The dynamic stability of degenerate systems under parametric excitation

The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

On a generalized dynamic model of bi-state social interaction processes

A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed in this study. The feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non-linear model and a higher order linear model.

Automatic Path Planning and Control Design for Autonomous Landing of UAVs using Dynamic Inversion

In this paper a nonlinear control has been designed using the dynamic inversion approach for automatic landing of unmanned aerial vehicles (UAVs), along with associated path planning. This is a difficult problem because of light weight of UAVs and strong coupling between longitudinal and lateral modes. The landing maneuver of the UAV is divided into approach, glideslope and flare. In the approach UAV aligns with the centerline of the runway by heading angle correction. In glideslope and flare the UAV follows straight line and exponential curves respectively in the pitch plane with no lateral deviations. The glideslope and flare path are scheduled as a function of approach distance from runway. The trajectory parameters are calculated such that the sink rate at touchdown remains within specified bounds. It is also ensured that the transition from the glideslope to flare path is smooth by ensuring C-1 continuity at the transition. In the outer loop, the roll rate command is generated by assuring a coordinated turn in the alignment segment and by assuring zero bank angle in the glideslope and flare segments. The pitch rate command is generated from the error in altitude to control the deviations from the landing trajectory. The yaw rate command is generated from the required heading correction. In the inner loop, the aileron, elevator and rudder deflections are computed together to track the required body rate commands. Moreover, it is also ensured that the forward velocity of the UAV at the touch down remains close to a desired value by manipulating the thrust of the vehicle. A nonlinear six-DOF model, which has been developed from extensive wind-tunnel testing, is used both for control design as well as to validate it.

Dynamic viscosity of ternary mixtures of dichlorodifluoromethane (R-12), chlorodifluoromethane (R-22), and dichlorotetrafluoroethane (R-114) vapors

The viscosities of ternary mixtures of R-12, R-22, and R-114 vapors were determined at ambient temperature and pressure within +-1% by using an oscillating disk viscometer. The empirical viscosity obtained by Wllke's equation compares very well with the experimental results obtained with this vlscometer. In the case of this ternary vapor mixture, as long as the molar fraction ratio of R-12 to R-114 Is maintained at approximately 2"' (=Inverse ratio of thelr molecular weights) the viscosity of the ternary mixture at ambient temperature and pressure remalns constant irrespective of the percentage of R-22 present in the mixture.

Dynamic pressure modulation for solar desalination system

Obtaining drinking water from seawater is usually done through the process of desalination. The conventional desalination processes at present are centralized, require huge capital cost, and enormous amount of concentrated energy from fossil fuel. Issues like optimal chamber pressure, pressure control and energy savings for desalination are not adequately addressed. This paper proposes a novel pressure control method by means of dynamic pressure modulation within the evaporation chamber. A performance index is proposed that results in a dynamic optimal external pressure and maximum energy saving for a specific flow rate. Experimental results from the laboratory setup that validate the proposed concepts are presented in the paper. (C) 2009 Elsevier B.V. All rights reserved.

Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography

Purpose: A computationally efficient algorithm (linear iterative type) based on singular value decomposition (SVD) of the Jacobian has been developed that can be used in rapid dynamic near-infrared (NIR) diffuse optical tomography. Methods: Numerical and experimental studies have been conducted to prove the computational efficacy of this SVD-based algorithm over conventional optical image reconstruction algorithms. Results: These studies indicate that the performance of linear iterative algorithms in terms of contrast recovery (quantitation of optical images) is better compared to nonlinear iterative (conventional) algorithms, provided the initial guess is close to the actual solution. The nonlinear algorithms can provide better quality images compared to the linear iterative type algorithms. Moreover, the analytical and numerical equivalence of the SVD-based algorithm to linear iterative algorithms was also established as a part of this work. It is also demonstrated that the SVD-based image reconstruction typically requires O(NN2) operations per iteration, as contrasted with linear and nonlinear iterative methods that, respectively, requir O(NN3) and O(NN6) operations, with ``NN'' being the number of unknown parameters in the optical image reconstruction procedure. Conclusions: This SVD-based computationally efficient algorithm can make the integration of image reconstruction procedure with the data acquisition feasible, in turn making the rapid dynamic NIR tomography viable in the clinic to continuously monitor hemodynamic changes in the tissue pathophysiology.

Compact fiber Bragg grating dynamic strain sensor cum broadband thermometer for thermally unstable ambience

An instrument for simultaneous measurement of dynamic strain and temperature in a thermally unstable ambience has been proposed, based on fiber Bragg grating technology. The instrument can function as a compact and stand-alone broadband thermometer and a dynamic strain gauge. It employs a source wavelength tracking procedure for linear dependence of the output on the measurand, offering high dynamic range. Two schemes have been demonstrated with their relative merits. As a thermometer, the present instrumental configuration can offer a linear response in excess of 500 degrees C that can be easily extended by adding a suitable grating and source without any alteration in the procedure. Temperature sensitivity is about 0.06 degrees C for a bandwidth of 1 Hz. For the current grating, the upper limit of strain measurement is about 150 mu epsilon with a sensitivity of about 80 n epsilon Hz(-1/2). The major source of uncertainty associated with dynamic strain measurement is the laser source intensity noise, which is of broad spectral band. A low noise source device or the use of optical power regulators can offer improved performance. The total harmonic distortion is less than 0.5% up to about 50 mu epsilon, 1.2% at 100 mu epsilon and about 2.3% at 150 mu epsilon. Calibrated results of temperature and strain measurement with the instrument have been presented. Traces of ultrasound signals recorded by the system at 200 kHz, in an ambience of 100-200 degrees C temperature fluctuation, have been included. Also, the vibration spectrum and engine temperature of a running internal combustion engine has been recorded as a realistic application of the system.

