Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

2019 ◽  
Vol 233 (4) ◽  
pp. 931-941
Author(s):  
Seyed Mahdi Abtahi
Keyword(s):  
Equations Of Motion ◽  
Time History ◽  
Melnikov Method ◽  
Spin Orbit ◽  
Attitude Dynamics ◽  
Inertia Moment ◽  
Coupled Equations ◽  
Highly Nonlinear ◽  
Complex Spin ◽  
The Mathematical Model

Interactions of the orbital motion on attitude dynamics of the gyrostat satellite are considered in this paper. The mathematical model is derived using the Hamiltonian method for the spin-orbit motion of the spacecraft followed by the reduction of the coupled equations of motion using the extended Deprit canonical transformation. The analytical Melnikov method is used innovatively to study chaos on the complex Spin-Orbit dynamics of the gyrostat satellite. Also, the numerical methods such as Lyapunov exponent criterion, Poincaré section, trajectories of phase portrait, and the time–history responses can be proved the heteroclinic bifurcation and chaotic vibrations in the highly nonlinear system. Using the results based on the Melnikov integral, the parameters of the spacecraft including the mass and inertia moment of satellite with respect to the altitude of orbit can be designed in order to control the bifurcation with a view to prevention of chaos in the system in the absence of an active control system.

Supplemental dampers in base-isolated buildings to mitigate large isolator displacement under earthquake excitations

2015 ◽  
Vol 48 (2) ◽  
pp. 100-117 ◽  
Author(s):  
Daniel H. Zelleke ◽  
Said Elias ◽  
Vasant A. Matsagar ◽  
Arvind K. Jain
Keyword(s):  
Equations Of Motion ◽  
Time History ◽  
Coupled Equations ◽  
History Analysis ◽  
Base Isolator ◽  
Fixed Base ◽  
Passive Dampers ◽  
Supplemental Dampers ◽  
Isolation Systems ◽  
Storey Building

The effect of viscous, viscoelastic, and friction supplemental dampers on the seismic response of base-isolated building supported by various isolation systems is investigated. Although base-isolated buildings have an advantage in reducing damage to the superstructure, the displacement at the isolation level is large, especially under near-fault ground motions. The influence of supplemental dampers in controlling the isolator displacement and other responses of base-isolated building is investigated using a multi-storey building frame. The coupled equations of motion are derived, solved and time history analysis is carried out on a building modeled with fifteen combinations of five isolation systems and three passive dampers. The seismic responses are compared with that of the fixed-base and base-isolated buildings. Based on the results, it is concluded that supplemental dampers are beneficial to control the large deformation at the isolator level. Parametric study is conducted and optimum ranges of damper parameters to achieve reduced isolator displacement without adverse effect on the other responses are determined. Further, it is concluded that the combination of the resilient-friction base isolator (R-FBI) and viscous damper is the most effective in reducing the bearing displacement without significant increase in superstructure forces.

About the Use of the Floating Frame in the Optimal Control of the Flexible Robot Arm

1992 ◽  
Vol 4 (4) ◽  
pp. 330-338 ◽  
Author(s):  
M. Bisiacco ◽  
◽  
R. Caracciolo ◽  
M. Giovagnoni ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Linear Model ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Robot Arm ◽  
Flexible Robot ◽  
Coupled Equations ◽  
Weakly Coupled ◽  
Tip Position ◽  
The Mathematical Model

The mathematical model of a single-link flexible manipulator is obtained by measuring transverse deflections in a rotating reference frame which is floating with respect to the link. The use of this particular frame, the rigidbody mode frame, enables one to obtain weakly coupled equations of motion. The size of the inertia coupling terms can be easily evaluated: these terms can be shown to be negligible thus leading to an essentially linear model. An example of optimal control of manipulator's tip position is numerically reproduced. The same controller is first applied to the mechanical model of the arm accounting for non-linear coupling and then to the linear model: the two responses are found to be very close to each other.

A Quasi-Vehicle/Bridge Interaction Model for High Speed Railways

2015 ◽  
Vol 31 (2) ◽  
pp. 217-225 ◽  
Author(s):  
J.-D. Yau ◽  
L. Frýba
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Interaction Model ◽  
Time History ◽  
Time Step ◽  
Moving Vehicle ◽  
Coupled Equations ◽  
History Analysis ◽  
High Speed Trains ◽  
Parametric Studies

ABSTRACTVehicle response is served as a reference to evaluate riding comfort of passengers and running safety of moving carriages for high speed trains. In analyzing the vehicle-bridge interaction (VBI) problems, two sets of coupled equations of motion for running vehicles and bridge need to be solved and the VBI system matrices must be updated and factorized at each time step in a time-history analysis. This paper proposed a quasi-VBI model to abridge the complicated computational process, in which the bridge is subjected to only moving static forces of the train loadings, and the moving vehicle over it is excited by the corresponding feedback bridge response. To examine the interacting degree of the vehicle with the bridge, a coupling evaluation index (CEI) is defined as a quantitative assessment of the VBI system. The numerical parametric studies reveal that (1) the mass ratio of vehicle to bridge is the most sensitive parameter affecting the bridge response; (2) increasing bridge damping can reduce the coupling degree of the VBI system at high speeds; (3) the present quasi-VBI model is an efficient and simple tool to predict the vehicle's response with enough accuracy based on engineering approximation.

