Login Register Cart 0
Generic placeholder image

Recent Patents on Mechanical Engineering

Editor-in-Chief

ISSN (Print): 2212-7976
ISSN (Online): 1874-477X

Back
Journal Home About Journal Editorial Board Journal Insight Current Issue Volumes/Issues
Subscribe
Research Article

Analytical Modeling on Vibration Analysis of Cracked Functionally Graded Plate Submerged in Fluid

Author(s): Shashank Soni*, Nitin K. Jain and Prasad V. Joshi

Volume 12, Issue 3, 2019

Page: [240 - 247] Pages: 8

DOI: 10.2174/2212797612666190531115429

Price: $65

Abstract

Background: It is established that the vibration response of submerged structures is quite different than that calculated in vacuum. Therefore, the study of vibration characteristics of submerged plate structures is important for safety and its designing purpose.

Objective: To investigate the fundamental frequency of partially cracked Functionally Graded (FG) submerged plate based on analytical approach.

Methods: The governing differential equation of the cracked-submerged plate is derived based on Kirchhoff’s thin classical plate theory in conjunction with the potential flow theory. The line spring model is used to incorporate the effect of crack in the form of additional bending whereas the effect of fluid medium is incorporated in form fluids forces associated with inertial effects of its surrounding fluids. The Bernoulli’s equation and velocity potential function are used to define the fluid forces acting on plate surface.

Results: An approximate solution for governing equation of coupled fluid-plate system is obtained by using the Galerkin’s method. For validation of the present results, they are compared with the existing results of the previous published work, which are in good agreements. New results for natural frequencies as affected by gradient index, crack length, level of submergence and immersed depth of plate are presented for Simply Supported (SSSS) boundary condition.

Conclusion: It has been concluded that the presence of crack and fluidic medium significantly affect the natural frequencies of the plate. It is observed that the increase in the length of crack and level of submergence decreases the fundamental frequency. In this paper, few patents have been discussed.

Keywords: Classical plate theory, crack, FGM plate, fluid-plate interaction, vibration, virtual added mass.

