Faculty Publications
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Item Differential quadrature solution for vibration control of functionally graded beams with Terfenol-D layer(Elsevier Inc. usjcs@elsevier.com, 2020) Patil, M.A.; Kadoli, R.The governing differential equation of motion for vibration control of a functionally graded material (FGM) beam using magnetostrictive layers is solved using differential quadrature method(DQM). It is known that, when differential quadrature is implemented directly for the solution of governing differential equation for vibration control of beam, it is required to convert the generalised eigenvalue problem into standard eigenvalue problem. However in the present work, the original differential equation of vibration control of beam is be separated into two simpler second and fourth order differential equations using the separation of variables in conjunction with the characteristics equation of damped single degree of freedom system. Solution of corresponding two simpler differential equation also yields damped natural frequency and damped factor comparable to that of the former approach. It is to be noted that using either of the solutions using differential quadrature method ? point description of the physical domain at boundary is used to obtained the differential quadrature equations for the various boundary conditions of the beam. In order to assure the accuracy of formulation and solution using DQM, convergence behavior of natural frequencies is examined for five combinations of boundary conditions and comparison studies from the two solution approaches is presented. The effect of the location of the magnetostrictive layers, material properties and control parameters on the vibration suppression are investigated. © 2020 Elsevier Inc.Item Influence of Winkler and viscoelastic foundation on free vibration of functionally graded beam integrated with Terfenol-D layer(Springer Science and Business Media Deutschland GmbH info@springer-sbm.com, 2020) Patil, M.A.; Kadoli, R.Free vibration of functionally graded beam integrated with Terfenol-D layer on Winkler-two parameter and viscoelastic foundation are studied by means of differential quadrature method within the framework of classical beam theory. The material properties of functionally graded beam integrated Terfenol-D layer are estimated by using the rule of mixture. The applied kinematic boundary conditions are implemented using ?-point and modified weighting coefficient approach. The solution of simply supported functionally graded material beam with Terfenol-D layer (FGMT) resting on the Winkler elastic foundation is obtained by using the technique of Navier. The numerical results obtained using differential quadrature method (DQM) and modified differential quadrature method (MDQM) are compared with exact results obtained from analytical formulation where excellent agreement is observed. The parametric study is carried out to encapsulate the influence of Winkler-two parameter and the viscoelastic foundation on the vibration characteristics of functionally graded beams integrated with Terfenol-D layer. © 2020, The Brazilian Society of Mechanical Sciences and Engineering.Item Buckling and free vibrations behaviour through differential quadrature method for foamed composites(Elsevier B.V., 2023) Duryodhana, D.; Waddar, S.; Bonthu, D.; Jeyaraj, P.; Powar, S.; Doddamani, M.The current work focuses on predicting the buckling and free vibration frequencies (fn) of cenosphere reinforced epoxy based syntactic foam beam under varying loads. Critical buckling loads (Ncr) and fn are predicted using the differential quadrature method (DQM). Ncr and fn have been calculated for beams of varying cenosphere volume fractions subjected to axial load under clamped-clamped (CC), clamped-simply (CS), simply-simply (SS), and clamped-free (CF) boundary conditions (BC′s). Upon increasing the cenosphere volume fraction, Ncr and fn of syntactic foam composites increases. These numerical outcomes are compared with the theoretical values evaluated through the Euler-Bernoulli hypothesis and further compared with experimental outcomes. Results are observed to be in precise agreement. The results of the DQM numerical analysis are given out for the different BC′s, aspect ratios, cenosphere volume fractions, and varying loads. It is perceived that depending on the BC′s, the type of axial varying loads and aspect ratios has a substantial effect on the Ncr and fn behaviour of the syntactic foam beams. A comparative study of the obtained results showed that the beam subjected to parabolic load under CC boundary conditions exhibited a higher buckling load. © 2023 The AuthorsItem 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.Item Investigation of moving load-induced vibrations in layered functionally graded Terfenol-D beams: a differential quadrature method and analytical approach(Taylor and Francis Ltd., 2024) Patil, M.A.; Saraf, S.; Kadoli, R.; Naskar, S.The paper investigates the potential of the full-sinusoidal Fourier series as a solution form for the deflection of layered functionally graded beams associated with smart actuators, drawing on the fundamental principles of classical Fourier series theory. The current method simplifies the difficult beam problem to a set of linear algebraic equations by using the Duhamel integration technique and the orthogonality of the trial function. The study takes into account generalized boundary conditions and moving forces, which are seldom discussed in previous research. Under the action of a moving load, the boundary value problem for a functionally graded beam integrated with Terfenol-D is efficiently addressed using the approach of combined differential and integral quadrature. The generalized boundary conditions may be easily achieved by adjusting the stiffness of the restraining springs. The significant agreement between the differential quadrature solution and the Fourier series solution underlines the efficiency and accuracy of both methods. Furthermore, the influences of various crucial physical characteristics on the natural frequencies and the essential flow velocities are explored, including boundary stiffness, foundation parameters, and geometric parameters. © 2024 Taylor & Francis Group, LLC.Item Sound radiation and transmission behavior of auxetic core quadrilateral sandwich panels under supersonic flow(Taylor and Francis Ltd., 2025) Prajapati, V.K.; Jeyaraj, P.; Mailan