On-line Dynamic Security Assessment: Determination of Critical Transmission Lines

The main objective of on-line dynamic security assessment is to take preventive action if required or decide remedial action if a contingency actually occurs. Stability limits are obtained for different contingencies. The mode of instability is one of the outputs of dynamic security analysis. When a power system becomes unstable, it splits initially into two groups of generators, and there is a unique cutset in the transmission network known as critical cutset across which the angles become unbounded. The knowledge of critical cutset is additional information obtained from dynamic security assessment, which can be used for initiating preventive control actions, deciding emergency control actions, and adaptive out-of-step relaying. In this article, an analytical technique for the fast prediction of the critical cutset by system simulation for a short duration is presented. Case studies on the New England ten-generator system are presented. The article also suggests the applications of the identification of critical cutsets.

Effect of recrystallization and grain growth on the mechanical properties of an extruded AZ21 Mg alloy

An experimental investigation into the effect of microstructural changes, which occur during post-extrusion annealing of a Mg based AZ21 alloy, on tensile and fatigue properties is conducted. Mechanical properties in the as-cast, as-extruded, and microstructural states that correspond to recovery, recrystallization and grain growth stages of annealing are compared. Results show that these microstructural changes do not alter the yield strength of the alloy markedly whereas significant differences were noted in the ultimate tensile strength as well as ductility. The initiation of abnormal grain growth (or secondary recrystallization) renders the tensile stress-strain response elastic perfectly plastic and results in a large drop in ductility, as high as similar to 60% during intermediate stages of abnormal grain growth, vis-A-vis the ductility of the as-extruded alloy. While the fatigue performance of all the wrought alloys is far superior to as expected, abnormal grain growth leads to a marked decrease in the endurance that of the as-cast alloy, limit. Possible microscopic origins of these are discussed. (C) 2009 Elsevier B.V. All rights reserved.

A Kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data

The problem of identification of stiffness, mass and damping properties of linear structural systems, based on multiple sets of measurement data originating from static and dynamic tests is considered. A strategy, within the framework of Kalman filter based dynamic state estimation, is proposed to tackle this problem. The static tests consists of measurement of response of the structure to slowly moving loads, and to static loads whose magnitude are varied incrementally; the dynamic tests involve measurement of a few elements of the frequency response function (FRF) matrix. These measurements are taken to be contaminated by additive Gaussian noise. An artificial independent variable τ, that simultaneously parameterizes the point of application of the moving load, the magnitude of the incrementally varied static load and the driving frequency in the FRFs, is introduced. The state vector is taken to consist of system parameters to be identified. The fact that these parameters are independent of the variable τ is taken to constitute the set of ‘process’ equations. The measurement equations are derived based on the mechanics of the problem and, quantities, such as displacements and/or strains, are taken to be measured. A recursive algorithm that employs a linearization strategy based on Neumann’s expansion of structural static and dynamic stiffness matrices, and, which provides posterior estimates of the mean and covariance of the unknown system parameters, is developed. The satisfactory performance of the proposed approach is illustrated by considering the problem of the identification of the dynamic properties of an inhomogeneous beam and the axial rigidities of members of a truss structure.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

Seismic damage estimation through measurable dynamic characteristics

Ductility based design of reinforced concrete structures implicitly assumes certain damage under the action of a design basis earthquake. The damage undergone by a structure needs to be quantified, so as to assess the post-seismic reparability and functionality of the structure. The paper presents an analytical method of quantification and location of seismic damage, through system identification methods. It may be noted that soft ground storied buildings are the major casualties in any earthquake and hence the example structure is a soft or weak first storied one, whose seismic response and temporal variation of damage are computed using a non-linear dynamic analysis program (IDARC) and compared with a normal structure. Time period based damage identification model is used and suitably calibrated with classic damage models. Regenerated stiffness of the three degrees of freedom model (for the three storied frame) is used to locate the damage, both on-line as well as after the seismic event. Multi resolution analysis using wavelets is also used for localized damage identification for soft storey columns.

A dynamic renormalization group study of active nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally irrelevant. We discover a special limit of parameters in which the equation of motion for the angle field bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterparts.

Dynamic simulation of activated sludge based wastewater treatment processes: Case studies with Titagarh Sewage Treatment Plant, India

STOAT has been extensively used for the dynamic simulation of an activated sludge based wastewater treatment plant in the Titagarh Sewage Treatment Plant, near Kolkata, India. Some alternative schemes were suggested. Different schemes were compared for the removal of Total Suspended Solids (TSS), b-COD, ammonia, nitrates etc. A combination of IAWQ#1 module with the Takacs module gave best results for the existing scenarios of the Titagarh Sewage Treatment Plant. The modified Bardenpho process was found most effective for reducing the mean b-COD level to as low as 31.4 mg/l, while the mean TSS level was as high as 100.98 mg/l as compared to the mean levels of TSS (92 62 mg/l) and b-COD (92.0 mg/l) in the existing plant. Scheme 2 gave a better scenario for the mean TSS level bringing it down to a mean value of 0.4 mg/l, but a higher mean value for the b-COD level at 54.89 mg/l. The Scheme Final could reduce the mean TSS level to 2.9 mg/l and the mean b-COD level to as low as 38.8 mg/l. The Final Scheme looks to be a technically viable scheme with respect to the overall effluent quality for the plant. (C) 2009 Elsevier B.V. All rights reserved.