scholarly journals Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

1997 ◽  
Vol 3 (4) ◽  
pp. 329-371
Author(s):  
Henryk Flashner ◽  
Ramesh S. Guttalu
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Mapping Method ◽  
Periodic Systems ◽  
Resonance Problem ◽  
Point Mapping ◽  
Analytical Stability ◽  
Functional Relations ◽  
Ground Resonance ◽  
The Stability

Apoint mappinganalysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.

An Analytical Study of Stability of Periodic Systems by Poincaré Mappings

1995 ◽  
Author(s):  
Ramesh S. Guttalu ◽  
Henryk Flashner
Keyword(s):  
Degrees Of Freedom ◽  
Mapping Method ◽  
Degree Of Freedom ◽  
Point Mapping ◽  
Analytical Stability ◽  
Functional Relations ◽  
Higher Dimensional ◽  
Period Mapping ◽  
The Stability ◽  
Bifurcation And Stability

Abstract The Poincaré map (point mapping) analysis approach is used to investigate the stability of multivariable periodic dynamical systems. The approach presented here is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system’s dynamics. It also allows to find analytical dependence of point mapping on system’s parameters. Analytical stability and bifurcation condition are then determined and expressed as functional relations between various system parameters. The approach is applied to investigate the parametric stability of flap motion of a rotor. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. To emphasize the applicability of the method for studying higher order systems, bifurcation and stability analysis of a two degree-of-freedom cantilever beam subjected to harmonic base motion is performed. The results of our analysis exhibit an excellent agreement with the “exact” (numerical integration) solution. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Extension of these methods to higher dimensional systems is not straightforward, and is usually very cumbersome.

Stability Analysis of Monument: A Case Study–Safdarjung Tomb

2010 ◽  
Vol 133-134 ◽  
pp. 403-410
Author(s):  
Adil Ahmad ◽  
Khalid Moin
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Seismic Load ◽  
New Delhi ◽  
Archaeological Survey ◽  
Central Dome ◽  
Lateral Forces ◽  
Shear Beam ◽  
The Stability ◽  
Lumped Masses

Present study deals with the stability analysis of an existing historical monument “Safdarjung Tomb” under Seismic Load. The tomb is situated at New Delhi, India. The building is classified as protected monument by the Archaeological Survey of India (ASI). This is a ground plus two storey masonry structure with a central dome. The basic seismic parameters have been evaluated using Bureau of Indian Standards (BIS) Codal method. Distribution of lateral forces is carried out to individual piers and walls using Rigidity Approach. The seismic performance of the building is studied under the gravity and earthquake loads. The building is modeled as a two-degree-of-freedom shear-beam system. The piers, which are located parallel to the direction of earthquake shaking are assumed to provide spring action. The mass of the walls and slabs are lumped at the storey levels. The lumped masses are assumed to be connected to each other through massless springs. The degree of each mass in horizontal direction is considered, neglecting the vertical translational and rotational degrees of freedom. Stiffness of the walls parallel to longitudinal and transverse directions of the building has been computed separately which was used for computation of lateral forces in each direction. The forces so evaluated are used in pier analysis to evaluate stress induced in various elements. The majority of the structural elements were found safe and the overall structure is stable. The stresses due to shear and bending are within permissible limit

Analytical Stability Analysis of Surface Vessel Trajectories for a Control-Oriented Model

2011 ◽  
Vol 6 (3) ◽  
Author(s):  
Alan M. Whitman ◽  
Hashem Ashrafiuon ◽  
Kenneth R. Muske
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Viscous Drag ◽  
Reduced Order ◽  
Analytical Stability ◽  
Straight Line ◽  
Vessel Motion ◽  
Damping Model ◽  
Surface Vessel ◽  
Three Degrees Of Freedom

An analytical stability analysis of the steady trajectory for a surface vessel with various damping models is presented in this work. The analysis is based on a control-oriented, three degrees-of-freedom model that considers vessel motion only in the horizontal plane. The goal of this study is to understand the vessel trajectories predicted by this reduced order model for model-based control design. Straight line and circular motion stability conditions for each trajectory are derived and presented for the various damping models. The results of this analysis show that either a straight line or a circular steady trajectory is possible, depending on the magnitude of the surge force and the form of the damping model used to represent viscous drag, vortex shedding, and losses due to the surface wake generated by the vessel motion. However, the straight line motion is much less likely for the vessel considered in this work.

Impulsive Parametric Excitation: Theory

1972 ◽  
Vol 39 (2) ◽  
pp. 551-558 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Stability Analysis ◽  
General Theory ◽  
Parametric Excitation ◽  
Periodic Systems ◽  
Stability Criteria ◽  
Dirac Delta ◽  
Special Cases ◽  
Delta Functions ◽  
Analytic Stability ◽  
The Stability

Given in this paper is the development of a theory for dynamical systems subjected to periodic impulsive parametric excitations. By periodic impulsive parametric excitation we mean those excitations representable by periodic coefficients which consist of sequences of Dirac delta functions. It turns out that for this class of periodic systems the stability analysis can be carried out in a remarkably simple and general manner without approximation. In the paper, after giving the general theory, many special cases are examined. In many instances simple and closed-form analytic stability criteria can be easily established.

Stability Analysis of a Cracked Rotor With Several Degrees of Freedom

2009 ◽  
Author(s):  
Roberto Ricci ◽  
Paolo Pennacchi
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Analytical Models ◽  
Cracked Rotor ◽  
Common Notion ◽  
Rotating Shafts ◽  
Stiffness Variation ◽  
The Stability ◽  
First Time ◽  
Breathing Mechanism

It is a common notion in literature that cracks in horizontal rotating shafts can cause instability of the system. Actually the stiffness variation due to the breathing mechanism may cause parametric excitation to the rotor system. This phenomenon has been investigated by means of both analytical models and simulation, but the studies are related to simple Jeffcott’s rotors. In this paper the method normally used to investigate the stability of cracked rotors, i.e. Floquet’s theory, is applied for the first time to a model of a real rotor with several degrees of freedom, considering also the bearings and the foundation. Huge calculation resources have been necessary and this may explain why this analysis was not performed before. The results are very different from those obtained by means of simple Jeffcott’s rotor.

Stability analysis of mechanisms having unpowered degrees of freedom

Robotica ◽  
1989 ◽  
Vol 7 (4) ◽  
pp. 349-357 ◽  
Author(s):  
B. Borovac ◽  
M. Vukobratović ◽  
D. Stokić
Keyword(s):  
Stability Analysis ◽  
Decomposition Method ◽  
Degrees Of Freedom ◽  
Complete System ◽  
Dynamic Effect ◽  
Numerical Example ◽  
Spatial Mechanisms ◽  
The Stability ◽  
First Time ◽  
Lyapunov Vector

SUMMARYThe stability analysis of active spatial mechanisms comprising both powered and unpowered joints is carried out for the first time using aggregation-decomposition method via Lyapunov vector functions. This method has already been used for analysis of mechanisms with all powered joints. To extend the application of the method to the stability analysis of mechanisms containing unpowered joints we developed modelling of special subsystem consisting of one powered and one unpowered joint. Then, we consider the stability of the complete system without neglecting any dynamic effect. The stability analysis is demonstrated by a numerical example of a particular biped system.

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