# Vibration analysis of rectangular plates coupled with fluid

**ABSTRACT** The approach developed in this paper applies to vibration analysis of rectangular plates coupled with fluid. This case is representative of certain key components of complex structures used in industries such as aerospace, nuclear and naval. The plates can be totally submerged in fluid or floating on its free surface. The mathematical model for the structure is developed using a combination of the finite element method and Sanders’ shell theory. The in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively. The mass and stiffness matrices are then determined by exact analytical integration. The velocity potential and Bernoulli’s equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the developed structural shape function is integrated over the structure-fluid interface to assess the virtual added mass due to the fluid. Variation of fluid level is considered in the calculation of the natural frequencies. The results are in close agreement with both experimental results and theoretical results using other analytical approaches.

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**ABSTRACT:**The stability analysis and active control of a nonlinear composite laminated plate in subsonic airflow are studied. The equation of motion of a plate with a piezoelectric patch in subsonic air flow is established by using the Hamilton’s principle with the assumed mode method. The perturbation aerodynamic pressure is derived from linear potential flow theory. For the linear system, the eigenfrequencies of the system are calculated for different flow velocities, and the critical instability flow velocity and the flutter flow velocity are obtained. For the nonlinear system, the bifurcation of the transverse displacement with respect to the flow velocity is analyzed by solving the equations of equilibrium of the nonlinear dynamic system. The effects of the ply angles on the critical instability flow velocities of the plate are analyzed. According to the mechanism for the instability of the plate in subsonic flow, the displacement feedback control strategy is adopted to stabilize the system. The influences of the control gain on the critical instability velocity of the plate are analyzed. From the analysis and numerical simulations, it can be concluded that with the ply angle increasing from \(0^{\circ }\) to \(90^{\circ }\) , the critical instability flow velocity of the plate has a maximum at a finite critical angle. When the flow velocity exceeds the critical instability flow velocity, the stable point of the nonlinear system deviates from the zero point of the system. It also can be concluded that the displacement feedback control can effectively improve the aerodynamic properties of the plate by providing the active stiffness for the unstable system. With displacement feedback control gain increasing, the critical instability flow velocity increases.Journal of Engineering Mathematics 12/2014; 89(1). DOI:10.1007/s10665-014-9708-3 · 1.07 Impact Factor -
##### Dataset: 1)ARTICLES-(14-10-2014)

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**ABSTRACT:**Based on the powerful Computational Structural Dynamics method coupled to a Computational Fluid Dynamics approach, the PolyMAX algorithm is used along with the simulation of two-way fluid–structure interactions, as a new virtual testing method for estimating the structural modal parameters and damping ratios of a vibrating structure in either air or some other fluid. The viscosity and motion of fluid are accounted for, as are the shape of the flow passage and a variety of boundary conditions. The method is shown to be able to simulate the vibration of a structure within a real operating environment in which the structure experiences a specified excitation load while the vibration responses of the structure are obtained through a two-way FSI model. Based on the PolyMAX method for estimating the modal parameters, these vibration responses are processed and analyzed. Finally, the dynamic parameters (i.e., the natural frequencies and the damping ratios) of the vibrating structure are identified. For validation, the natural frequencies and damping ratios of two simple submerged cantilever plates were simulated both in air and water and the simulated results were found to agree closely with experimental data.Journal of Fluids and Structures 04/2015; 54:548-565. DOI:10.1016/j.jfluidstructs.2015.01.001 · 2.23 Impact Factor