Faculty Publications

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Publications by NITK Faculty

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Author: search.filters.author.Jeyaraj, J.Subject: search.filters.subject.Equations of motion

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    Vibration analysis of a tapered laminated thick composite plate with ply drop-offs
    (Springer Verlag service@springer.de, 2015) Edwin Sudhagar, P.; Arumugam, A.; Vasudevan, R.; Jeyaraj, J.
    In this study, vibration characteristics of a tapered laminated thick composite plate have been investigated using finite element method by including the shear deformation and rotary inertia effects. The governing differential equations of motion of a tapered laminated thick composite plate are presented in the finite element formulation based on first-order shear deformation theory for three types of taper configurations. The effectiveness of the developed finite element formulation in identifying the various dynamic properties of a tapered laminated thick composite plate is demonstrated by comparing natural frequencies evaluated using the present FEM with those obtained from the experimental measurements and presented in the available literature. Various parametric studies are also performed to investigate the effect of taper configurations, aspect ratio, taper angle, angle ply orientation and boundary conditions on free and forced vibration responses of the structures. The comparison of the transverse free vibration mode shapes of the uniform and tapered composite plates under various boundary conditions is also presented. The forced vibration response of a composite plate is investigated to study the dynamic response of tapered composite plate under the harmonic force excitation in various tapered configurations. It is concluded that the dynamic properties of laminated thick composite plates could be tailored by dropping off the plies to yield various tapered composite plate. © 2015, Springer-Verlag Berlin Heidelberg.
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    Structural optimization of rotating tapered laminated thick composite plates with ply drop-offs
    (Springer Netherlands, 2017) Edwin Sudhagar, P.; Arumugam, A.; Vasudevan, V.; Jeyaraj, J.
    In this study, structural optimization of rotating tapered thick laminated composite plates with ply drop-offs has been investigated numerically. The governing differential equations of motion of the tapered composite plate have been presented including the energy associated with the inertia force, coriolis force, displacement dependent centrifugal force and initial stress resultants due to steady state rotation. Four noded quadrilateral finite element has been formulated based on the first order shear deformation theory. Finite element analysis results are validated with experimental results for natural frequencies of the tapered plate with various configurations. Various cases of optimization problems are formulated with different objective functions in terms of maximization of natural frequencies and damping factors (individually and combined) and solved using genetic algorithm in order to obtain optimal ply sequence and ply orientation. It is shown that the optimization problem with maximization of fundamental modal damping factor without rotating condition yields the optimal layout as 90° for all the layers in the plate. It is also observed that maximization of the fundamental modal damping factor yields identical optimal orientation for uniform and all the configurations of a tapered composite plate. © 2015, Springer Science+Business Media Dordrecht.
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    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. © 2022
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    Nonlinear flutter of 2D variable stiffness curvilinear fibers composite laminates by a higher-order shear flexible beam theory with Poisson's effect
    (Elsevier Ltd, 2022) Manickam, G.; Vasudevan, V.; Gunasekaran, V.; Jeyaraj, J.; Mohamed, H.
    In this work, the nonlinear supersonic panel flutter characteristics of two-dimensional variable stiffness curvilinear fibres based laminated composite panels are studied using a higher-order shear flexible theory represented by sine function coupled with first-order approximation leading to quasi-aerodynamic theory. The structural formation takes care of geometric nonlinearity with von Karman's assumptions. The beam constitutive equation is modified for the laminated beam with general lay-up by accounting for Poisson's effect. The nonlinear dynamic equilibrium equations developed by Lagrangian equations of motion are solved using finite element approach in conjunction with the direct iterative solution procedure. For limit cycle oscillation, critical dynamic pressure is predicted iteratively through eigenvalue analysis, thereby identifying the first coalescence of vibrational modes. Also, the flutter behavior of two-dimensional panel under static differential pressure is investigated considering nonlinear static equilibrium position of panel obtained by Newton-Raphson's iterative approach and then followed by modes coalescence approach. These solution procedures are tested against the results in literature. A thorough numerical investigation is done to show the effect of the curvilinear fiber path orientation, limited cycle amplitude, static differential pressure, panel thickness, panel end condition flexibilities and thermal environment on the nonlinear supersonic panel flutter of two-dimensional variable stiffness laminated panels. © 2022
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    Buckling and vibration of beams using Ritz method: Effects of axial grading of GPL and axially varying load
    (Taylor and Francis Ltd., 2024) Patil, H.H.; Jeyaraj, J.; Eltaher, M.A.
    The present work discusses buckling and vibration characteristics of axially functionally graded (AFG) graphene platelet (GPL) composite beams exposed to axially varying loads (AVLs). Timoshenko beam composition with five different types of axial grading GPLs subjected to six different types of AVLs are studied. The effective elastic properties are obtained using Halpin-Tsai model and the equations of motion are obtained following the Hamilton’s principle. Then the equations are solved for buckling and vibration analysis using the Ritz method. Influences of nature of axial grading of GPLs and load, content of GPL, and structural boundary conditions are investigated through detailed parametric studies. It is found that the grading pattern of GPLs not only influences the buckling load, but also changes buckling mode shapes of the beam at specific type of AVL. Furthermore, results reveal that buckling and vibration characteristics of beam enhanced in case of AFGM-A type for most of the load cases studied. The proposed study will be helpful for the structural engineers to select the nature of graded distribution of GPLs for the given type of AVL and design the structural member. © 2023 Taylor & Francis Group, LLC.
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    Aeroelastic flutter behaviour of beam: effect of graded GPL and porosity
    (Taylor and Francis Ltd., 2024) Kotriwar, G.; Jeyaraj, J.
    The present study investigates the aeroelastic flutter characteristics of the graphene platelets (GPL) reinforced metal foam beam. Closed-cell metal foam beams having graded distribution of pores and functionally graded reinforcement of GPLs are considered in this study. The closed-cell metal foam model has been used for deriving the mechanical properties of the foam matrix, which makes provision for determining the relation between the co-efficient of porosity and the co-efficient of density. Modified Halpin-Tsai micromechanics is used to obtain the effective Young’s modulus of the GPLs reinforced composite beam, Density and Poisson’s ratio are calculated with the help of the rule of mixture. The Hamilton’s principle together with the Ritz method, employing the first-order piston theory gives the governing equations of motion for aeroelastic flutter characteristics of the beam for different end conditions. Juxtaposition of dimensionless natural frequencies with the results previously published by others is executed for validating the correctness of the approach followed in the present model. A study of various parameters has been executed, and the results in tables and graphs present the influence of porosity as well as GPLs reinforcement, different boundary conditions and thermal loading on aeroelastic flutter characteristics of the FG-GPL reinforced metal foam beam. © 2023 Taylor & Francis Group, LLC.