Faculty Publications
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Item Effect of boundary conditions and convection on thermally induced motion of beams subjected to internal heating(2007) Malik, P.; Kadoli, R.; Ganesan, N.Numerical exercises are presented on the thermally induced motion of internally heated beams under various heat transfer and structural boundary conditions. The dynamic displacement and dynamic thermal moment of the beam are analyzed taking into consideration that the temperature gradient is independent as well as dependent on the beam displacement. The effect of length to thickness ratio of the beam on the thermally induced vibration is also investigated. The type of boundary conditions has its influence on the magnitude of dynamic displacement and dynamic thermal moment. A sustained thermally induced motion is observed with progress of time when the temperature gradient being evaluated is dependent on the forced convection generated due to beam motion. A finite element method (FEM) is used to solve the structural equation of motion as well as the heat transfer equation. © Springer-Verlag 2007.Item Static analysis of functionally graded beams using higher order shear deformation theory(2008) Kadoli, R.; Akhtar, K.; Ganesan, N.Displacement field based on higher order shear deformation theory is implemented to study the static behavior of functionally graded metal-ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGM beam is presented. Two stiffness matrices are thus derived so that one among them will reflect the influence of rotation of the normal and the other shear rotation. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick FGM beam under uniform distributed load for clamped-clamped and simply supported boundary conditions are discussed in depth. The effect of power law exponent for various combination of metal-ceramic FGM beam on the deflection and stresses are also commented. The studies reveal that, depending on whether the loading is on the ceramic rich face or metal rich face of the beam, the static deflection and the static stresses in the beam do not remain the same. © 2007 Elsevier Inc. All rights reserved.Item Thermo-elastic response of SUS316-Al2O3 functionally graded beams under various heat loads(Elsevier Ltd, 2017) Malik, P.; Kadoli, R.Geometric nonlinearity and temperature dependent material properties are accounted for in the theoretical analysis of time dependent thermo-elastic response of thin functionally graded material (FGM) SUS316-Al2O3 beam subjected to various heat loads. A two dimensional Lagrangian rectangular finite element is used to obtain the temperature distribution on the transverse plane of the beam. Nonlinear thermo-elastic deflection and thermal stresses are evaluated for various structural and thermal boundary conditions. Thermo-elastic oscillations are observed in case of beams subjected to step, concentrated line and shock heat load whereas thermo-elastic deflection is observed for beams subjected to moving heat load. As the thermal load increases, the nonlinear thermal deflection of FGM beam are higher compared to linear analysis. In general, temperature dependency of material properties influence the amplitude of thermal oscillations. High thermal stresses are induced in beams with pin-pin and clamp-pin boundary condition as compared to hinge-hinge beam. © 2017 Elsevier LtdItem Thermal induced motion of functionally graded beams subjected to surface heating(Ain Shams University, 2018) Malik, P.; Kadoli, R.Thin beam of the functionally graded (FG) type subjected to a step heat input on one surface and insulated or exposed to convective heat loss on the opposite surface is under consideration for the evaluation of thermal induced motion. The dynamic displacement and dynamic thermal moment of the beam are analysed when the temperature gradient is independent of the beam displacement. The power law index dictates the metal–ceramic distribution across thickness of the beam and its effect on the thermal vibration of the beam is examined. The article discusses, in depth, the influence of various factors such as length to thickness ratio of beam, heat transfer boundary conditions, physical boundary conditions, and metal–ceramic combination on the thermal oscillations of FG beam. It is found that attenuation of the amplitude of static thermal deflection and superimposed thermal oscillations is a strong function of the metal–ceramic combination for the FG beam. © 2015 Faculty of Engineering, Ain Shams UniversityItem 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 Bending and vibration studies of FG porous sandwich beam with viscoelastic boundary conditions: FE approach(Taylor and Francis Ltd., 2023) Patil, R.; Joladarashi, S.; Kadoli, R.Bending and vibration characteristics of FG porous sandwich beam with viscoelastic boundary conditions are investigated. Complex shear modulus and associated loss factor are considered for the viscoelastic interlayer. The beam is constrained by viscoelastic supports (VES) at either end. Complex stiffness model is adopted for VES. The transverse deflection, natural frequency, loss factors, and mode shapes are obtained by varying VES stiffness. Furthermore, the study is extended to sandwich beams with various (H, O, V, and X) porosity patterns. The results convey that VES contribution in vibration damping is more predominant when the supports are less stiff (more viscous). © 2022 Taylor & Francis Group, LLC.Item 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 Effect of porosity and viscoelastic boundary conditions on FG sandwich beams in thermal environment: Buckling and vibration studies(Elsevier Ltd, 2023) Patil, R.; Joladarashi, S.; Kadoli, R.The present study is carried out to investigate the combined effect of porosity and temperature on the buckling and vibration attributes of FG sandwich beams in the thermal environment using FE formulation. The modeled sandwich beam consisting of the viscoelastic core material is restrained by viscoelastic boundary conditions (VBCs). The FG face layers and core are subjected to temperature-dependent material properties. Complex stiffness model is adopted for VBCs. Porosity patterns such as H, V, X, and O are incorporated into FG face layers. The Lagrange equation is used to derive the sandwich beam's equilibrium equations of motion in static and dynamic conditions. The derived equilibrium equations are solved for buckling and vibration of the beam using the FE solution. Lagrange and Hermite shape functions are assumed for axial and transverse displacements. Critical buckling temperature (CBT), natural frequency (NF), and loss factors (LF) are obtained for various temperatures and boundary stiffness values (BSVs). Transverse buckling and vibration mode shapes are extracted for changing BSVs. The behavior of NF and LF at buckling temperature is also discussed. The existence of porosities ameliorates the buckling characteristics of the sandwich beam. VBCs expedite the vibration damping of sandwich beams alongside the viscoelastic core. The natural frequency and loss factor reach zero and infinity, respectively, when the temperature reaches CBT. © 2023 Institution of Structural EngineersItem 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.