scholarly journals Complex interplay between stress perturbations and viscoelastic relaxation in a two-asperity fault model

2017 ◽  
Author(s):  
Emanuele Lorenzano ◽  
Michele Dragoni
Keyword(s):  
Degrees Of Freedom ◽  
Discrete Dynamical System ◽  
The State ◽  
Viscoelastic Relaxation ◽  
State Variables ◽  
Simple Correlation ◽  
Complex Interplay ◽  
Viscoelastic Deformation ◽  
Tectonic Loading ◽  
Three Degrees Of Freedom

Abstract. We consider a plane fault with two asperities embedded in a shear zone, subject to a uniform strain rate owing to tectonic loading. After an earthquake, the static stress field is relaxed by viscoelastic deformation. We treat the fault as a discrete dynamical system with three degrees of freedom: the slip deficits of the asperities and the variation of their difference due to viscoelastic deformation. The dynamics of the system is described in terms of one sticking mode and three slipping modes. We consider the effect of stress transfers connected to earthquakes produced by neighbouring faults. The perturbation is studied in terms of a vector in the state space, whose components are the changes in the state variables of the system. The interplay between the stress perturbation and the viscoelastic relaxation significantly complicates the evolution of the fault and its seismic activity. We show that the presence of viscoelastic relaxation prevents any simple correlation between the change of Coulomb stresses on the asperities and the anticipation or delay of their failures. As an application, we study the effects of the 1999 Hector Mine, California, earthquake on the post-seismic evolution of the fault that generated the 1992 Landers, California, earthquake, which we model as a two-mode event associated with the consecutive failure of two asperities.

scholarly journals Complex interplay between stress perturbations and viscoelastic relaxation in a two-asperity fault model

2018 ◽  
Vol 25 (1) ◽  
pp. 251-265
Author(s):  
Emanuele Lorenzano ◽  
Michele Dragoni
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Discrete Dynamical System ◽  
Fault Model ◽  
Viscoelastic Relaxation ◽  
Simple Correlation ◽  
Complex Interplay ◽  
Viscoelastic Deformation ◽  
Single Asperity ◽  
Tectonic Loading

Abstract. We consider a plane fault with two asperities embedded in a shear zone, subject to a uniform strain rate owing to tectonic loading. After an earthquake, the static stress field is relaxed by viscoelastic deformation in the asthenosphere. We treat the fault as a discrete dynamical system with 3 degrees of freedom: the slip deficits of the asperities and the variation of their difference due to viscoelastic deformation. The evolution of the fault is described in terms of inter-seismic intervals and slip episodes, which may involve the slip of a single asperity or both. We consider the effect of stress transfers connected to earthquakes produced by neighbouring faults. The perturbation alters the slip deficits of both asperities and the stress redistribution on the fault associated with viscoelastic relaxation. The interplay between the stress perturbation and the viscoelastic relaxation significantly complicates the evolution of the fault and its seismic activity. We show that the presence of viscoelastic relaxation prevents any simple correlation between the change of Coulomb stresses on the asperities and the anticipation or delay of their failures. As an application, we study the effects of the 1999 Hector Mine, California, earthquake on the post-seismic evolution of the fault that generated the 1992 Landers, California, earthquake, which we model as a two-mode event associated with the consecutive failure of two asperities.

scholarly journals Factors controlling the sequence of asperity failures in a fault model

2018 ◽  
Author(s):  
Emanuele Lorenzano ◽  
Michele Dragoni
Keyword(s):  
Degrees Of Freedom ◽  
Seismic Event ◽  
Frictional Resistance ◽  
Fault Model ◽  
Seismic Events ◽  
Viscoelastic Relaxation ◽  
Viscoelastic Deformation ◽  
Tectonic Loading ◽  
The Difference ◽  
Three Degrees Of Freedom

Abstract. We consider a fault with two asperities embedded in a shear zone subject to a uniform strain rate owing to tectonic loading. The static stress field generated by seismic events undergoes viscoelastic relaxation as a consequence of the rheological properties of the asthenosphere. We treat the fault as a dynamical system whose basic elements are the asperities. The system has three degrees of freedom: the slip deficits of the asperities and the variation of their difference due to viscoelastic deformation. The dynamics of the system can be described in terms of one sticking mode and three slipping modes, for which we provide analytical solutions. We discuss how the stress state at the beginning of the interseismic interval preceding a seismic event controls the sequence of slipping modes during the event. We focus on the events associated with the separate (consecutive) slips of the asperities and investigate how they are affected by the seismic efficiency of the fault, by the difference in frictional resistance of the asperities and by the intensity of coupling between the asperities.

scholarly journals Stress states and moment rates of a two-asperity fault in the presence of viscoelastic relaxation

2015 ◽  
Vol 2 (1) ◽  
pp. 297-327
Author(s):  
M. Dragoni ◽  
E. Lorenzano
Keyword(s):  
Discrete Dynamical System ◽  
Constant Strain Rate ◽  
The State ◽  
Viscoelastic Deformation ◽  
Initial State ◽  
Tectonic Plates ◽  
Stress States ◽  
The Moment ◽  
Postseismic Relaxation ◽  
The Relationship

