The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Open-circuit potential-time transient of the magnesium anode

On interrupting polarisation, the magnesium anode exhibits a negative overshoot in potential followed by a slow recovery to a steady state value. A model has been proposed to explain the opencircuit potential-time transient in terms of a spontaneous passivation of the metal and the consequent changes in the corrosion potential. Theoretical expressions have been derived for the timedependence of the open-circuit electrode potential. Calculated, potential-time curves thus obtained are in qualitative agreement with experimental data. A possible application of this phenomenon to develop non-destructive quality control tests of Mg, Li and Al-based dry cells has been pointed out.

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.

Development of a transient gradient enhanced non local continuum damage mechanics model for masonry

Due to the advent of varied types of masonry systems a comprehensive failure mechanism of masonry essential for the understanding of its behaviour is impossible to be determined from experimental testing. As masonry is predominantly used in wall structures a biaxial stress state dominates its failure mechanism. Biaxial testing will therefore be necessary for each type of masonry, which is expensive and time consuming. A computational method would be advantageous; however masonry is complex to model which requires advanced computational modelling methods. This thesis has formulated a damage mechanics inspired modelling method and has shown that the method effectively determines the failure mechanisms and deformation characteristics of masonry under biaxial states of loading.

Time-Domain Measurement of Voltage Induction by Transient EM Fields

An efficient measurement technique for studying the effect of transient electromagnetic fields under controlled conditions has been described. Broad-band TEM fields with a rise-time of a few nanoseconds were generated using a stripline method. Theoretical results are obtained and experimental measurements which confirm these results are described. The work will form the basis for a study of the susceptibility of digital integrated circuits and their interconnections to transient electromagnetic fields.

Transient NEMP Field Coupling With Buried Shielded Cables

The interaction of transient electromagnetic field due to an NEMP with buried cables has been studied in this paper. The cables studied were of two types: shielded as well as unshielded cables. Using transmission line analysis, the induced voltage and current are computed at the load end of the cable for different soil conductivities, different depths of burial of cable and for different lengths of the cable. Effect of shielding on the induced voltage on the cable inner conductor as well as the dependence of the induced voltage on the shield thickness are also studied.

Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Transient response of nonlinear magneto-optic rotation in a paraffin-coated Rb vapor cell

We study resonant nonlinear magneto-optic rotation (NMOR) in a paraffin-coated Rb vapor cell as the magnetic field is swept. At low sweep rates, the nonlinear rotation appears as a narrow resonance signal with a linewidth of about ``300 mu G''(2 pi x 420 Hz). At high sweep rates, the signal shows transient response with an oscillatory decay. The decay time constant is of order 100 ms. The behavior is different for transitions starting from the lower or the upper hyperfine level of the ground state because of optical pumping effects.

Support vector machine approach for the switching transient peak overvoltages during line energization

At the time of restoration transmission line switching is one of the major causes, which creates transient overvoltages. Though detailed Electro Magnetic Transient studies are carried out extensively for the planning and design of transmission systems, such studies are not common in a day-today operation of power systems. However it is important for the operator to ensure during restoration of supply that peak overvoltages resulting from the switching operations are well within safe limits. This paper presents a support vector machine approach to classify the various cases of line energization in the category of safe or unsafe based upon the peak value of overvoltage at the receiving end of line. Operator can define the threshold value of voltage to assign the data pattern in either of the class. For illustration of proposed approach the power system used for switching transient peak overvoltages tests is a 400 kV equivalent system of an Indian southern gri

Fracture analysis of stiffened panels under combined tensile, bending, and shear loads

The objective is to present the formulation of numerically integrated modified virtual crack closure integral technique for concentrically and eccentrically stiffened panels for computation of strain-energy release rate and stress intensity factor based on linear elastic fracture mechanics principles. Fracture analysis of cracked stiffened panels under combined tensile, bending, and shear loads has been conducted by employing the stiffened plate/shell finite element model, MQL9S2. This model can be used to analyze plates with arbitrarily located concentric/eccentric stiffeners, without increasing the total number of degrees of freedom, of the plate element. Parametric studies on fracture analysis of stiffened plates under combined tensile and moment loads have been conducted. Based on the results of parametric,studies, polynomial curve fitting has been carried out to get best-fit equations corresponding to each of the stiffener positions. These equations can be used for computation of stress intensity factor for cracked stiffened plates subjected to tensile and moment loads for a given plate size, stiffener configuration, and stiffener position without conducting finite element analysis.

Frequency characteristics of very fast transient currents in a 245-kV GIS

The conducted as well as the induced voltages on control cables and control circuits due to transient electromagnetic (EM) fields generated during switching operations in a gas-insulated substation (GIS) depend on the waveshape of the very fast transient overvoltages and the associated very-fast transient currents (VFTCs). The aim of this paper is to build a basis for characterizing the VFTC generated in gas-insulated switchgear and the,associated equipment during switching operations for the study of transient coupling phenomena. The peak magnitudes of VFTC and their dominant frequency content at various locations have been computed in a 245-kV GIS for different switching operations as well as substation configurations. Finally, the influence of the substation layout on the frequency spectrum, dominant frequencies, and the highest possible frequency component of the VFTC at various distances from the switch have been reported.

Response spectrum of non-linear spring mass system subjected to transient disturbances

The transient response spectrum of a cubic spring mass system subjected to a step function input is obtained. An approximate method is adopted where non-linear restoring force characteristic is replaced by two linear segments, so that the mean square error between them is a minimum. The effect of viscous damping on the peak response is also discussed for various values of the damping constant and the non-linearity restoring force parameter.

Some transient characteristics of electrically heated tungsten filaments

Temperature-time characteristics of tungsten filaments heated electrically under constant voltage in vacuum have been analysed. The analysis is carried out over the temperature range 300-2500°K, taking into account the actual variations with temperature of the various parameters involved, as reported by Jones and Langmuir (1927). The analysis leads to the conclusion that the temperature-time relationship is exponential throughout the range. The time constant is shown to be proportional to the diameter of the filament and T f-4.2 where Tf is the final temperature of the filament. The results of the analysis are applied to derive the voltage variations (continuous and discrete types) required to keep the transient current within specified limits during the rapid switching on of filaments as met with in high power thermionic valves.

Microcracking in concrete under repeated compressive loads

The nature of microcracks formed in concrete under repeated uniaxial compressive loads are investigated by experiments on prismatic specimens. The distribution and orientation of cracks formed are studied by optical microscopic techniques. The basic failure mechanism of concrete at the phenomenological and internal structural level are examined by the formation and propagation of cracks. The tests have indicated that local tensile failures constitute the dominant mode of fracture, with the bond cracks forming the major percentage of the total magnitude of cracks. Significant differences were observed in the proportion of bond cracks formed under static and repeated load systems.