The Nonlinear Dynamics Study Of One Type Of Cylindrical Tank

The dynamics and safety issues of tank are research topics which are proverbially concerned by academicians all over the world. The vibration of the wall and soleplate of chemical reactor, fermentor and tank which caused by interaction of fluid and solid is a kind of complicated flow-induced vibration. Now many academicians have studied dynamics of the tank mainly from linear aspects, but in which the vibration characteristics of the tank cannot be completely reflected. To represent the characteristics of the tank under the flow-induced, this paper used the elastic plate theory and nonlinear theory, nonlinear vibration equations of the shell and plate had been established by considering of many nonlinear factors. The researches of these models were analyzed analytically, numerically and practically. The main results have acquired are as follows:(1) Considering of damping, geometric nonlinearity and added mass, a nonlinear vibration equation which excited by pulsating flow had been established by using Donnell's shallow-shell theory. Partial differential equations were transformed into ordinary differential equations by using Galerkin method. By means of the method of the multiple scales, the first approximate solution of the primary resonance of the system was acquired, the transition variety and bifurcation diagram of the unfolding parametric plane were given, then analyzed the singularity and the stability of this system, acquired the impact of structure parameter such as damping and mass to the stability of the running system. Furthermore, acquired at which ratio of damping and mass the system could run most stable. Numerical analysis of this system was accomplished to study the impact of system parameters, such as the damping and pulsating frequency.(2) In order to further research the dynamics of the cylindrical tank, a nonlinear vibration equation of the cylindrical tank plate which on the non-linear elastic foundation had been established. Partial differential equations were transformed into ordinary differential equations by using Galerkin method. By means of the method of the multiple scales, the first approximate solution of the primary resonance-primary parametric resonance of the system was acquired. Analyzed the vibration characteristics of the plate which on the nonlinear elastic foundation and revealed the impact of the various parameters to the amplitude and resonance region of the plate by numerical analysis. These parameters included the nonlinear stiffness, damping coefficient, thickness of the plate and parametric vibration coefficient.(3) By determining the various spectrums of the structure surface pressure, the mean square average response of the structural components could be given by using the random vibration theory. Then the impact of the structural characteristics to the vibration of the structure was analyzed, such as the shape of tank and buffle, stiffness, structural damping, fluid damping and structural material properties. Based on the above analysis, some constructive measures about controlling and reducing the vibration which caused by turbulence was advanced.(4) Acquired and analyzed modal of the cylindrical tank at different depth of water by impacting test. Measured a variety of work patterns under work condition and analyzed spectrums by dynamic signal instrument, and the vibration characteristics under the turbulence condition were acquired. Validated the previous theoretical assumptions and approximations were reasonable and the results were reliable.