Faculty Publications
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Item Acoustic Response of an Isotropic Beam under Axially Variable Loads Using Ritz and Rayleigh Integral Methods(Polska Akademia Nauk, 2022) Somi Naidu, S.N.; Jeyaraj, J.; Mailan Chinnapandi, L.B.; Reddi Chintapalli, V.S.N.R.Vibro-acoustic response of an isotropic beam under the action of variable axial loads (VALs), is presented in the study. Effects of six different types of VALs and three types of end conditions on buckling, free vibration and sound radiation characteristics are investigated. Static buckling and free vibration behaviours using shear and normal deformable theorem and Ritz method. However, the forced vibration response is evaluated using modal superposition method and the acoustic radiation characteristics are obtained using Rayleigh integral. The nature of variation of VALs and end conditions are influencing buckling and free vibration characteristics remarkably. Results indicate that the acoustic response is highly sensitive to the nature of VAL and intensity of the VAL. In general, sound power at resonance decreases when the magnitude of VAL is increased. © © 2022 S.N. Balireddy et al.Item Static stability and free vibration characteristics of a micro laminated beam under varying axial load using modified couple stress theory and Ritz method(Elsevier Ltd, 2022) Priyanka, R.; Jeyaraj, J.This paper explores the buckling and free vibration behaviors of micro laminated composite beams (MLCBs) exposed to varying axial loads using the modified couple stress theory (MCST), with arbitrary boundary conditions and layups. The size effect is captured in MCST by taking into account the material length scale parameters. In the axial direction, the applied load has either constant, linear, or parabolic variations. The equilibrium equations are derived and solved using Hamilton's principle and Ritz method respectively. The size effect is observed to be more pronounced when the thickness of the beam is similar to the material length scale parameter, and it nearly vanishes as the beam thickness increases. The small size effect variation is different for different boundary conditions. For parabolically increasing loading case, the rate of reduction of the fundamental frequency with an increase in applied load intensity is greater compared to other loadings. © 2021 Elsevier LtdItem Stability and dynamic behaviour of bi-directional functionally graded beam subjected to variable axial load(Elsevier Ltd, 2022) Somi Naidu, S.N.; Jeyaraj, J.The current study emphasizes static stability and dynamic characteristics of bi-directional functionally graded beams subjected to variable axial loads using the Ritz method and Reddy's beam theory. The material property is varied as a function of the gradation pattern along with the length and thickness directions. The solutions procedures are tested against the results in the literature to show the accuracy of the present method. The influence of uniform, linear, and parabolic axial loads along the length of the beam on buckling and vibration responses are investigated. There is a remarkable variation observed in both the responses, by changing the material properties from isotropic to bi-direction functionally graded. Furthermore, the study reveals that higher stiffness is achieved by the material gradation index increment along the thickness direction compared to the lengthwise gradation index increment. Even the variations in the aspect ratios and end conditions are depicting significant variations in the buckling and vibration responses. Buckling and free vibration modes are also highly sensitive to the nature of variable axial loads and gradation index. © 2022 Elsevier LtdItem Stability and dynamic behavior of porous FGM beam: influence of graded porosity, graphene platelets, and axially varying loads(Springer Science and Business Media Deutschland GmbH, 2022) Priyanka, R.; Twinkle, C.M.; Jeyaraj, J.This paper investigates the free vibration and buckling behaviors of functionally graded graphene platelets (FG-GPLs) reinforced porous beam under axially variable loads. The internal pores and GPLs are either uniformly or non-uniformly distributed along the thickness direction. Halpin–Tsai micromechanics model is used to calculate the effective elastic modulus. The variation of Poisson’s ratio along the thickness and the relation between mass density and porosity coefficients are determined using mechanical properties of closed-cell solid under the Gaussian random scheme. The equilibrium equations are derived by Hamilton’s principles, and critical buckling load and dimensionless natural frequency are determined by Ritz formulation. Results revealed that buckling and free vibration behavior of the porous FG-GPL beam are influenced by the GPLs grading pattern and the type of axially varying load. Furthermore, the grading pattern of porosity has more influence on the buckling behavior compared to the free vibration behavior. It is also observed that buckling mode and the fundamental vibration mode of the porous FG-GPL are influenced by the loading conditions and remain unaffected by the grading pattern of porosities and GPLs. © 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.Item Free vibration and buckling response of functionally graded triply periodic minimal surface beams considering neutral axis dislocation(SAGE Publications Inc., 