Dynamical stability of bi-directionally graded moving beams
Subject Areas : Mechanics of SolidsMohammad Hasan Babaei Rochi 1 , Jalil Jamali 2
1 - Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Mechanical Engineering Departments, Shoushtar Azad University, Shoushtar, Iran
Keywords: Free vibration, Functionally graded axially moving beam, Instability, Differential quadrature method, Higher-order shear deformation theory.,
Abstract :
This article gravitates toward analyzing the vibration response of a moving beam functionally graded (FG) in two orthogonal directions. In order to gain a high level of accuracy, higher-order shear deformation theory for beam structures is employed to define the displacement field and determine the system’s governing differential equations. Also, this study considers the effect of different sets of boundary conditions to find the oscillatory response of the system in a more comprehensive way. This matter leads the authors to utilize the differential quadrature method (DQM) as a numerical solution to solve the governing differential equations. The accuracy of the applied solution is examined and confirmed by comparing its results with those available in the literature. In this study, the natural frequency of a moving beam with varying properties along both the axial and transverse directions was investigated. The study examined the influence of boundary conditions, gradational properties, axial velocity, and the parameter L/h on the natural frequency. One of the applicable results for related industries is that designers should pay special attention to the FG power index, and the type of boundary conditions of the moving beams. This study provides novel insights to adjust design factors in order to gain a high level of vibration response for moving loads.
[1] Sekkal M, Bouiadjra RB, Benyoucef S, Tounsi A, Ghazwani MH, Alnujaie A. Effect of material distribution on bending and buckling response of a bidirectional FG beam exposed to a combined transverses and variable axially loads. Mechanics Based Design of Structures and Machines 2023;0:1–20. https://doi.org/10.1080/15397734.2023.2172032.
[2] Chami GMB, Kahil A, Hadji L. Influence of porosity on the fundamental natural frequencies of FG sandwich beams. Materials Today: Proceedings 2022;53:107–12.
[3] Zhao S, Zhang Y, Zhang Y, Yang J, Kitipornchai S. Vibrational characteristics of functionally graded graphene origami-enabled auxetic metamaterial beams based on machine learning assisted models. Aerospace Science and Technology 2022;130:107906.
[4] Liu Z, Yan X, Qi M, Huang D, Zhang X, Lin L. Electrostatic flapping-wing actuator with improved lift force by the pivot-spar bracket design. Sensors and Actuators A: Physical 2018;280:295–302.
[5] Bouzidi I, Hadjoui A, Fellah A. Dynamic analysis of functionally graded rotor-blade system using the classical version of the finite element method. Mechanics Based Design of Structures and Machines 2021;49:1080–108.
[6] Murari B, Zhao S, Zhang Y, Yang J. Static and dynamic instability of functionally graded graphene origami-enabled auxetic metamaterial beams with variable thickness in fluid. Ocean Engineering 2023;280:114859.
[7] Zhou X, Jing L. Large deflection response of sandwich beams with layered-gradient foam cores subjected to low-velocity impact. International Journal of Impact Engineering 2023;172:104429.
[8] Pradhan N, Sarangi S. Analysis of functionally graded beams subjected to Thermo-mechanical loading using finite element method. Materials Today: Proceedings 2018;5:19490–6.
[9] Kar UK, Srinivas J. Vibration analysis of Bi-directional FG-GNPs reinforced rotating micro-beam under Thermo-mechanical loading. Materials Today: Proceedings 2023;78:752–9.
[10] Meksi A, Sekkal M, Bouiadjra RB, Benyoucef S, Tounsi A. Assessing the effect of temperature-dependent properties on the dynamic behavior of FG porous beams rested on variable elastic foundation. Structural Engineering and Mechanics 2023;85:717.
[11] Jiang F, Ding Y, Song Y, Geng F, Wang Z. CFRP strengthening of fatigue cracks at U-rib to diaphragm welds in orthotropic steel bridge decks: Experimental study, optimization, and decision-making. vol. 43, Elsevier; 2022, p. 1216–29.
[12] Pang F, Gao C, Li H, Jia D, Wang X, Miao X. Vibration analysis of FG beams under arbitrary load with general boundary conditions: Theoretical and experimental comparative research. Thin-Walled Structures 2022;179:109605.
