Kartik Venkatraman

A numerical technique to predict periodic and quasi-periodic response of nonlinear dynamic systems

A frequency domain based algorithm using Fourier approximation and Galerkin error minimization has been used to obtain the periodic orbits of large order nonlinear dynamic systems. The stability of these periodic response is determined through a bifurcation analysis using Floquet theory. This technique is applicable to dynamic systems having both analytic and nonanalytic nonlinearities. This technique is compared with numerical time integration and is found to be much faster in predicting the steady state periodic response.

Dynamics of Flexible Structures With Nonlinear Joints

The focus of the present study is to use a technique based on Fourier approximation and Galerkin error minimization to determine periodic solutions of nonlinear jointed flexible structures, and study the effect of joint nonlinearity on the global dynamics of an otherwise linear flexible structure. Results presented here show that the Fourier-Galerkin algorithm is a fast tool for computing periodic motion of nonlinear dynamic systems as compared to time-integration, and the effect of nonlinear joints on the dynamics of an otherwise linear flexible structure modeled as a multi degree of freedom system can be significant.

Period-doubling phenomenon observed in the dynamic stall vortex patterns

Dynamic stall is a nonlinear unsteady aerodynamic phenomenon resulting in stall delay during the time dependent movement of an airfoil at angles of attack higher than its static stall angle. This is observed during helicopter forward flights, rapid pitching of fighter aircraft, or in turbine rotor blades, and so on. The most important features of the flowfield are the leading and trailing edge vortex structures. Their growth, evolution, subsequent shedding into the outer field, and their mutual interactions influence aerodynamic loads significantly during the dynamic stall process. Various past and recent studies have been dedicated to visualizing the vorticity flowfield as system parameters are varied, experimentally and numerically. One of the earlier studies on dynamic stall was reported by McCroskey et al. [1]. The influence of various airfoil profiles and leading edge geometries was investigated. Experimental investigations on rapidly pitching airfoils was reported by Walker et al. [2]. Numerical simulations for a rapidly pitching airfoil with a compressible flow model were presented by Visbal and Shang [3] and Visbal [4]. Numerical simulations for a sinusoidally pitching airfoil were taken up by Tuncer et al. [5]. The effect of reduced frequency, albeit in a low range of variation, was highlighted. Ohmi et al. [6] presented experimental as well as numerical simulation results for a sinusoidally oscillating airfoil. Among other parameters like the Reynolds number, mean angle of attack, and elastic axis, reduced frequency was found to be the most significant one. Akbari and Price [7] have also investigated a similar parametric variation in a sinusoidally oscillating airfoil, though at lower range of reduced frequencies.

Molecular dynamic simulations of elastomer structure and its influence on anisotropic stress under time-varying strain

We investigate the evolution of polymer structure and its influence on uniaxial anisotropic stress under time-varying uniaxial strain, and the role of external control variables such as temperature, strain rate, chain length, and density, using molecular dynamics simulation. At temperatures higher than glass transition, stress anisotropy in the system is reduced even though the bond stretch is greater at higher temperatures. There is a significant increase in the stress level with increasing density. At higher densities, the uncoiling of the chains is suppressed and the major contribution to the deformation is by internal deformation of the chains. At faster rates of loading stress anisotropy increases. The deformation mechanism is mostly due to bond stretch and bond bending rather than overall shape and size. Stress levels increase with longer chain length. There is a critical value of the functionality of the cross-linkers beyond which the uniaxial stress developed increases caused primarily by bond stretching due to increased constraint on the motion of the monomers. Stacking of the chains in the system also plays a dominant role in the behaviour in terms of excluded volume interactions. Low density, high temperature, low values of functionality of cross-linkers, and short chain length facilitate chain uncoiling and chain slipping in cross-linked polymers.

Dielectric barrier discharge plasma interaction with the airflow over an airfoil

The effect of various parameters on the velocity of the induced jet produced by a dielectric barrier discharge (DBD) plasma was studied experimentally. The glow discharge was created at atmospheric conditions by using a high voltage RF power supply. Flow visualization and photographic studies of the plasma were performed. The parametric investigation of the characteristics of the plasma show that the width of the plasma in the uniform glow discharge regime was an indication of the velocity induced under stagnant conditions. It was observed that the spanwise overlap of the two electrodes, dielectric thickness, voltage and frequency of the applied voltage are the major parameters that govern the velocity and the extent of plasma in the streamwise direction.

Effect of Magnetic-Field on Stress–Strain Behavior of Magneto-Sensitive Elastomers

Magneto-sensitive materials are a class of active materials whose mechanical properties are sensitive to an externally applied magnetic field. These materials exhibit non-linear and elastic/viscoelastic behavior and can undergo large deformation. In the present work, we study the effect of the external magnetic field on dynamic stress–strain behavior of a system consisting of linear polymer chains with uniformly dispersed ferrite particles in it. Molecular dynamics simulation is used as a numerical tool for this study. At moderate magnetic field strengths, change in the constitutive behavior is not significant, but as we increase the field strength, material becomes stiffer. We also study the effect of the magnetic particles on constitutive behavior by varying the volume fraction of the same.

A molecular dynamics simulation of stress-strain behavior of elastomers

L Lagrangian r Position of atom b Bond vector x Atoms scaled position with respect to cell dimensions p Momenta of atom H Transformation matrix τ Cauchy stress g Numbers of degrees of freedom f Functionality of the cross linker Text Externally applied temperature on the system s Dynamic parameter to control the temperature t Real time τ Scaled time θ Bond angle φ Dihedral angle m Mass of the monomer

Studies on an aerial propellant transfer space plane (APTSP)

This paper presents a study of a fully reusable earth-to-orbit launch vehicle concept with horizontal take-off and landing, employing a turbojet engine for low speed, and a rocket for high-speed acceleration and space operations. This concept uses existing technology to the maximum possible extent, thereby reducing development time, cost and effort. It uses the experience in aerial filling of military aircrafts for propellant filling at an altitude of 13 km at a flight speed of M=0.85. Aerial filling of propellant reduces the take-off weight significantly thereby minimizing the structural weight of the vehicle. The vehicle takes off horizontally and uses turbojet engines till the end of the propellant filling operation. The rocket engines provide thrust for the next phase till the injection of a satellite at LEO. A sensitivity analysis of the mission with respect to rocket engine specific impulse and overall vehicle structural factor is also presented in this paper. A conceptual design of space plane with a payload capability of 10 ton to LEO is carried out. The study shows that the realization of an aerial propellant transfer space plane is possible with limited development of new technology thus reducing the demands on the finances required for achieving the objectives.