• Do Van Thom Le Quy Don Technical University
  • Doan Hong Duc University of Engineering and Technology, Vietnam National University
  • Phung Van Minh Le Quy Don Technical University
  • Nguyen Son Tung Le Quy Don Technical University



finite element, phase-field theory, FGM, crack, stiffened plates, vibration


This paper presents the new numerical results of vibration response analysis of cracked FGM plate based on phase-field theory and finite element method. Effects of geometrical and material properties on the vibration behaviors of the plate are investigated in this work. The computed results show that the crack and stiffener have a strong influence on both the vibration responses and vibration mode shapes of the structure. The computed results can be used as a good reference to study some related mechanical problems.


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Author Biographies

Do Van Thom, Le Quy Don Technical University

Faculty of Mechanical Engineering

Doan Hong Duc, University of Engineering and Technology, Vietnam National University

Advanced Materials and Structures Laboratory

Phung Van Minh, Le Quy Don Technical University

Faculty of Mechanical Engineering

Nguyen Son Tung, Le Quy Don Technical University

Faculty of Mechanical Engineering


Rabczuk T. and Areias P., M., A. -A meshfree thin shell for arbitrary evolving cracks based on an external enrichment, Comput. Model. Eng. Sci, 16 (2006) 115–130.

Natarajan S., M.Baiz P., Bordas S., Rabczuk T. and Kerfridena P. -Natural frequencies of cracked functionally graded material plates by the extended finite element method, Compos. Struct, 93 (2011) 3082–3092.

Chau-Dinh T., Goangseup Zi., Phill-Seung L., Rabczuk T. and Jeong-Hoon S. - Phantom-node method for shell models with arbitrary cracks, Comput. Struct. 92–93 (2012) 242–256.

Ghorashi S. Sh., Valizadeh N., Mohammadi S. and Rabczuk T. - T-spline based XIGA for fracture analysis of orthotropic media,” Comput. Struct. 147 (2015) 138–146.

Kitipornchai S., Ke L. L., Yang J. and Xiang Y. - Nonlinear vibration of edge cracked functionally graded Timoshenko beams, J. Sound Vib. 324 (2009) 962–982.

Huang C. S., Leissa A. W. and Chan C. W. - Vibrations of rectangular plates with internal cracks or slits, Int. J. Mech. Sci. 53 (2011) 436–445.

Huang C. S., Leissa A. W. and Li R. S. - Accurate vibration analysis of thick, cracked rectangular plates, J. Sound Vib. 330 (2011) 2079–2093.

Huang C. S., McGee O. G. and Chang M. J. - Vibrations of cracked rectangular FGM thick plates, Compos. Struct. 93 (2011) 1747–1764.

Huang C. S., McGee O. G. and Wang K. P. - Three-dimensional vibrations of cracked rectangular parallelepipeds of functionally graded material, Int. J. Mech. Sci. 70 (2013) 1–25.

Nam V.H., Duc H.D., Nguyen M.K., Thom V.D. and Hong T.T. - Phase-field buckling analysis of cracked stiffened functionally graded plates. Comp. Struct. 217 (2019) 50-59.

Tinh Q. B., Thom V. D., Lan H. Th. T., Duc H. D., Satoyuki T., Dat T. Ph., Thien-An Ng.V., Tiantang Y. and Sohichi H. - On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory, Comp. part B 92 (2016) 218-241.

Krawczuk M. and Gdansk. - Natural vibrations of rectangular plates with a through crack, Arch. Appl. Mech., 63 (1993) 491-504.

Qian G.L., Gu S.N. and Jiang J.S. - A finite element model of cracked plates application to vibration problems, Comp. Struct., 39 (1991) 483-487.

Aksu G. - Free vibration analysis of stiffened plates by including the effect of inplane inertia, J. Appl. Mech. 49 (1982) 206–212.

Mukherjee A. and Mukhopadhyay M. - Finite element free vibration of eccentrically stiffened plates, Comp. Struct. 30 (6) (1988) 1303–1317.

Harik I.E., Guo M. - Finite element analysis of eccentrically stiffened plates in free vibration, Comp. Struct. 49 (6) (1993) 1007–1015.

Bhimaraddi A., Carr A.J., Moss P.J. - Finite element analysis of laminated shells of revolution with laminated stiffeners, Comp. Struct. 33 (1) (1989) 295–305.

Peng L.X., Liew K.M. and Kitipornchai S. - Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method, J. Sound Vibr. 289 (2006) 421-449.

Wattanasakulpong N., Prusty G.B. and Kelly D.W. - Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading, J. Sandw. Struct. Mater. 15 (2013) 583-606.

Huang X.L. and Shen H.S. - Nonlinear vibration and dynamic response of functionally graded plates in thermal environments, Int. J. Solids Struct. 41 (2004) 2403-2427.

Thom V.D., Duc H.D., Duc N.D. and Tinh Q.B. - Phase-field thermal buckling analysis for cracked functionally graded composite plates considering neutral surface, Comp. Struct. 182 (2017) 524-548.

Thom V.D., Tinh Q.B., Yu T.T., Dat P.T. and Chung T.N. - Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment, J. Comp. Scie. 21 (2017) 164-181

Duc HD, Tinh QB, Thom VD, Duc ND. - A rate-dependent hybrid phase field model for dynamic crack propagation, J. Appl. Phys. 122 (2017) 115102 1-4.

Duc N.D., Truong T.D., Thom V.D. and Duc H.D. - On the Buckling Behavior of Multi-cracked FGM Plates, Procc. Inter. Conf. Adv. Comp. Mech. 2017, Lecture Notes in Mechanical Engineering: 29-45.

Phuc M.P., Thom V.D., Duc H.D. and Duc N.D. - The stability of cracked rectangular plate with variable thickness using phase-field method, Thin-Wall. Struct. 129 (2018) 157-165.

Reddy J.N. - Analysis of Functionally Graded Plates, Inter. J. Num. Meth. Eng. 47 (2000) 663-684.

Miehe C., Hofacker M. and Welschinger F. - A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits, Comp.Meth. Appl. Mech. Eng. 199 (2010) 2766-2778.

Doan H.D., Bui Q.T., Nguyen D.D. and Fushinobu K. - Hybrid phase field simulation of dynamic crack propagation in functionally graded glass-filled epoxy, Comp. Part B. 99 (2016) 266-276.

Michael J.B., Clemens V.V., Michael A.S., Thomas J.R.H. and Chad M.L. - A phase-field description of dynamic brittle fracture, Comp. Meth. Appl. Mech. Eng. 217–220 (2012) 77–95.

Josef K., Marreddy A., Lorenzis L.D., Hector G. and Alessandro R. - Phase-field description of brittle fracture in plates and shells, Comp. Meth. Appl. Mech. Eng. 312 (2016) 374-394.

Bourdin B., Francfort G.A. and Marigo J.J. - The variational approach to fracture, J. Elast. 91 (2008) 5–148.






Mechanical Engineering - Mechatronics