« Previous Next »
[1]
Lamb H. On the vibrations of an elastic plate in contact with water. Proc R Soc Lond A 2016; 98: 205-16.
[http://dx.doi.org/10.1098/rspa.1920.0064]
[2]
Powell JH, Roberts T. On the frequency of vibration of circular diaphragms. Proc Phys Soc Lond 1922; 35: 170-82.
[http://dx.doi.org/10.1088/1478-7814/35/1/321]
[3]
Haddara MR, Cao S. A Study of the dynamic response of submerged rectangular flat plates. Mar Structures 1996; 9: 913-33.
[http://dx.doi.org/10.1016/0951-8339(96)00006-8]
[4]
Lindholm U, Kana D, Chu W, Abramson H. elastic vibration characteristics of cantilever plates in water. J Sh Res 1965; 9: 11-36.
[5]
Muthuveerappan G, Ganesan N, Veluswami MA. A note on vibration of a cantilever plate immersed. J Sound Vibrat 1979; 63(3): 385-91.
[http://dx.doi.org/10.1016/0022-460X(79)90681-3]
[6]
Kwak MK. Hydroelastic vibration of rectangular plates. J Appl Mech 1996; 63: 110-5.
[http://dx.doi.org/10.1115/1.2787184]
[7]
Fu Y, Price WG. Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid. J Sound Vibrat 1987; 118: 495-513.
[http://dx.doi.org/10.1016/0022-460X(87)90366-X]
[8]
Kwak MK, Kim KC. Axisymmetric vibration of circular plates in contact with fluid. J Sound Vibrat 1991; 146: 381-9.
[http://dx.doi.org/10.1016/0022-460X(91)90696-H]
[9]
Amabili M, Frosali G, Kwak MK. Free vibrations of annular plates coupled with fluids. J Sound Vibrat 1996; 191: 825-46.
[http://dx.doi.org/10.1006/jsvi.1996.0158]
[10]
Khorshid K, Farhadi S. Free vibration analysis of a laminated composite rectangular plate in contact with a bounded fluid. Compos Struct 2013; 104: 176-86.
[http://dx.doi.org/10.1016/j.compstruct.2013.04.005]
[11]
Chang T. Deterministic and random vibration analysis of fluid-contacting transversely isotropic magneto-electro-elastic plates. Comput Fluids 2013; 84: 247-54.
[http://dx.doi.org/10.1016/j.compfluid.2013.06.009]
[12]
Chang TP. On the natural frequency of transversely isotropic magneto-electro-elastic plates in contact with fluid. Appl Math Model 2013; 37: 2503-15.
[http://dx.doi.org/10.1016/j.apm.2012.06.016]
[13]
Vu VH, Thomas M, Lakis AA, Marcouiller L. Effect of added mass on submerged vibrated plates. Proceedings of the 25th Seminar on Machinery Vibration. St. John, Canada January. 2007.
[14]
Robinson NJ, Palmer SC. A modal analysis of a rectangular plate floating on an incompressible liquid. J Sound Vibrat 1990; 142: 453-60.
[http://dx.doi.org/10.1016/0022-460X(90)90661-I]
[15]
Wang Y. Study on the dynamic behavior of axially moving rectangular plates partially submersed in fluid. Acta Mech Solida Sinica 2015; 28: 706-21.
[http://dx.doi.org/10.1016/S0894-9166(16)30011-8]
[16]
Facci AL, Porfiri M. Analysis of three-dimensional effects in oscillating cantilevers immersed in viscous fluids. J Fluids Structures 2013; 38: 205-22.
[http://dx.doi.org/10.1016/j.jfluidstructs.2012.11.006]
[17]
Kramer MR, Liu Z, Young YL. Free vibration of cantilevered composite plates in air and in water. Compos Struct 2013; 95: 254-63.
[http://dx.doi.org/10.1016/j.compstruct.2012.07.017]
[18]
Seung D, Hee B, Vladimir N, Muk T. Natural vibration analysis of rectangular bottom plate structures in contact with fluid. Ocean Eng 2015; 103: 171-9.
[http://dx.doi.org/10.1016/j.oceaneng.2015.04.078]
[19]
McLachlan NW. The accession to inertia of flexible discs vibrating in a fluid. Proc Phys Soc 1932; 44: 546-55.
[http://dx.doi.org/10.1088/0959-5309/44/5/303]
[20]
Montero de Espinosa F, Gallego-Juárez JA. On the resonance frequencies of water-loaded circular plates. J Sound Vibrat 1984; 94: 217-22.
[http://dx.doi.org/10.1016/S0022-460X(84)80031-0]
[21]
Lakis AA, Paidoussis MP. Free vibration of cylindrical shells partially filled with liquid. J Sound Vibrat 1971; 19(1): 1-5.
[http://dx.doi.org/10.1016/0022-460X(71)90417-2]
[22]
