3-DIMENSIONAL Flutter Kinematic Structural Stability (original) (raw)
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Divergence and Flutter Instabilities of Some Constrained Two-Degree-of-Freedom Systems
Journal of Engineering Mechanics, 2014
It is now well known that a variety of instability modes can appear before the conventional plastic limit condition is met. In this note, both flutter and divergence instability modes are investigated. First, the criterion for detecting their occurrence is established, and the case of kinematically constrained discrete systems is investigated. Based on an illustrative example, the competition between the occurrences of each of these instability modes is analyzed, showing that the prevalence of a given mode is strongly related to both the loading conditions and the stiffness properties of the material system at hand.
On the Divergence and Flutter Instabilities of Some Constrained Two-Degree-of-Freedom Systems
2013
It is now well known that a variety of instability modes can appear before the conventional plastic limit condition is met. In this note, both flutter and divergence instability modes are investigated. First, the criterion for detecting their occurrence is established, and the case of kinematically constrained discrete systems is investigated. Based on an illustrative example, the competition between the occurrences of each of these instability modes is analyzed, showing that the prevalence of a given mode is strongly related to both the loading conditions and the stiffness properties of the material system at hand.
Journal of Applied Mechanics, 2020
Two types of non-holonomic constraints (imposing a prescription on velocity) are analyzed, connected to an end of a (visco)elastic rod, straight in its undeformed configuration. The equations governing the nonlinear dynamics are obtained and then linearized near the trivial equilibrium configuration. The two constraints are shown to lead to the same equations governing the linearized dynamics of the Beck (or Pflüger) column in one case and of the Reut column in the other. Although the structural systems are fully conservative (when viscosity is set to zero), they exhibit flutter and divergence instability. In addition, the Ziegler's destabilization paradox is found when dissipation sources are introduced. It follows that these features are proven to be not only a consequence of “unrealistic non-conservative loads” (as often stated in the literature); rather, the models proposed by Beck, Reut, and Ziegler can exactly describe the linearized dynamics of structures subject to non-h...
International Journal of Non-Linear Mechanics, 2003
The present paper deals with a study of the benign and catastrophic characters of the utter instability boundary of 2-D lifting surfaces in a supersonic ow ÿeld. The objectives of this work are: (i) to contribute to a better understanding of the implications of aerodynamic and physical non-linearities on the character of the utter boundary and (ii), to outline the e ects exerted in the same respect by some important parameters of the aeroelastic system. With the aim of addressing this problem, the method based on the First Liapunov Quantity is used to study the bifurcational behavior of the aeroelastic system in the vicinity of the utter boundary. The expected outcomes of this study are: (a) to greatly enhance the scope and reliability of the aeroelastic analysis and design criteria of advanced aircraft and, (b) to provide a theoretical basis for the analysis of more complex non-linear aeroelastic systems.
Non-holonomic constraints inducing flutter instability in structures under conservative loadings
Journal of the Mechanics and Physics of Solids, 2020
Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and destabilizing effects connected to dissipation phenomena) can be obtained in structural systems loaded by conservative forces, as a consequence of the application of non-holonomic constraints. These constraints may be realized through a 'perfect skate' (or a non-sliding wheel), or, more in general, through the slipless contact between two circular rigid cylinders, one of which is free of rotating about its axis. The motion of the structure produced by these dynamic instabilities may reach a limit cycle, a feature that can be exploited for soft robotics applications, especially for the realization of limbless locomotion.
Aeroelastic modeling and stability analysis: A robust approach to the flutter problem
International Journal of Robust and Nonlinear Control
In this paper a general approach to address modeling of aeroelastic systems, with the final goal to apply µ analysis, is discussed. The chosen test bed is the typical section with unsteady aerodynamic loads, which enables basic modeling features to be captured and so extend the gained knowledge to practical problems treated with modern techniques. The aerodynamic operator has a non-rational dependence on the Laplace variable s and hence two formulations for the problem are available: frequency domain or state-space (adopting rational approximations). The study attempts to draw a parallel between the two consequent LFT modeling processes, emphasizing critical differences and their effect on the predictions obtained with µ analysis. A peculiarity of this twofold formulation is that aerodynamic uncertainties are inherently treated differently and therefore the families of plants originated by the possible LFT definitions are investigated. One of the main results of the paper is to propose a unified framework to address the robust modeling task, which enables the advantages of both the approaches to be retained. On the analysis side, the application of µ analysis to the different models is shown, emphasizing its capability to gain insight into the problem.
Effect of Control Constraints on Active Stabilization of Flutter Instability
The effect of amplitude and rate control constraints in active flutter suppression is analysed for a number of different state feedback control laws considering mathematical model of two degree-of freedom nonlinear aeroelastic airfoil system with trailing and leading edge flaps. The size of region of attraction is used as an additional metric to select a set of acceptable control laws designed by eigenstructure assignment and nonlinear dynamic inversion methods.
Inclusion of Mechanical Dampers in the Multimodal Flutter Analysis of Slender Structures
Advances in Fluid Mechanics XIII
Sometimes slender structures are reinforced with mechanical dampers to reduce the vibrations caused by aeroelastic phenomena like flutter. However the formulation of flutter analysis only considers the classical damping ratio to take into account the structural damping. This paper explains the procedure used for adding mechanical dampers with a known constant to the analysis software FLAS. This code was developed at Universidade da Coruña to calculate the critical wind speed for flutter instability. An example of a solar tracker with two rows of flat panels is shown. In this slender structure two mechanical dampers are used to reduce the vibrations caused by the wind in structure interaction. The solar tracker has been studied for five different positions of the angle of attack. Results of flutter speed for several values of the dampers constant and global structural damping ratio are presented.