Seismic Response Evaluation of Buildings Considering Soil Flexibility

2011 ◽  
Vol 243-249 ◽  
pp. 1383-1390 ◽  
Author(s):  
Magdy S. El-Azab ◽  
Sayed Mahmoud ◽  
Ayman Abd-Elhameed
Keyword(s):  
Seismic Response ◽  
Shear Wave ◽  
Equations Of Motion ◽  
Computational Simulation ◽  
Time History ◽  
Velocity Variation ◽  
Peak Response ◽  
Coupled Equations ◽  
Soil Flexibility ◽  
Response Amplification

This research attempts to investigate the effect of soil-structure interaction (SSI) on the seismic response of buildings. Computational simulation of a one storey building having different natural periods is performed using time history analysis. Different earthquake motions with different peak ground accelerations (PGA) levels are used as excitations. The ground motion records have been selected in order to ensure low, moderate, and high PGA levels. Moreover, sandy soil with several values of shear wave velocities is used in order to investigate the sensitivity of the seismic response to the velocity variation. An efficient discrete-element model which represents the rotational and horizontal degrees of freedom of the soil mass is considered in the analysis. The coupled equations of motion for the building model with SSI are presented and solved in incremental form using the Newmark's step by step iteration method. In general, the results of the study in terms of response, peak response and peak response amplification show significant changes in considering and ignoring SSI effect. In particular, the numbers of significant cycles of large response amplitude for the building have been increased due to the inclusion of SSI. Moreover, considering the soil flexibility amplifies the peak response of buildings with low natural periods. Furthermore, it has been found that, shear wave velocity variation shows appreciable changes in the peak dynamic response amplification and seems to be insignificant at high natural periods for all levels of earthquake excitations considered.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

The Simulation Study for Auto Electrical Seat Controller Based on Fuzzy Control Technology

2011 ◽  
Vol 383-390 ◽  
pp. 7328-7331
Author(s):  
Lan Jiang Zhang ◽  
Gui Jie Wang
Keyword(s):  
Control System ◽  
Fuzzy Control ◽  
Effective Means ◽  
Nonlinear Function ◽  
Control Technology ◽  
Highly Nonlinear ◽  
Adjustment System ◽  
The Mathematical Model ◽  
Seat Adjustment ◽  
Controlled Object

Designed the control system policy for automobile electric seat using fuzzy control technology, therefore established its control model by Fuzzy Logic Toolbox, and carried on the off-line simulation to choose controller's optimum control parameters. From the dynamic viewpoint, the auto electric seat adjustment system is not only a complex nonlinear function which includes the location of the DC servo motor and the speed, but also contains serious nonlinear coupling interference, so the system is a highly nonlinear strong coupling, variable multivariable system. Application of traditional control methods (such as traditional PID) is difficult to meet its order requirements, so the research is highly robust method of intelligent control is an effective way to solve the problem. Fuzzy control technology has become the field in which drawn greater attention and researched in recent years. It doesn’t depend on the mathematical model of controlled object, has a good robustness, and nonlinear control characteristics, so it is an effective means to control the object with time-varying, non- linear parameters. In this paper, fuzzy control technology to achieve the orders of auto electric seat adjustment control system functions in the Literature [1], and the tracking of the system was simulated.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

A Seismic Effective Method for Double-Layer Reticulated Shell Using Buckling-Restrained Braces

2010 ◽  
Vol 163-167 ◽  
pp. 2852-2856
Author(s):  
Chang Wu ◽  
Xiu Li Wang
Keyword(s):  
Double Layer ◽  
Seismic Performance ◽  
Linear Time ◽  
Ground Motions ◽  
Equations Of Motion ◽  
Time History ◽  
Original Structure ◽  
Loading Test ◽  
Strong Earthquakes ◽  
Buckling Restrained Braces

In this study a kind of buckling-restrained braces (BRBs) as energy dissipation dampers is attempted for seismic performance of large span double-layer reticulated shell and the effectiveness of BRBs to protect structures against strong earthquakes is numerically studied. The hysteretic curve of such members is obtained through the simulation of the cyclic-loading test, and the equations of motion of the system under earthquake excitations are established. BRBs are then placed at certain locations on the example reticulated shell to replace some normal members, and the damping effect of the two installation schemes of BRBs is investigated by non-linear time-history analyses under various ground motions representing major earthquake events. Compared with the seismic behavior of the original structure without BRBs, satisfactory seismic performance is seen in the upgraded models, which clarifies the BRBs can reduce the vibration response of spatial reticulated structure effectively and the new system has wide space to develop double layer reticulated shell.

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

Tilt-Wing Rotorcraft Dynamic Analysis Using Multibody Formulation

1992 ◽  
Author(s):  
Patrick J. O’Heron ◽  
Parviz E. Nikravesh ◽  
Ara Arabyan ◽  
Donald L. Kunz
Keyword(s):  
Flight Control ◽  
High Speed ◽  
Equations Of Motion ◽  
Flight Path ◽  
Minimal Set ◽  
Near Wake ◽  
Highly Nonlinear ◽  
Nonlinear Transient ◽  
Nonlinear Transient Dynamics ◽  
Rotor Assembly

Abstract A model is presented that can be used to simulate the highly nonlinear transient dynamics associated with advanced rotorcraft conversion processes. Multibody equations of motion of the fuselage, the tilting wing, and the rotor assembly are derived using a minimal set of coordinates. An enhanced aerodynamics model is employed to account for unsteadiness and nonlinearity in the near-wake aerodynamics, with a dynamic uniform inflow to compute the far-wake aerodynamics, and a flight control system is employed to compute the blade pitch settings that are necessary to achieve a desired flight path. The model is subjected to a demanding flight path simulation to illustrate that it can perform vertical take-off, hover, tilt-wing conversion, and high-speed forward flight maneuvers effectively.

Sign in / Sign up

Export Citation Format

Share Document