Ergin A, Ugurlu B. Linear vibration analysis of cantilever plates partially submerged in fluid. J Fluids Structures 2003; 17: 927-39.
[http://dx.doi.org/10.1016/S0889-9746(03)00050-1]
[23]
Meylan M. The forced vibration of a thin plate floating on an infinite liquid. J Sound Vibrat 1997; 205: 1-18.
[http://dx.doi.org/10.1006/jsvi.1997.1033]
[24]
Kerboua Y, Lakis AA, Thomas M, Marcouiller L. Vibration analysis of rectangular plates coupled with fluid. Appl Math Model 2008; 32: 2570-86.
[http://dx.doi.org/10.1016/j.apm.2007.09.004]
[25]
Li J, Guo XH, Luo J, Li HY, Wang YQ. Analytical study on inherent properties of a unidirectional vibrating steel strip partially immersed in fluid. Shock and Vib 2013; 20: 793-807.
[http://dx.doi.org/10.1155/2013/827596]
[26]
Hosseini-Hashemi S, Karimi M, Rokni H. Natural frequencies of rectangular Mindlin plates coupled with stationary fluid. Appl Math Model 2012; 36: 764-78.
[http://dx.doi.org/10.1016/j.apm.2011.07.007]
[27]
Liu T, Wang K, Dong QW, Liu MS. Hydroelastic natural vibrations of perforated plates with cracks. Procedia Eng 2009; 1: 129-33.
[http://dx.doi.org/10.1016/j.proeng.2009.06.030]
[28]
Si XH, Lu WX, Chu FL. Modal analysis of circular plates with radial side cracks and in contact with water on one side based on the Rayleigh - Ritz method. J Sound Vibrat 2012; 331: 231-51.
[http://dx.doi.org/10.1016/j.jsv.2011.08.026]
[29]
Si X, Lu W, Chu F. Dynamic analysis of rectangular plates with a single side crack and in contact with water on one side based on the Rayleigh - Ritz method. J Fluids Structures 2012; 34: 90-104.
[http://dx.doi.org/10.1016/j.jfluidstructs.2012.06.005]
[30]
Rezaei AS, Saidi AR. Exact solution for free vibration of thick rectangular plates made of porous materials. Compos Struct 2015; 134: 1051-61.
[http://dx.doi.org/10.1016/j.compstruct.2015.08.125]
[31]
Hernández E. Approximation of the vibration modes of a plate and shells coupled with a fluid. J Appl Mech 2006; 73: 1005-10.
[http://dx.doi.org/10.1115/1.2173675]
[32]
Sharma S, Gupta US, Singhal P. Vibration analysis of non-homogeneous orthotropic rectangular plates of variable thickness resting on winkler foundation. J Appl Sci Eng 2012; 15: 291-300.
[33]
Liew KM, Huang YQ, Reddy JN. Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput Methods Appl Mech Eng 2003; 192: 2203-22.
[http://dx.doi.org/10.1016/S0045-7825(03)00238-X]
[34]
Reddy JN, Phan ND. Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J Sound Vibrat 1985; 98: 157-70.
[http://dx.doi.org/10.1016/0022-460X(85)90383-9]
[35]
Reddy JN, Huang CL. Large amplitude free vibrations of annular plates of varying thickness. J Sound Vibrat 1981; 79: 387-96.
[http://dx.doi.org/10.1016/0022-460X(81)90317-5]
[36]
Panda HS, Sahu SK, Parhi PK. Hygrothermal effects on the free vibration on delaminated woven fiber composite plates-numerical and experimental results. Compos Struct 2013; 96: 502-13.
[http://dx.doi.org/10.1016/j.compstruct.2012.08.057]
[37]
Cheng ZQ, Reddy JN. Green’s functions for infinite and semi-infinite anisotropic thin plates. J Appl Mech 2003; 70: 260-71.
[http://dx.doi.org/10.1115/1.1533806]
[38]
Serduoun S, Cherif S, Sebbane O. Free vibration analysis sandwich plates coupled with fluid. IJERT 2015; 4: 43-51.
[39]
Gupta US, Sharma S, Singhal P. Vibration analysis of non-homogeneous rectangular orthotropic plates. J Appl Sci Eng 2015; 2: 202-11.
[40]
Sih GC. Transient hygrothermal stresses in plates with and without cavities. Fibre Sci Technol 1983; 18: 181-201.
[http://dx.doi.org/10.1016/0015-0568(83)90040-4]
[41]
Soldatos KP. A refined laminated plate and shell theory with applications. J Sound Vibrat 1991; 144: 109-29.
[http://dx.doi.org/10.1016/0022-460X(91)90736-4]
[42]
Shimpi RP, Patel HG. Free vibrations of plate using two variable refined plate theory. J Sound Vibrat 2006; 296: 979-99.
[http://dx.doi.org/10.1016/j.jsv.2006.03.030]
