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The dynamic stability of rectangular flexible plate often becomes a problem. As the flexible plate, the papers in a high-speed printing machine, the thin plastic, the thin metal, the fluttering flag and the oscillating doom roof are enumerated. In this paper, the dynamic stability of cantilevered rectangular plate is estimated in three-dimensional model. The fluid is assumed to be treated as an ideal fluid in a subsonic domain, and the fluid pressure is calculated using the velocity potential theory. This fluid pressure is determined by using the integral equations for the pressure along the span and the pressure along the chord under the boundary conditions in the Fourier space. The lateral deflection of plate is assumed to be expressed as a product of the cantilevered beam mode in the streamwise direction and the free-free bending beam mode in the spanwise direction. Applying the Galerkin method for the equation of motion of an elastic plate, the three-dimensional coupled equation of motion of a cantilevered rectangular plate is derived. The complex eigenvalue analysis is performed for the stability analysis. Changing the mass ratio and the aspect ratio, the root loci, the vibration modes of the plate and the fluid pressure are investigated. And, the relationship between the critical fluid velocity and the mass ratio taking the aspect ratio as a parameter is investigated.

In this paper, dynamic stability analysis methods of a beam subjected to a confined annular axial flow are dealt with. Such structures are submarine resources production pipeline, reactor core structures of nuclear power plants, high-speed trains passing thorough a tunnel, a piping system in the field of ocean mining, and so on. The relation between the annular axial flow velocity and the unstable dynamics of structures are clarified. We have compared two analysis methods which can evaluate the dynamic instability of such structures. In first analysis method, the fluid is treated as viscous fluid, and is governed by the Navier-Stokes equation, and the beam structure is treated as the Euler-Bernoulli beam. This is called as the viscous fluid solution namely NS solution hereafter. In second analysis method reported by (Rinaldi and Paidoussis, 2012), the fluid is treated as ideal fluid. Then the viscosity effect is added to the equation of motion. This is called as the ideal fluid solution namely R&P solution hereafter. The complex eigenvalue analysis of the fluid structure coupled equation of motion is performed in order to clear up the dynamic instability. Performing the parametric studies, the comparison between both solutions is investigated. When the fluid viscosity becomes large, the difference in the critical velocity between the viscous fluid solution namely NS solution and the ideal fluid solution namely R&P solution is found to be generated. The destabilization effect appears due to the fluid viscosity force terms of the added stiffness of the fluid-structure coupled equation only in the viscous fluid solution.

The stability of a flexible cantilevered plate subjected to a parallel flow is investigated. As the flexible flat plates, the papers in a high speed printing machine, the thin plastic and metal films, the fluttering flag and the oscillating doom roof are enumerated. The fluid is assumed to be treated as an ideal fluid in a subsonic domain, and the fluid pressure is calculated using the velocity potential theory. The coupled equation of motion of a flexible cantilevered plate is derived into consideration with the added mass, added damping and added stiffness respectively. The complex eigenvalue analysis is performed for the stability analysis. In order to consider the accuracy of dynamic stability analysis, three stability analysis method are proposed. Firstly, the analysis method based on boundary conditions in the half space surrounded by leading edge and trailing edge is performed. Hereafter, let's call it the coupled solution. Secondly, the analysis method based on the non-circulatory aerodynamic theory is performed. Let's call it the non-circulatory solution.Thirdly, the analysis method which fulfills Kutta condition is performed. Let's call it the circulatory solution.The following is made to be clear through three solutions. When the mass ratio of a fluid system for a structure system is small, the flutter of the lower mode such as a second mode become predominant. And, when the mass ratio is large, the higher mode flutter appears. Although the critical velocities of the coupled solution and the non-circulatory solution are higher than that of the circulatory solution in the second mode flutter with lower mass ratio, the critical velocities of the circulatory solution becomes higher than those of the coupled solution and the non-circulatory solution when the mass ratio increases.

The evaluation methodologies of flow induced vibration on the dynamic stability of elastic beam structure are investigated. In this paper, the instability analysis methods of a beam subjected to a confined annular axial flow are dealt with. Such structures are reactor core structures of nuclear power plants, high-speed trains passing thorough a tunnel, and submarine resources production pipeline, so on. The relation between the annular axial flow velocity and the unstable dynamics of structures has to be clarified. We have compared two analysis methods which can evaluate the dynamic instability of such structures. In first analysis method, the fluid is treated as viscous fluid, and is governed by the Navier-Stokes equation, and the beam structure is treated as the Euler-Bernoulli beam. This is called as the viscous flow solution hereafter. In second analysis method, the fluid is treated as ideal fluid. The viscosity effect is added to the equation of motion. This is called as the nonviscous flow solution hereafter. The complex eigenvalue analysis of the fluid structure coupled equation of motion is performed in order to clarify the dynamic instability. Performing the parametric studies, the comparison between both solutions is investigated. Moreover, the numerical solutions are compared with the experiments which have already reported by one of authors. When an annular gap becomes smaller than other dimensions, it is found that the difference in the critical velocity between the viscous flow solution and the nonviscous flow solution is generated.

As the herringbone-grooved journal gas bearing can rotate silently at high speed with low friction, and moreover it can be small-sized, it is used a lot in the fields such as information appliances. In this paper, the equation of motion of the herringbone-grooved journal gas bearing is derived using the gas force which can be obtained by applying the Navier-Stokes equation for the grooved and the ridged parts of a journal. The stability analysis can be performed when a journal rotates with a high speed by using the stability analysis method of Routh-Hurwitz, the root locus of complex eigenvalue analysis, and the time history analysis due to transient response vibration. Comparing with the already published analytical results, the physical meanings which have not been clarified in the conventional study are reported as for the stability of herringbone-grooved journal gas bearing. The stability chart is shown to be determined by considering the forward whirl and the backward whirl. In addition, it is reported that the present analysis results show a good agreement with the already reported experimental results. Furthermore, the parameters study as for the specification of gas bearing is performed, and it is shown that the stability chart changes due to the influence of specifications complicatedly.