[13] Simonetti SK, Turkalj G, Lanc D. Thermal buckling analysis of thin-walled closed section FG beam-type structures. Thin-Walled Structures 2022;181:110075.
[14] Genel ÖE, Tüfekci E. Bending-bending coupled static analysis of functionally graded and porous pretwisted cantilever beams using initial values method. Mechanics Based Design of Structures and Machines 2023;0:1–24. https://doi.org/10.1080/15397734.2023.2185632.
[15] Wu K, Liu Z, Ding Q, Gu F, Ball A. Torsional vibration responses of the engine crankshaft-gearbox coupled system with misfire and breathing slant crack based on instantaneous angular speed. Mechanical Systems and Signal Processing 2022;173:109052.
[16] Scheidl J, Vetyukov Y. Review and perspectives in applied mechanics of axially moving flexible structures. Acta Mechanica 2023;234:1331–64.
[17] Phi LT, Nguyen T-T, Kang J, Lee J. Vibration and buckling optimization of thin-walled functionally graded open-section beams. Thin-Walled Structures 2022;170:108586.
[18] Zhang L, Xu Z, Gao M, Xu R, Wang G. Static, dynamic and buckling responses of random functionally graded beams reinforced by graphene platelets. Engineering Structures 2023;291:116476.
[19] Hirannaiah S, Swaminathan K, Rajanna T. Thermo-mechanical vibration and buckling analysis of porous FG sandwich plates with geometric discontinuity based on physical neutral surface. Mechanics of Advanced Materials and Structures 2023:1–25.
[20] Alsheyab MA, Khasawneh MA. Evaluating fatigue performance of Bailey asphalt mixtures containing natural river sand at varied strain and air void levels. Mechanics of Advanced Materials and Structures 2023:1–12.
[21] Abo-Bakr H, Abo-Bakr R, Mohamed S, Eltaher M. Weight optimization of axially functionally graded microbeams under buckling and vibration behaviors. Mechanics Based Design of Structures and Machines 2023;51:213–34.
[22] Li C, Shen H-S, Yang J. Design and nonlinear dynamics of FG curved sandwich beams with self-adapted auxetic 3D double-V meta-lattice core. Engineering Structures 2022;272:115023.
[23] Momeni S, Zabihollah A, Behzad M. Effects of size and location of magnetorheological segments on random vibration response of laminated composite beams using an N-layer of layerwise theory. Journal of Thermoplastic Composite Materials 2023:08927057231154427.
[24] Murari B, Zhao S, Zhang Y, Yang J. Graphene origami-enabled auxetic metamaterial tapered beams in fluid: Nonlinear vibration and postbuckling analyses via physics-embedded machine learning model. Applied Mathematical Modelling 2023.
[25] Lezgy-Nazargah M, Karamanli A, Vo TP. Bending, buckling and free vibration analyses of shallow-to-deep FG curved sandwich beams using a global–local refined shear deformation theory. vol. 52, Elsevier; 2023, p. 568–81.
[26] Yapicioglu A, Dincer I. A newly developed renewable energy driven multigeneration system with hot silica sand storage for power, hydrogen, freshwater and cooling production. Sustainable Energy Technologies and Assessments 2023;55:102938.
[27] Palmquist A, Jolic M, Hryha E, Shah FA. Complex geometry and integrated macro-porosity: Clinical applications of electron beam melting to fabricate bespoke bone-anchored implants. Acta Biomaterialia 2023;156:125–45.
[28] Rouf S, Malik A, Raina A, Haq MIU, Naveed N, Zolfagharian A, et al. Functionally graded additive manufacturing for orthopedic applications. Journal of Orthopaedics 2022;33:70–80.
[29] Lee J-H, Lee H-L, Park I-Y, On S-W, Byun S-H, Yang B-E. Effectiveness of creating digital twins with different digital dentition models and cone-beam computed tomography. Scientific Reports 2023;13:10603.
[30] Bazmara M, Silani M, Mianroodi M. Physics-informed neural networks for nonlinear bending of 3D functionally graded beam. vol. 49, Elsevier; 2023, p. 152–62.
[31] Nguyen-Xuan H, Tran KQ, Thai CH, Lee J. Modelling of functionally graded triply periodic minimal surface (FG-TPMS) plates. Composite Structures 2023;315:116981.