[43]
Rice J, Levy N. The part-through surface crack in an elastic plate. J Appl Mech 1972; 1: 185-94.
[http://dx.doi.org/10.1115/1.3422609]
[44]
Delale F, Erdogan F. Line-spring model for surface cracks in a reissner plate. Int J Eng Sci 1981; 19: 1331-40.
[http://dx.doi.org/10.1016/0020-7225(81)90016-1]
[45]
Israr A, Cartmell MP, Manoach E, Trendafilova I, Ostachowicz W, Krawczuk M, et al. Analytical modelling and vibration analysis of cracked rectangular plates with different loading and boundary conditions. J Appl Mech 2009; 76: 1-9.
[http://dx.doi.org/10.1115/1.2998755]
[46]
Joshi PV, Jain NK, Ramtekkar GD. Analytical modeling for vibration analysis of thin rectangular orthotropic/functionally graded plates with an internal crack. J Sound Vibrat 2015; 344: 377-98.
[http://dx.doi.org/10.1016/j.jsv.2015.01.026]
[47]
Gupta A, Jain NK, Salhotra R, Joshi PV. Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory. Int J Mech Sci 2015; 100: 269-82.
[http://dx.doi.org/10.1016/j.ijmecsci.2015.07.004]
[48]
Abrate S. Functionally graded plates behave like homogeneous plates. Compos, Part B Eng 2008; 39: 151-8.
[http://dx.doi.org/10.1016/j.compositesb.2007.02.026]
[49]
Woo J, Meguid SA, Ong LS. Nonlinear free vibration behavior of functionally graded plates. J Sound Vibrat 2006; 289: 595-611.
[http://dx.doi.org/10.1016/j.jsv.2005.02.031]
[50]
Hosseini-Hashemi S, Rokni Damavandi Taher H, Akhavan H, Omidi M. Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl Math Model 2010; 34: 1276-91.
[http://dx.doi.org/10.1016/j.apm.2009.08.008]
[51]
Talha M, Singh BN. Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl Math Model 2010; 34: 3991-4011.
[http://dx.doi.org/10.1016/j.apm.2010.03.034]
[52]
Reddy J, Cheng Z. Frequency of functionally graded plates with three-dimensional asymptotic approach. J Eng Mech 2003; 129: 896-900.
[http://dx.doi.org/10.1061/(ASCE)0733-9399(2003)129:8(896)]
[53]
Joshi PV, Jain NK, Ramtekkar GD. Analytical modeling and vibration analysis of internally cracked rectangular plates. J Sound Vibrat 2014; 333: 5851-64.
[http://dx.doi.org/10.1016/j.jsv.2014.06.028]
[54]
Joshi PV, Jain NK, Ramtekkar GD. Effect of thermal environment on free vibration of cracked rectangular plate: An analytical approach. Thin-walled Struct 2015; 91: 38-49.
[http://dx.doi.org/10.1016/j.tws.2015.02.004]
[55]
Joshi PV, Jain NK, Ramtekkar GD, Virdi GS. Vibration and buckling analysis of partially cracked thin orthotropic rectangular plates in thermal environment. Thin-walled Struct 2016; 109: 143-58.
[http://dx.doi.org/10.1016/j.tws.2016.09.020]
[56]
Soni S, Jain NK, Joshi PV. Vibration analysis of partially cracked plate submerged in fluid. J Sound Vibrat 2018; 412: 28-57.
[http://dx.doi.org/10.1016/j.jsv.2017.09.016]
[57]
Soni S, Jain NK, Joshi PV. Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid. Nonlinear Dyn 2017; 90(1): 137-70.
[http://dx.doi.org/10.1007/s11071-017-3652-5]
[58]
Natarajan S, Chakraborty S, Thangavel M, Bordas S, Rabczuk T. Size-dependent free flexural vibration behavior of functionally graded nanoplates. Comput Mater Sci 2012; 65: 74-80.
[http://dx.doi.org/10.1016/j.commatsci.2012.06.031]
[59]
Natarajan S, Baiz PM, Bordas S, Rabczuk T, Kerfriden P. Natural frequencies of cracked functionally graded material plates by the extended finite element method. Compos Struct 2011; 93: 3082-92.
[http://dx.doi.org/10.1016/j.compstruct.2011.04.007]
[60]
Natarajan S, Chakraborty S, Ganapathi M, Subramanian M. A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method. Eur J Mech A, Solids 2014; 44: 136-47.
[http://dx.doi.org/10.1016/j.euromechsol.2013.10.003]
[61]
Kim YW. Temperature dependent vibration analysis of functionally graded rectangular plates. J Sound Vibrat 2005; 284: 531-49.
[http://dx.doi.org/10.1016/j.jsv.2004.06.043]
[62]