Abstract. A fault containing two asperities with different strengths is considered. The fault is embedded in a viscoelastic shear zone, subject to a constant strain rate by the motions of adjacent tectonic plates. The fault is modelled as a discrete dynamical system where the average values of stress, friction and slip on each asperity are considered. The state of the fault is described by three variables: the slip deficits of the asperities and the viscoelastic deformation. The system has four dynamic modes, for which the analytical solutions are calculated. The relationship between the state of the fault before a seismic event and the sequence of slipping modes in the event is enlightened. Since the moment rate depends on the number and sequence of slipping modes, the knowledge of the source function of an earthquake constrains the orbit of the system in the phase space. If the source functions of a larger number of consecutive earthquakes were known, the orbit could be constrained more and more and its evolution could be predicted with a smaller uncertainty. The model is applied to the 1964 Alaska earthquake, which was the effect of the failure of two asperities and for which a remarkable postseismic relaxation has been observed in the subsequent decades. The evolution of the system after the 1964 event depends on the state from which the event was originated, that is constrained by the observed moment rate. The possible durations of the interseismic interval and the possible moment rates of the next earthquake are calculated as functions of the initial state.

A Method for Solving Large-Scale Multiloop Constrained Dynamical Systems Using Structural Decomposition

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Tao Xiong ◽  
Jianwan Ding ◽  
Yizhong Wu ◽  
Liping Chen ◽  
Wenjie Hou
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
The State ◽  
State Variables ◽  
Structural Decomposition ◽  
Multiple Degrees Of Freedom ◽  
Constraint Equations ◽  
Constrained Dynamical Systems ◽  
Algebraic Constraint

A structural decomposition method based on symbol operation for solving differential algebraic equations (DAEs) is developed. Constrained dynamical systems are represented in terms of DAEs. State-space methods are universal for solving DAEs in general forms, but for complex systems with multiple degrees-of-freedom, these methods will become difficult and time consuming because they involve detecting Jacobian singularities and reselecting the state variables. Therefore, we adopted a strategy of dividing and conquering. A large-scale system with multiple degrees-of-freedom can be divided into several subsystems based on the topology. Next, the problem of selecting all of the state variables from the whole system can be transformed into selecting one or several from each subsystem successively. At the same time, Jacobian singularities can also be easily detected in each subsystem. To decompose the original dynamical system completely, as the algebraic constraint equations are underdetermined, we proposed a principle of minimum variable reference degree to achieve the bipartite matching. Subsequently, the subsystems are determined by aggregating the strongly connected components in the algebraic constraint equations. After that determination, the free variables remain; therefore, a merging algorithm is proposed to allocate these variables into each subsystem optimally. Several examples are given to show that the proposed method is not only easy to implement but also efficient.

Trajectory Control of an Automated Guided Vehicle Using Feedback Linearization

2006 ◽  
Author(s):  
S. M. Mehdi Ansarey M. ◽  
M. J. Mahjoob
Keyword(s):  
Control System ◽  
Feedback Linearization ◽  
Degrees Of Freedom ◽  
Automated Guided Vehicle ◽  
State Variables ◽  
Discrete Curvatures ◽  
Steering Mechanism ◽  
Dynamics And Control ◽  
And Control ◽  
Three Degrees Of Freedom

In this paper, the dynamics and control of an automated guided vehicle (AGV) is described. The objective is to control the vehicle direction and location with respect to a prescribed trajectory. This is accomplished based on an optimum control strategy using vehicle state variables. A four-wheel vehicle with three degrees of freedom including longitudinal, lateral and yaw motion is considered. The nonlinearity of the tire and steering mechanism is also included. The control system design for circular, straight forward and composite path is presented based on feedback linearization. Some trajectory simulation for discrete curvatures is carried out. The controller was implemented within MATLAB environment. The design was also evaluated using ADAMS full vehicle assembly. The results demonstrated the accuracy of the model and the effectiveness of the developed control system.

Nonlinear Observers for Constrained Systems

2009 ◽  
Author(s):  
Giscard A. Kfoury ◽  
Nabil G. Chalhoub
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
The State ◽  
Constrained Systems ◽  
State Variables ◽  
Nonlinear Observers ◽  
Constraint Equations ◽  
Single Cylinder Engine ◽  
Robust Observers ◽  
Selection Of

Three procedures for designing robust observers to estimate the state variables of nonlinear constrained systems have been developed in this work. All observers are based on the sliding mode methodology and assume that the number of transducers matches that of the degrees of freedom of the system. The conceptual differences between the proposed observer designs are in the number and selection of the sliding surfaces along with the formulations pertaining to their nominal models. The observers have been applied to estimate the state variables of a crank-slider mechanism of a single cylinder engine. The simulation results demonstrate the capabilities of the observers in accurately estimating the state variables of the system, including the superfluous ones, in the presence of significant structured and unstructured uncertainties. In addition, the results show that the nominal constraint equations are satisfied by the estimated state variables.

