Dynamic characteristics of cracked simply supported bidirectional functionally graded Rayleigh beam

Karamanlı, 2018, Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory, Compos. Struct., 189, 127, 10.1016/j.compstruct.2018.01.060 Ihmood, 2022, Free vibration of new type functionally graded materials pipe conveying fluid using differential quadrature method, AIP Conf. Proc., 2386, 10.1063/5.0066803 Li, 2014, Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories, Appl. Math. Mech. (English Ed., 35, 591, 10.1007/s10483-014-1815-6 Elaikh, 2020, Free vibration and flutter stability of interconnected double graded micro pipes system conveying fluid, IOP Conf. Ser. Mater. Sci. Eng., 928, 10.1088/1757-899X/928/2/022128 Aydogdu, 2008, Semi-inverse method for vibration and buckling of axially functionally graded beams, J. Reinforc. Plast. Compos., 27, 683, 10.1177/0731684407081369 Talib, 2019, Stability of FG material micro-pipe conveying fluid, 10, 211 Aydogdu, 2007, Free vibration analysis of functionally graded beams with simply supported edges, Mater. Des., 28, 1651, 10.1016/j.matdes.2006.02.007 Mohanty, 2012, Static and dynamic stability analysis of a functionally graded timoshenko beam, Int. J. Struct. Stabil. Dynam., 12, 1, 10.1142/S0219455412500253 Wattanasakulpong, 2012, Free vibration analysis of functionally graded beams with general elastically end constraints by DTM, World J. Mech., 2, 297, 10.4236/wjm.2012.26036 Thai, 2012, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, Int. J. Mech. Sci., 62, 57, 10.1016/j.ijmecsci.2012.05.014 Civalek, 2021, Forced vibration analysis of composite beams reinforced by carbon nanotubes, Nanomaterials, 11, 1, 10.3390/nano11030571 Al Rjoub, 2017, Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method, KSCE J. Civ. Eng., 21, 792, 10.1007/s12205-016-0149-6 Ziou, 2016, Numerical modelling of a Timoshenko FGM beam using the finite element method, Int. J. Struct. Eng., 7, 239, 10.1504/IJSTRUCTE.2016.077719 Lee, 2017, Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, Int. J. Mech. Sci., 122, 1, 10.1016/j.ijmecsci.2017.01.011 Akgöz, 2015, A novel microstructure-dependent shear deformable beam model, Int. J. Mech. Sci., 99, 10, 10.1016/j.ijmecsci.2015.05.003 Banerjee, 2018, Free vibration of functionally graded beams and frameworks using the dynamic stiffness method, J. Sound Vib., 422, 34, 10.1016/j.jsv.2018.02.010 Bonthu, 2023, 3D printed functionally graded foams response under transverse load, Results Mater, 19 Rahmani, 2020, Finite element analysis of functionally graded beams using different beam theories, Civ. Eng. J., 6, 2086, 10.28991/cej-2020-03091604 Şimşek, 2016, Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions, Compos. Struct., 149, 304, 10.1016/j.compstruct.2016.04.034 Alshorbagy, 2011, Free vibration characteristics of a functionally graded beam by finite element method, Appl. Math. Model., 35, 412, 10.1016/j.apm.2010.07.006 Lu, 2020, Nonlinear parametric dynamics of bidirectional functionally graded beams, Shock Vib., 2020 Rajasekaran, 2018, Free vibration analysis of bi-directional functionally graded single/multi-cracked beams, Int. J. Mech. Sci., 144, 341, 10.1016/j.ijmecsci.2018.06.004 Zhao, 2019, Free vibration analysis of cracked Euler-Bernoulli beam by laplace transformation considering stiffness reduction, Rom. J. Acoust. Vib., 16, 166 Tan, 2017, Direct and inverse problems on free vibration of cracked multiple I-section beam with different boundary conditions, Adv. Mech. Eng., 9, 1, 10.1177/1687814017737261 Swamidas, 