Huang CS, Yang PJ, Chang MJ. Three-dimensional vibration analyses of functionally graded material rectangular plates with through internal cracks. Compos Struct 2012; 94: 2764-76.
[http://dx.doi.org/10.1016/j.compstruct.2012.04.003]
[63]
Vel SS, Batra RC. Three-dimensional exact solution for the vibration of functionally graded rectangular plates. J Sound Vibrat 2004; 272: 703-30.
[http://dx.doi.org/10.1016/S0022-460X(03)00412-7]
[64]
Tajeddini V, Ohadi A, Sadighi M. Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation. Int J Mech Sci 2011; 53: 300-8.
[http://dx.doi.org/10.1016/j.ijmecsci.2011.01.011]
[65]
Mohammadimehr M, Salemi M, Rousta Navi B. Bending, buckling and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM. Compos Struct 2016; 138: 361-80.
[http://dx.doi.org/10.1016/j.compstruct.2015.11.055]
[66]
Natarajan S, Ferreira AJM, Bordas S, Carrera E, Cinefra M, Zenkour AM. Analysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method. Math Probl Eng 2014; 20: 1-13.
[http://dx.doi.org/10.1155/2014/247932]
[67]
Valizadeh N, Natarajan S, Gonzalez-Estrada OA, Rabczuk T, Bui TQ, Bordas SPA. NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter. Compos Struct 2013; 99: 309-26.
[http://dx.doi.org/10.1016/j.compstruct.2012.11.008]
[68]
Thai H, Choi D. A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates. Compos Struct 2013; 101: 332-40.
[http://dx.doi.org/10.1016/j.compstruct.2013.02.019]
[69]
Jha DK, Kant T, Singh RK. Free vibration response of functionally graded thick plates with shear and normal deformations effects. Compos Struct 2013; 96: 799-823.
[http://dx.doi.org/10.1016/j.compstruct.2012.09.034]
[70]
Vel SS, Batra RC. Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J 2002; 40: 1421-33.
[http://dx.doi.org/10.2514/2.1805]
[71]
Natarajan S, Baiz PM, Ganapathi M, Kerfriden P, Bordas S. Linear free flexural vibration of cracked functionally graded plates in thermal environment. Comput Struc 2011; 89: 1535-46.
[http://dx.doi.org/10.1016/j.compstruc.2011.04.002]
[72]
Jha DK, Kant T, Singh RK. Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates. Nucl Eng Des 2012; 250: 8-13.
[http://dx.doi.org/10.1016/j.nucengdes.2012.05.001]
[73]
Reddy JN. Analysis of functionally graded plates. Int J Numer Methods Eng 2000; 47: 663-84.
[http://dx.doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3< 663:AID-NME787>3.0.CO;2-8]
[74]
Chakraverty S, Pradhan KK. Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions. Aerosp Sci Technol 2014; 36: 132-56.
[http://dx.doi.org/10.1016/j.ast.2014.04.005]
[75]
Jha DK, Kant T, Singh RK. Free vibration of functionally graded plates with a higher-order shear and normal deformation theory. Int J Struct Stab Dyn 2013; 131350004
[http://dx.doi.org/ 10.1142/S0219455413500041]
[76]
Jha DK, Kant T, Singh RK. A critical review of recent research on functionally graded plates. Compos Struct 2013; 96: 833-49.
[http://dx.doi.org/10.1016/j.compstruct.2012.09.001]
[77]
Kim D-M. Vibration-lead plate for flat type speaker, mounted between voice coil plate and vibration plate. US20130161122 (2011)
[78]
Kim D-M. Flat type speaker having vibration-lead plate attached on top of vibration plate. US9271060 (2016)
[79]
Craft C, Kemeny Z. Trowel-Grinder-Polisher Machines. US20180369981 (2018).
[80]
Li YB, Yao MH, Zhang W. Multi-mode vibration power generator. AU2015208446 (2015).
[81]
Jeongh SH, Oh WY, Jang GH, Nam JH, Kim YJ. Vibration generating device. US9833812 (2015).
[82]
Leissa AW. Vibration of Plates, US Government Printing Office, NASA SP-160, 1969
[83]
Aksel B, Erdogan F. Interaction of part-through cracks in a flat plate, National Aeronautics and Space Administration Contractor Report, US NASA-CR- 177926, NAS 1.26:177926, April 1985.

Rights & Permissions Print Cite
Article Metrics
17
1
© 2024 Bentham Science Publishers | Privacy Policy