Salil S. Kulkarni

Structural Health Monitoring and Damage Prognosis in Fatigue

A conceptual structural health monitoring (SHM) system to monitor fatigue damage is discussed in this study. The first part of the study is concerned with damage prognosis. A methodology to use the data from a pre-crack damage monitoring system to predict the number of cycles to macrocrack-initiation in a probabilistic sense, is presented. Issues related to quantifying damage, a damage evolution law, and numerical evaluation of the probability of macrocrack initiation are discussed. The second part of the study deals with quantifying the effects of imperfect inspections during the growth of a macrocrack. The probability that there eXists an undetected critical crack is the quantity of interest. An analytical eXpression for this quantity is derived for the case of a two-dimensional crack. A Monte Carlo simulation method to quantify the effects of imperfect inspections is also presented. Numerical results are presented for two eXamples of surface-breaking cracks with different geometries.

Studies on the dynamics of a supercavitating projectile

Due to imperfect water entry, a high speed supercavitating projectile, while moving in the forward direction, rotates inside the cavity. This rotation leads to a series of impacts between the projectile tail and the cavity wall. The impacts affiect the trajectory as well as the stability of motion of the projectile. The present paper discusses the in-fiight dynamics of such a projectile. Equations of motion of the projectile are developed for two distinct phases of motion - Phase I: the projectile moves in the cavity without interaction with the cavity wall, and Phase II: the tail impacts on the cavity wall.The equations are found to be coupled and nonlinear. A simple model based on the concepts of flow planes is used to determine the forces acting on the projectile during impact. The effect of the mass distribution on the projectile dynamics is also studied. The results show that despite the impacts with the cavity wall, the projectile nearly follows a straight line path. The frequency of the impacts between the projectile tail and cavity boundary increases initially,reaches a maximum, and then decreases gradually. The results also indicate that the frequency of impacts decreases with the projectiles moment of inertia. It is also shown that the impact of the projectile with the cavity wall can be modelled as an impact with a rigid barrier with variable coefficient of restitution. A functional form of the coefficient of restitution is proposed, and it is shown that the proposed form predicts the impact behaviour quite well.

Static and Dynamic Analysis of Electrostatically Actuated Microcantilevers Using the Spectral Element Method

The objective of this paper is to present the Spectral Element Method (SEM) as an accurate and efficient design tool for static and dynamic simulations of cantilever based MEMS devices. The microcantilever under consideration is modeled as a Timoshenko beam and discretized using the spectral element formulation that accounts for fringing field and the nonlinearity arising from the electrostatic driving force. The static analysis has been carried out using Picard’s iteration method and the static pull-in displacement and voltage have been calculated. An eigenvalue analysis of this beam is also carried out to determine its natural frequencies. In addition, the dynamics of this cantilever is studied using the explicit Newmark predictor-corrector method to generate the time history. In all cases, the results have been compared to the one-dimensional Finite Element Method and three-dimensional finite element method (implemented through the commercial package COMSOL Multiphysics) to examine the accuracy and computational speed of the proposed SEM. The results of the simulations were also compared to those obtained by experiments in the existing scientific literature.These comparisons lead to the inference that the SEM is able to reproduce the static and dynamic response of the beam to a high degree of accuracy. It was also found that several numerical features inherent in the SEM lead to a significantly faster computation than the corresponding finite element method for equivalent degrees of freedom. This advantage was verified by using the SEM to carry out static and dynamic simulations of variable width microcantilevers.We therefore propose that the SEM is a viable tool for the MEMS community to accurately and quickly determine the static and dynamic pull-in parameters, frequency eigenvalues, and static and dynamic behavior at the design stage.Copyright

Regularization of pattern formation in heteroepitaxial thin films through surface diffusivity modulation

A numerical study is presented to demonstrate the influence of local diffusion variation during laser-thermal treatment on the growth dynamics of silicon-germanium thin films. A surface morphology evolution equation is developed with the assumption that the diffusivity is a spatially varying function induced by a sinusoidal surface temperature profile. Results show that an initially flat film evolves into patterns through the thermal modulation, indicating that the growth can be controlled by enhancing local diffusivity. The present study is expected to provide a path for future laser-annealing experiments to produce regularized quantum dots.

Mean value theorems for integral equations in 2D potential theory

This paper presents a number of theorems, with proofs, related to mean values of certain integrals that arise in integral formulations for boundary value problems in two-dimensional potential theory. These theorems can be useful, for example, for the understanding and evaluation of new integral formulations and for simplifying existing ones.

The Dirichlet problem for elliptic systems in multiconnected rough regions

We present a new integral formulation for the L 2 Dirichlet boundary value problem associated with second order elliptic systems in multiconnected regions with rough boundaries. This study has been motivated by displacement prescribed problems arising in solid mechanics and our results are relevant to their numerical treatment.

Local solutions in potential theory and linear elasticity using Monte Carlo methods

A numerical method called the boundary walk method is described in this paper. The boundary walk method is a local method in the sense that it directly gives the solution at the point of interest. It is based on a global integral representation of the unknown solution in the form of potentials, followed by evaluating the integrals in the resulting series solutions using Monte Carlo simulation. The boundary walk method has been applied to solve interior problems in potential theory with either Dirichlet or Neumann boundary conditions. It has also been applied to solve interior problems in linear elasticity with either displacement or traction boundary conditions. Weakly singular integral formulations in linear elasticity, to which the boundary walk method has been applied, are also derived. Finally, numerical results, which are computed by applying the boundary walk method to solve some two-dimensional problems over convex domains in potential theory and linear elasticity, are presented. These solutions are compared with the known analytical solutions (when available) or with solutions from the standard boundary element method.

Experimental Measurement of Vibration of Liquid Droplet at Low Bond Numbers Using ESPI

The vibration of droplets finds multiple applications in inkjet printing, combustion sprays, drop atomization etc. In many of these processes, the primary interest is to estimate the resonant frequencies and mode shapes of the vibrating drops. Previous works show extensive characterization of vibrating droplets in a gravity dominated regime, where Bond numbers (ratio of gravitational and surface tension effects) are greater than 2. In the present work, vibrations of small size droplets, in the capillary regime, with Bond number in the range 0.24–1.37 are considered on hydrophilic and hydrophobic surfaces. The surface of the vibrating drop at resonance is characterized using a novel interferometric method: Electronic Speckle Pattern Interferometry (ESPI) is explored. The resonant frequencies obtained through the interferometric patterns of ESPI is found to be in good agreement with a theoretical model considering a 1D capillary-gravity wave.

Approach to Eliminate Couplant-Effect in Acoustic Nonlinearity Measurements

An approach to eliminate couplant‐effect in acoustic nonlinearity measurements for fatigued components is proposed in this paper. Measurements are performed on a fatigued steel 4340 specimen using both the conventional and proposed techniques. It is observed that the coefficients of variation of the nonlinearity parameter obtained using the proposed technique is approximately half of that obtained using the conventional technique.

An acoustic nonlinearity measurement technique with built-in couplant effect elimination

A modified technique to measure acoustic nonlinearity in fatigued components is proposed in this paper. As opposed to the conventional technique to measure acoustic nonlinearity, the proposed technique eliminates the couplant effects between the transducers and the specimen. The proposed technique is compared with the conventional technique by performing nonlinearity measurements on a fatigued aluminum alloy specimen and calculating the coefficient of variation (COV) of the nonlinearity parameter. Preliminary results show that the COV of the nonlinearity parameter obtained using the modified technique is approximately half of that obtained using conventional technique. It is therefore felt that the proposed technique will help to reduce the variability in the nonlinearity measurements in fatigued components.