Faculty Publications
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Item An analytical method to determine the response of a micro capacitive pressure sensor(2011) Simha, A.; Kulkarni, S.M.; Meenatchi Sundaram, S.The response of a capacitive pressure sensor is generally represented by a fourth order partial differential equation which is complex to solve and does not possess an exact solution. Several attempts have been made earlier through various techniques such as the Galerkin method, Finite Difference Method etc. In this paper an attempt has been made to develop a simple approximate analytical approach to determine the response of a capacitive pressure sensor whose diaphragm is designed to undergo very small deflections (typically less than 25 % of the thickness). The nonuniform gap between the electrodes is mathematically expressed as a combination of the initial gap between the electrodes (in the undeformed state) and a displacement function in (x, y). The proposed displacement function is then utilized in evaluating the capacitance as a function of the applied pressure. The results obtained from the analytical approach are benchmarked against those obtained from COMSOL Multiphysics®, a popular Finite Element Analysis tool in the MEMS industry. It is observed that the results obtained from COMSOL Multiphysics® and those from the analytical approach are in good agreement with a maximum deviation of about 3.38 %. © 2011 IFSA.Item An exact solution for vibro-acoustic response of smart sandwich panels with MEE composite Layer(Elsevier Ltd, 2022) Arunkumar, M.P.; Bhagat, V.S.; Geng, Q.; Li, Y.; Jeyaraj, J.To the best of our knowledge, this is the first endeavor to provide an exact solution for a vibro-acoustic response of Magneto-electro-elastic (MEE) composite plate and sandwich panels with MEE facings. The governing equation of motion is developed using Hamilton's principle considering the third-order shear deformation theory to account for transverse shear. Based on boundary conditions and the Maxwell equation, the variation of electric and magnetic potentials are adopted along the thickness of the MEE composite layer. Analysis of the vibro-acoustic response of sandwich panels which are extensively used in aerospace structures such as cellular, trapezoidal, triangular, and honeycomb are presented. Influences of electric and magnetic potential on the vibro-acoustic response are also presented for the different types of truss core and honeycomb core sandwich panels. © 2022Item The exact solutions for Kudryashov and Sinelshchikov equation with variable coefficients(Institute of Physics, 2022) Jisha, J.; Dubey, R.K.; Benton, D.; Rashid, A.The Kudryashov and Sinelshchikov (KS) equation address pressure waves in liquid-gas bubble mixtures while considering heat transport and viscosity. This study mainly includes two types of generalized solutions: polynomial function traveling wave solutions and rational function traveling wave solutions. In this study, we constructed the KS equation's exact traveling and solitary wave solutions with variable coefficients by the generalized unified method (GUM). These newly created solutions play a significant role in mathematical physics, optical fiber physics, plasma physics, and other applied science disciplines. We illustrated the dynamical behavior of the discovered solutions in three dimensions. We proposed the possibility of discussing wave interaction and other wave structures using bilinear form related to the Hirota method for the fractional solutions. © 2022 IOP Publishing Ltd.Item An exact solution for vibro-acoustic response of MEE composite plate(Elsevier Ltd, 2022) Arunkumar, M.P.; Bhagat, V.S.; Swetha, S.; Geng, Q.; Jeyaraj, J.; Li, Y.To the best of our knowledge, this is the first endeavor to present an exact solution to predict vibro-acoustic characteristics of Magneto-electro-elastic (MEE) composite plate. The transverse and in-plane fields are considered based on thin-plate conditions. The variation of electric and magnetic potentials is determined according to electromagnetic boundary conditions and the Maxwell equation. The stress resultants and mass inertias are used in Hamilton's principle to generate the governing equation. Here the mathematical formulation is developed using third-order shear deformation theory. Also in this work, the dynamic displacement responses are provided by finding five undetermined mode coefficients relevant to u, v, w, ϕx, and ϕy to predict forced vibration response. The forced vibration response obtained based on the developed governing equation is used to calculate the acoustic characteristics using the Rayleigh integral. The effect of magnetic and electric potential is shown in the acoustic responses. From the results, it is understood that the acoustic responses are highly influenced by the applied magnetic and electric potential. The radiation efficiency of the MEE plate did not show any variations in the lower frequency and it shows the variation near the resonant frequencies on the application of electric and magnetic potential. © 2022 Elsevier LtdItem Theoretical evolution of thermal behaviour of Ti-6Al-4V subjected to selective laser melting: A powder free approach(Elsevier GmbH, 2023) Dutta, J.; Bhanja, D.; Narendranath, S.Additive manufacturing (AM) processes are considered to be the pillar of the next industrial revolution due to their inherent qualities such as design flexibility, the ability to produce complex parts and prototypes, lower cost due to the reduced requirement of materials and curtailed lead time for manufacturing. Selective laser melting (SLM) is one of the most popular metallic AM technologies since it enables accurate control over part dimensions and fabrication of high resolution features. This research paper is aimed to develop an exact analytical model of three-dimensional thermal response captured in SLM of Ti based alloy (Ti-6Al-4V). A physical model has been proposed to predict the temperature profile during the metal additive manufacturing process with consideration of the effect of thermal history developed during moving laser heat source interaction. The corresponding mathematical solution is developed by employing an amalgamation of ‘Duhamel's theorem’ and ‘Finite Integral Transform method’. The parametric laser-substrate interaction phenomenon is the prime deciding factor for the successful accomplishment of the manufacturing process. This research paper theoretically investigates the thermal characteristics (peak temperature, temperature distribution curvature, pulse time, optical penetration depth, time of laser exposure, laser absorption radius, and so on) by employing Fourier's heat conduction model with a moving laser heat source. The theoretical estimation has been validated by the existing mathematical as well as experimental research outcomes. Present work might be an asset for deciding the design of process variables and protocols in terms of laser based additive manufacturing specifically the selective laser melting process. © 2022 Elsevier GmbHItem Analytical solution for free vibration of symmetric Terfenol-D layered functionally graded beam with different boundary conditions(Springer Science and Business Media Deutschland GmbH, 2023) Patil, M.A.; Kadoli, R.A unified analytical approach is established to predict the frequency behaviour of symmetric functionally layer-wise graded beams with an integrated Terfenol-D layer under simply supported, clamped-clamped, and clamped-simply supported boundary conditions. In contrast to previous research, the analytical solution relies on transcendental equations. Terfenol-D layered functionally graded beam uses Reddy’s generalised beam theory as the basis for its governing equation. First-order shear deformation and rotating inertia were taken into consideration in the study. To ensure the accuracy of the analytical solution, comparisons are made with the current differential quadrature solution based on Euler–Bernoulli beam theory. The current analytical solution yields frequency results that are in good agreement with those obtained by the differential quadrature approach. The present analytical means is straightforward and easy to understand as compared to previous researcher’s work. © 2023, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.