to establish the resonance conditions. The liquid sloshing mass is replaced by a mechanical model in the form of a simple pendulum experiencing impacts with the tank
.. walls. The impact loads were modeled based on a phenomenological representation in the form ;of a power function with a high exponent. In this case the system equations of motion include impact non-linearities (selected to be of fifth power) and cubic structural geometric non¬Jinearities. When the first mode is parametrically excited in the absence of internal resonance, the system experiences hard nonlinear behavior and the impact loading reduced the response
,amplitude. In the presence of internal resonance, the numerical integration yielded fixed or non¬. 1tIti0nary solutions depending on initial conditions for non-impact and impact cases.
On the other hand, when the second mode is parametrically excited in the absence of internal resonance, the impact loading results in complex response behavior characterized by multiple steady state solutions, where the response switches from soft to hard nonlinear characteristics. In the presence of internal resonance and for all cases the first mode amplitude reaches its zero equilibrium value, while the second mode amplitude reaches a non-zero value depending on initial conditions.
Under combined parametric resonance and in the absence of internal resonance, the system possesses a single steady state response in the non-impact and impact cases. However, the system behaves like a soft system for the non-impact and like a hard system in the impact case. In the presence of internal resonance, for the non-impact loading, the response did not achieve MY stationary state regardless of initial conditions and internal detuning parameter. Under restricted conditions of zero phase angles, fixed solution were obtained. For the impact loading, the system possessed only fixed point within a very narrow range of internal detuning parameter. Away from this region, the response was found to be quasi-periodic or chaotic depending on initial conditions and internal detuning parameter.