Formulation of the Aeroelastic Instability Problem of Rectangular Plates in Uniform Flow Based on the Hamiltonian Mechanics for the Constrained System

2014 ◽  
Author(s):  
Kensuke Hara ◽  
Masahiro Watanabe
Keyword(s):  
Stability Analysis ◽  
Lagrange Multiplier ◽  
Evolution Equations ◽  
Velocity Potential ◽  
Mixed Boundary ◽  
Hamiltonian Mechanics ◽  
Rectangular Plates ◽  
Constrained System ◽  
Aeroelastic Instability ◽  
The Stability

This paper addresses a formulation and an aeroelastic instability analysis of a plate in a uniform incompressible and irrotational flow based on the classical variational principle framework. Because of an intrinsic algebraic relation between the plate displacement and the velocity potential, this system has to be formulated as the constrained system. In this study, we tried to apply the Hamiltonian mechanics to the formulation of the fluid-structure interaction problem with mixed boundary condition. As a result, we obtain the canonical equations, that consist of the evolution equations for the plate displacement, the velocity potential, the Lagrange multiplier and canonically conjugate momenta for those physical quantities. In particular, it was found that the Lagrange multiplier was just the pressure. In other words, the equations of time evolution could be derived for not only the plate displacement and the velocity potential but also the pressure (the Lagrange multiplier). The stability of this system was analyzed by the eigenvalue analysis. Then, flutter modes, their frequencies and growth rates were discussed. The proposed technique has the advantage that it can reduce iteration procedures in the stability analysis. As a consequence, it can be expected that the stability of this system can be evaluated efficiently. This paper introduces a formulation of the only two dimensional problem, and the stability analysis of a clamped-free plate is implemented as an numerical example. Howerver, this formulation can be applied to three dimensional problems without intrinsic difficulties.

Stability Analysis of Rectangular Plates in Incompressible Flow With Fourier Multiplier Operators

2013 ◽  
Author(s):  
Kensuke Hara ◽  
Masahiro Watanabe
Keyword(s):  
Integral Equation ◽  
Stability Analysis ◽  
Fourier Multiplier ◽  
Fourier Transforms ◽  
Mixed Boundary ◽  
Computation Time ◽  
Rectangular Plates ◽  
Multiplier Operator ◽  
Fourier Multiplier Operator ◽  
Interaction Problem

This paper describes a development of a method which improves the computational efficiency for a linear stability analysis of a plate in an uniform incompressible and irrotational flow. We introduce the Fourier multiplier operator to formulate the fluid and plate interaction problem with the mixed boundary condition. In previous typical approaches, a singular integral equation often appears in the formulation of a pressure distribution on the plate. The computation time for solving the integral equation is one of the problem encountered in the stability analysis. Applying the Fourier multiplier operator to this system, the equation of the plate-fluid interaction problem can be formulated with a pair of the Fourier and the inverse Fourier transforms. Moreover, the integration to derive the equations of motion can be efficiently carried out by using the discrete Fourier transform.

Stability of a Stationary Flexible Cantilevered Plate in an Axial Flow

2014 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Keiji Matsumoto
Keyword(s):  
Stability Analysis ◽  
Velocity Potential ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Axial Flow ◽  
Complex Eigenvalue ◽  
Flexible Plate ◽  
Moving Plate ◽  
Cantilevered Plate ◽  
The Stability

As the flexible plates, the papers in printing machines, the thin plastic and metal films, and the fluttering flag are enumerated. In this paper, the flexible plate is assumed to be stationary in an axial flow although both the stationary plate and the axially moving plate can be thought. 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 in consideration of the added mass, added damping and added stiffness, respectively. The velocity potential is obtained by assuming the unsteady axial fluid velocity to be zero at the trailing edge of a flexible cantilevered plate, neglecting the effect of a circulation. The complex eigenvalue analysis is performed for the stability analysis. In order to investigate the validity of the proposed analysis, another stability analysis is also performed by using the non-circulatory aerodynamic theory. The comparison between both solutions is investigated and discussed. Changing the velocities of a fluid and the specifications of a plate as parametric studies, the effects of these parameters on the stability of a flexible cantilevered plate are investigated.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

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