Browsing by Subject "Stability Analysis"
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Item Issues in autonomous mobile sensor networks(2009-05-15) Dharne, Avinash GopalAutonomous mobile sensor networks consist of a number of autonomous mobile robots equipped with various sensors and tasked with a common mission. This thesis considers the topology control of such an ad hoc mobile sensor network. In particular, I studied the problem of controlling the size, with respect to a distance metric, of the network for general interactive forcing among agents. Developed is a stability result, allowing one to design force laws to control the spread of the network. Many of the current results assume a known and/or fixed topology of the graph representing the communication between the nodes, i.e. the graph laplacian is assumed constant. They also assume fixed and known force-laws. Hence, the results are limited to time-invariant dynamics. The research considers stability analysis of sensor networks, unconstrained by specific forcing functions or algorithms, and communication topologies. Since the graph topologies are allowed to change as the agents move about, the system dynamics become discontinuous in nature. Filippov?s calculus of differential equations with discontinuous right hand sides is used to formally characterize the multi-agent system with the above attributes. Lyapunov?s Stability Theory, applied to discontinuous systems, is then used to derive bounds on the norm of the system states given bounds on its initial states and input. The above derived stability results lend themselves to the derivation of methods for the design of algorithms or force-laws for mobile sensor networks. The efficacy of the derived results is illustrated through several examples where it is shown how they may be used for synthesizing a topology managing strategy. Examples are given of designing force-laws that limit the network in a desired area.Item Magneto-Thermo-Mechanical Coupling, Stability Analysis and Phenomenological Constitutive Modeling of Magnetic Shape Memory Alloys(2012-12-06) Haldar, Krishnendu 1978-Magnetic shape memory alloys (MSMAs) are a class of active materials that de- form under magnetic and mechanical loading conditions. This work is concerned with the modeling of MSMAs constitutive responses. The hysteretic magneto-mechanical responses of such materials are governed by two major mechanisms which are variant reorientation and field induced phase transformation (FIPT). The most widely used material for variant reorientation is Ni2 MnGa which can produce up to 6% magnetic field induced strain (MFIS) under 5 MPa actuation stress. The major drawback of this material is a low blocking stress, which is overcome in the NiMnCoIn material system through FIPT. This magnetic alloy can exhibit 5% MFIS under 125 MPa actuation stress. The focus of this work is to capture the key magneto-thermo-mechanical responses of such mechanisms through phenomenological modeling. In this work a detailed thermodynamic framework for the electromagnetic interaction within a continuum solid is presented. A Gibbs free energy function is postulated after identifying the external and internal state variables. Material symmetry restrictions are imposed on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals whereas continuous symmetry is considered for polycrystalline materials. The constitutive equations are derived in a thermodynamically consistent way. A specific form of Gibbs free energy for FIPT is proposed and the explicit form of the constitutive equations is derived from the generalized formulation. The model is calibrated from experimental data and different predictions of magneto-thermo-mechanical loading conditions are presented. The generalized constitutive equations are then reduced to capture variant reorientation. A coupled magneto-mechanical boundary value problem (BVP) is solved that accounts for variant reorientation to investigate the influence of the demagnetization effect on the magnetic field and the effect of Maxwell stress on the Cauchy stress. The BVP, which mimics a real experiment, provides a methodology to correlate the difference between the externally measured magnetic data and internal magnetic field of the specimen due to the demagnetization effect. The numerical results show that localization zones appear inside the material between a certain ranges of applied magnetic field. Stability analysis is performed for variant reorientation to analyze these numerical observations. Detailed numerical and analytical analysis is presented to investigate these localization zones. Magnetostatic stability analysis reveals that the MSMA material system becomes unstable when localizations appear due to non-linear magnetization response. Coupled magneto-mechanical stability analysis shows that magnetically induced localization creates stress-localizations in the unstable zones. A parametric study is performed to show the constraints on material parameters for stable and unstable material responses.