2004, Identification of cracking in beam structures using timoshenko and euler formulations, J. Eng. Mech., 130, 1297, 10.1061/(ASCE)0733-9399(2004)130:11(1297) Akbaş, 2016, Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory, Int. J. Struct. Stabil. Dynam., 16, 1 Lin, 2004, Direct and inverse methods on free vibration analysis of simply supported beams with a crack, Eng. Struct., 26, 427, 10.1016/j.engstruct.2003.10.014 Akbas, 2017, Forced vibration analysis of functionally graded nanobeams, Int. J. Appl. Mech., 9, 10.1142/S1758825117501009 Yan, 2011, Forced vibration of edge-cracked functionally graded beams due to a transverse moving load, Procedia Eng., 14, 3293, 10.1016/j.proeng.2011.07.416 Akbaş, 2018, Bending of a cracked functionally graded nanobeam, Adv. Nano Res., 6, 219 Van Lien, 2017, Free vibration analysis of multiple cracked functionally graded timoshenko beams, Lat. Am. J. Solid. Struct., 1752, 10.1590/1679-78253693 Shabani, 2020, Free vibration analysis of functionally graded beams with cracks, J. Appl. Comput. Mech., 6, 908 Akbaş, 2018, Forced vibration analysis of cracked nanobeams, J. Brazilian Soc. Mech. Sci. Eng., 40, 39, 10.1007/s40430-018-1315-1 Akbaş, 2013, Free vibration characteristics of edge cracked functionally graded beams by using finite element method, Int. J. Eng. Trends Technol., 4, 4590 Van Lien, 2019, A new form of frequency equation for functionally graded timoshenko beams with arbitrary number of open transverse cracks, Iran. J. Sci. Technol. - Trans. Mech. Eng., 43, 235, 10.1007/s40997-018-0152-2 Elaikh, 2022, Investigation of transverse vibration characteristics of cracked axially moving functionally graded beam under thermal load, Trends Sci, 19, 10.48048/tis.2022.1349 Agboola, 2022, Effect of mass per unit length on freely vibrating simply supported Rayleigh beam, WSEAS Trans. Fluid Mech., 17, 173, 10.37394/232013.2022.17.17 Akbaş, 2016, Wave propagation in edge cracked functionally graded beams under impact force, JVC/Journal Vib. Control, 22, 2443, 10.1177/1077546314547531 Nejad, 2016, Non-local analysis of free vibration of bi-directional functionally graded Euler-Bernoulli nano-beams, Int. J. Eng. Sci., 105, 1, 10.1016/j.ijengsci.2016.04.011 Zhu, 2019, Vibration and stability analysis of a simply-supported Rayleigh beam with spinning and axial motions, Appl. Math. Model., 66, 362, 10.1016/j.apm.2018.09.021 Bachaya, 2021, Transverse vibration of cracked graded Rayleigh beam with axial motion, Univ. Thi-Qar J. Eng. Sci. Shariati, 2020, Stability and dynamics of viscoelastic moving Rayleigh beams with an asymmetrical distribution of material parameters, Symmetry (Basel), 12, 586, 10.3390/sym12040586 Fernández-Sáez, 1999, Approximate calculation of the fundamental frequency for bending vibrations of cracked beams, J. Sound Vib., 225, 345, 10.1006/jsvi.1999.2251 Zhu, 2020, Vibrational power flow analysis of cracked functionally graded beams, Thin-Walled Struct., 150 Van Lien, 2019, Free and forced vibration analysis of multiple cracked fgm multi span continuous beams using dynamic stiffness method, Lat. Am. J. Solid. Struct., 16 Gee, 2022, Undamped free vibration analysis of functionally graded beams: a dynamic finite element approach, Appl. Mech., 3, 1223, 10.3390/applmech3040070 Pradhan, 2018, Implementation of numerical approximations in studying vibration of functionally graded beams, Int. J. Dyn. Control, 6, 1023, 10.1007/s40435-017-0375-x Şimşek, 2009, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Compos. Struct., 90, 465, 10.1016/j.compstruct.2009.04.024