[32] Goker F, Russillo A, Baj A, Giannì A, Beltramini G, Rossi D, et al. Custom made/patient specific alloplastic total temporomandibular joint replacement in immature patient: a case report and short review of literature. European Review for Medical and Pharmacological Sciences 2022;26:26–34.
[33] Tabarrok B, Leech C, Kim Y. On the dynamics of an axially moving beam. Journal of the Franklin Institute 1974;297:201–20.
[34] Kong L, Parker R. Approximate eigensolutions of axially moving beams with small flexural stiffness. Journal of Sound and Vibration 2004;276:459–69.
[35] Öz H, Pakdemirli M, Boyacı H. Non-linear vibrations and stability of an axially moving beam with time-dependent velocity. International Journal of Non-Linear Mechanics 2001;36:107–15.
[36] Beni YT. Size dependent coupled electromechanical torsional analysis of porous FG flexoelectric micro/nanotubes. Mechanical Systems and Signal Processing 2022;178:109281.
[37] Beni ZT, Beni YT. Dynamic stability analysis of size-dependent viscoelastic/piezoelectric nano-beam. International Journal of Structural Stability and Dynamics 2022;22:2250050.
[38] Sze K, Chen S and, Huang J. The incremental harmonic balance method for nonlinear vibration of axially moving beams. Journal of Sound and Vibration 2005;281:611–26.
[39] Chen S, Huang J, Sze K. Multidimensional Lindstedt–Poincaré method for nonlinear vibration of axially moving beams. Journal of Sound and Vibration 2007;306:1–11.
[40] Ding H, Chen L-Q. Natural frequencies of nonlinear vibration of axially moving beams. Nonlinear Dynamics 2011;63:125–34.
[41] Karimipour I, Beni YT. Nonlinear dynamic analysis of nonlocal composite laminated toroidal shell segments subjected to mechanical shock. Communications in Nonlinear Science and Numerical Simulation 2022;106:106105.
[42] Larbi LO, Kaci A, Houari MSA, Tounsi A. An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams#. Mechanics Based Design of Structures and Machines 2013;41:421–33.
[43] Şimşek M. Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions. Composite Structures 2016;149:304–14. https://doi.org/10.1016/j.compstruct.2016.04.034.
[44] Reddy J, Chin C. Thermomechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses 1998;21:593–626.
[45] Sadd MH. Elasticity: theory, applications, and numerics. Academic Press; 2009.
[46] Miraliyari O, Jafari Mehrabadi S, Najafizadeh M. Nonlinear Free Vibration Analysis of Functionally Graded Sandwich Beam with Magnetorheological Fluid Core Using Timoshenko Beam Theory. Journal of Solid Mechanics 2023;15:120–43.
[47] Ghorbanpour Arani A, Pakize M, Irani Rahaghi M, Khoddami Maraghi Z, Niknejad S. Vibrational Study on Multilayer Sandwich Plates: Porous FGM Core, Nanocomposite and Piezoelectric Face Sheets. Journal of Solid Mechanics 2022.
[48] Karbasizadeh A, Ghorbanpour Arani A, Niknejad S, Khoddami Maraghi Z. Free Damped Vibration Analysis of Sandwich Plates with CNT-Reinforced MRE Core and Laminated Three-Phase Polymer/GPL/Fiber Face Sheets. Journal of Solid Mechanics 2023.
[49] Mihankhah A, Khoddami Maraghi Z, Ghorbanpour Arani A, Niknejad S. Vibrations of Multi-layer Beam with Nanocomposite face sheets Reinforced with Graphene Platelets and Porous Core. Journal of Solid Mechanics 2023.
[50] Khosravi M, Jafari Mehrabadi S, Malekzadeh Fard K. Vibration Behavior of Thick Sandwich Composite Beam with Flexible Core Resting on Incompressible Fluid Foundation. Journal of Solid Mechanics 2023;15:50–65.
[51] Tornabene F, Fantuzzi N, Ubertini F, Viola E. Strong formulation finite element method based on differential quadrature: a survey. Applied Mechanics Reviews 2015;67.
[52] Şimşek M. Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions. Composite Structures 2015;133:968–78. https://doi.org/10.1016/j.compstruct.2015.08.021.