2023) Kurup, M.; Pitchaimani, J.The work pioneers a novel investigation into the free vibration and buckling behavior of triply periodic minimal surface beams, characterized by diverse distribution profiles. Using Euler-Bernoulli theory, under various boundary conditions, the investigation is carried out on four TPMS (Triply Periodic Minimal Surface) patterns, mainly gyroid, primitive, diamond and IWP (I-graph-wrapped package). The neutral axis would not coincide with the geometric center of the functionally graded beams so the neutral shift effect is taken into consideration appropriately. Governing differential equations are derived and the solutions are obtained numerically using the Ritz method. The mode shapes have also been calculated. It can be concluded that the type of pattern and distribution profile, boundary conditions, grade and neutral axis shift effect play a vital role in the prediction of vibration and buckling properties. © The Author(s) 2023.Item 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.Item 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.Item Sound radiation characteristics of a beam under supersonic airflow and non-uniform temperature field(Elsevier Masson s.r.l., 2024) Patil, H.H.; Pitchaimani, J.This paper investigates vibro-acoustic behaviour of an isotropic beam subjected to in-plane varying temperature field and supersonic flow. For a given elevated temperature and non-uniform temperature (NUFT) field, the aerodynamic pressure (ADP) is varied in fraction of its critical value, and the consequent effect on sound radiation characteristics is investigated. Shear and normal deformable beam theory (SNDBT) based kinematics is used, and equations of motion are obtained using Hamilton's principle. Following that, the Ritz method is used to solve the equations. To start with, aeroelastic flutter and vibro-acoustic response characteristics (as a function of critical aerodynamic pressure (λcr)) are analyzed without considering any thermal stress effect. Following that, for a given temperature field, the critical buckling temperature (ΔTcr) of the beam is obtained. Then, the impact of thermal stress caused by the NUFT field on the flutter and sound radiation characteristics is studied. The study observed that the combined effects of the NUFT field and variable ADP significantly impacted the beam's flutter and vibro-acoustic responses. © 2024 Elsevier Masson SASItem Nonlinear buckling and free vibration analysis of auxetic graphene origami composite beams under nonuniform thermal environment(Taylor and Francis Ltd., 2025) Shashiraj; Pitchaimani, J.; Kattimani, S.This study examines the thermo-mechanical behavior of auxetic metamaterial beams enhanced by graphene origami (GOri) under spatially varying nonuniform temperature distributions (SVTD). Utilizing Timoshenko beam theory considering von-Kármánn type nonlinear strain–displacement relationship, GOri beams are modeled as layered structures. The Ritz method is employed to solve equilibrium equations, analyzing the impact of GOri distribution patterns, content, and folding degree on post-buckling and vibration paths. The effects of five SVTDs, three end conditions, and three GOri distribution patterns on buckling, post-buckling behavior, and nonlinear free vibration characteristics are explored. Findings reveal that the parabolic temperature distribution with peak temperatures at beam ends (P-MAE) results in higher critical temperatures and nonlinear free vibration frequencies. This research provides crucial insights into the design and optimization of GOri-enabled metamaterial structures in complex thermal environments, highlighting the significant influence of nonuniform temperature distributions along the beam’s length. © 2024 Taylor & Francis Group, LLC.Item Non-linear transient vibration response of graphene origami enhanced metamaterial beams under spatially-varying temperature distributions(Elsevier Ltd, 2025) Shashiraj; Pitchaimani, J.; Kattimani, S.Understanding the dynamic behavior of advanced materials under varying conditions is crucial for the development of resilient and efficient structural systems. This research investigates the non-linear transient response of auxetic metamaterial beams enhanced with graphene origami under spatially varying non-uniform thermal environment. Using Timoshenko beam theory with von-Kármánn type non-linear strain–displacement relations, graphene origami beams are modeled as layered structures. The equilibrium equations are solved using the Ritz method, with a focus on how different graphene origami distribution patterns, content levels, and folding degrees influence the transient response under various time-dependent forces. Non-linear motion equations are solved using the Newmark-Beta method. This study evaluates the impact of five distinct non-uniform temperature distributions, seven types of time-dependent loadings, three boundary conditions, and three configurations of graphene origami distribution on the vibration characteristics. Results indicate that parabolic temperature distributions with peak temperatures at the beam ends lead to substantially decreased dynamic deflections. This research provides valuable insights into the structural dynamics of graphene origami-enhanced metamaterial beams within complex thermal environments, highlighting the considerable influence of spatial temperature variations along the length of the beam. © 2025