Modeling and Predictive Control of an Unmanned Underwater Vehicle

2019 ◽  
Author(s):  
Renato Rodriguez Nunez ◽  
Damoon Soudbakhsh
Keyword(s):  
Feedback Linearization ◽  
Degrees Of Freedom ◽  
Travel Speed ◽  
The State ◽  
Operating Conditions ◽  
State Variables ◽  
Unmanned Underwater Vehicles ◽  
Six Degrees Of Freedom ◽  
State Space System ◽  
Predictive Controller

Abstract This paper presents a model and optimal controller for Unmanned Underwater Vehicles (UUVs). We present a nonlinear six degrees of freedom model of the UUV that includes hydrodynamic and hydrostatic terms. To design the controller, we simplify the model using the geometry of the UUV as well as its operating conditions such as the depth and expected travel speed. Instead of designing a controller for the state space system, we used feedback linearization technique to decouple the motions. Then, a set of controllers were designed for each motion. To incorporate the constraints on the input and the state variables, we designed a fast Model Predictive Controller (MPC) for the UUV and compared its performance with a conventional controller.

scholarly journals Stress states and moment rates of a two-asperity fault in the presence of viscoelastic relaxation

2015 ◽  
Vol 22 (3) ◽  
pp. 349-359 ◽  
Author(s):  
M. Dragoni ◽  
E. Lorenzano
Keyword(s):  
Discrete Dynamical System ◽  
Constant Strain Rate ◽  
The State ◽  
Viscoelastic Deformation ◽  
Initial State ◽  
Tectonic Plates ◽  
Stress States ◽  
The Moment ◽  
The Relationship ◽  
1964 Alaska

Abstract. A fault containing two asperities with different strengths is considered. The fault is embedded in a shear zone subject to a constant strain rate by the motions of adjacent tectonic plates. The fault is modelled as a discrete dynamical system where the average values of stress, friction and slip on each asperity are considered. The state of the fault is described by three variables: the slip deficits of the asperities and the viscoelastic deformation. The system has four dynamic modes, for which analytical solutions are calculated. The relationship between the state of the fault before a seismic event and the sequence of slipping modes in the event is enlightened. Since the moment rate depends on the number and sequence of slipping modes, the knowledge of the source function of an earthquake constrains the orbit of the system in the phase space. If the source functions of a larger number of consecutive earthquakes were known, the orbit could be constrained more and more and its evolution could be predicted with a smaller uncertainty. The model is applied to the 1964 Alaska earthquake, which was the effect of the failure of two asperities and for which a remarkable post-seismic relaxation has been observed in the subsequent decades. The evolution of the system after the 1964 event depends on the state from which the event was originated, that is constrained by the observed moment rate. The possible durations of the interseismic interval and the possible moment rates of the next earthquake are calculated as functions of the initial state.

Observability, Reconstructibility and Observer Design for Linear Mechanical Systems Unobservable in Absence of Impacts†

2003 ◽  
Vol 125 (4) ◽  
pp. 549-562 ◽  
Author(s):  
Francesco Martinelli ◽  
Laura Menini ◽  
Antonio Tornambe`
Keyword(s):  
Structural Properties ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
The State ◽  
Observer Design ◽  
State Variables ◽  
Multiple Degrees Of Freedom ◽  
Position Variable

This paper deals with a class of mechanical systems, constituted by two composite bodies which interact with each other only during collisions: since only one position variable of only one body is measured, the whole system would not be observable without impacts. Each body is possibly constituted by several masses connected by linear springs, so that the internal deformations can be taken into account (the so-called multiple-degrees-of-freedom impacts). For two relevant and different cases, the structural properties of observability and reconstructibility are studied, and observers are proposed in order to estimate all the state variables, including those that would be unobservable in absence of impacts.

Parametric study and sensitivity analysis of automated vehicles

Robotica ◽  
1995 ◽  
Vol 13 (5) ◽  
pp. 469-475
Author(s):  
M. G. Mehrabi ◽  
R. M. H. Cheng ◽  
A. Hemam
Keyword(s):  
Parametric Study ◽  
Degrees Of Freedom ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Kinematic Parameters ◽  
Automated Vehicles ◽  
State Response ◽  
Sensitivity Theory ◽  
Stiffness And Damping

SummaryThis paper presents a parametric study of automated vehicles using the sensitivity theory. A sixth order dynamic model of an axisymmetric vehicle is developed in the state space format to represent its 3 degrees-of-freedom motion in the lateral, yaw and roll modes. Variations of the important parameters of the vehicle are grouped into three separate vectors: with the elements consisting of inertia, stiffness and damping, and geometric-kinematic parameters respectively. The effect of every element of these vectors on the state variables is studied carefully, a comparison being made among the state variables to reveal the relative influence of the parameter-induced variations. This helps better understanding which mode of the system is more affected by changes in particular parameters and the severity in the transient response and in the steady-state response. Then the effects of a particular vector on the performance of the system is studied.

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