Chinnapandi, L.B.Vibroacoustic performance of a quadrilateral sandwich plate under the synergetic effect of aerodynamic pressure and harmonic excitation is analyzed numerically. Layered approach is adopted to model the sandwich plate by considering the equivalent properties of the core and facings. Governing equations, developed utilizing Hamilton’s principle are solved based on differential quadrature approach to analyze the flutter frequency and forced vibration response. Subsequently, Rayleigh integral is used to estimate the acoustic response characteristics. Effect of geometric properties of the core (cell size, wall thickness, and inclined angle) and plate (leading, and trailing-edge angles) is examined. Critical aerodynamic pressure (CAP) is calculated first for the given case and the changes in response characteristics are investigated by varying the CAP. Results indicate that geometric parameters of the core does not influence the CAP, while the core thickness and the leading and trailing edge angles have significant effects. The sound power level (SWL) and transmission loss are observed to be maximum at CAP except in some cases of leading and trailing edge angles. © 2025 Taylor & Francis Group, LLC.Item Vibro-acoustics analysis of auxetic core quadrilateral sandwich panel(Springer Science and Business Media Deutschland GmbH, 2025) Prajapati, V.K.; Pitchaimani, J.Vibro-acoustic response characteristics of re-entrant auxetic core quadrilateral sandwich plate are presented. The face sheets and the core of the sandwich panel are made of aluminum material. Mindlin plate kinematics is used to model the plate as a layered structure. Numerical simulation study is performed by using differential quadrature method and Rayleigh integral. Detailed investigation to analyze the effect of geometric parameters of the quadrilateral plate, unit cell parameters, Poisson’s ratio (positive, negative, and zero) of the core and excitation location on the vibro-acoustic performance is presented first time. Results revealed that vibro-acoustic performance of the plate is significantly affected by the geometric properties of the panel and the location of the excitation force. The sound radiation is observed to be high for cores with negative Poisson’s ratio, while sound transmission loss of the panel is not sensitive to the Poisson’s ratio cores. There is no change in response characteristics for a panel with same core density but having different Poisson’s ratio of the core. This work provides new insights into design of lightweight sandwich structures for noise control applications. © The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering 2024.Item Flutter behavior of quadrilateral auxetic core sandwich plate with bio-inspired three-phase composite facings numerical analysis and experimental verification(SAGE Publications Ltd, 2025) Prajapati, V.K.; Pitchaimani, J.Flutter characteristics of auxetic core quadrilateral sandwich plates with three-phase bio-inspired laminated composite facings are presented. The core is made of aluminum, while the facings are made of graphene nanoplatelets dispersed in bio-inspired glass fiber/epoxy laminates. The equations of motion are obtained using Reissner-Mindlin plate theory and Hamilton’s approach and then solved with the help of differential quadrature method. Experimental verification of free vibration is done for isotropic and hexagonal honeycomb core sandwich panels. Influences of core parameters (aspect ratio, inclined angle, and thickness-to-width ratio), mass fraction of graphene nanoplatelets and fibers, various graphene nanoplatelet distribution patterns, the geometry and aspect ratio of the plate, and bio-inspired layup scheme of laminated facings on the flutter characteristic are explored. The critical aerodynamic pressure is not sensitive to the core parameters and the dispersion pattern of graphene nanoplatelets. Critical aerodynamic pressure of the panel increases significantly with increase in the mass fractions of fiber and graphene nanoplatelet. Furthermore, the increase in the plate angles results in reduced critical aerodynamic pressure. Facing laminate made of helicoidal type bio-inspired lay-up scheme with lower rotation angle enhances the critical aerodynamic pressure compared to the conventional uni-directional, cross-ply, and quasi-isotropic lay-ups. © IMechE 2024.Item Applicability Two-Dimensional Differential Integral Quadrature Method in Vibration Analysis of Multi-Directional Functionally Graded Porous Viscoelastic Plates(John Wiley and Sons Ltd, 2025) Mohamed, S.A.; Mohamed, N.; Assie, A.E.; Eltaher, M.A.; Pitchaimani, J.; Abo-Bakr, R.This study formulates a differential integral quadrature method (DIQM) to analyze the free vibration characteristics of multi-directional functionally graded material (MFGM) viscoelastic porous plates. The kinematic relations are derived using a unified shear deformation plate theory, while material behavior is governed by the integer-order Kelvin-Voigt viscoelastic constitutive model. Power-law functions define the spatial gradation of material constituents along the length, width, and thickness directions. Two distinct porosity distributions are incorporated to characterize void and cavity variations through the plate's thickness. Hamilton's variational principle yields five coupled governing equations expressed as partial differential equations with variable coefficients. The differential quadrature method (DQM) discretizes these governing equations, with integral quadrature method (IQM) efficiently resolving the variable coefficients. This discretization results in an algebraic system constituting a quadratic eigenvalue problem. The eigenvalues' real and imaginary components provide the damping coefficients and natural frequencies, respectively. The proposed model and solution methodology are validated against established unified shear formulations, MFGM porous plates, and viscoelastic plate solutions available in literature. Comprehensive parametric studies systematically investigate the influence of material gradation indices, porosity parameters, boundary conditions, and viscoelastic coefficients on the natural vibration response of thick MFGM viscoelastic porous plates. The results demonstrate that an increase in either of the material gradation indices leads to a decrease in both of the real and imaginary parts of the fundamental frequencies. © 2025 John Wiley & Sons Ltd.