Uncertainty Propagation Analysis in Free Vibration of Uncertain Composite Plate Using Stochastic Finite Element Method

Document Type : Research Article

Authors

1 University of Tehran

2 Iranian space research center

Abstract

Material uncertainty is more widespread in composite material than the other engineering materials. This uncertainty makes response of these types of structures to be nondeterministic. In order to predict structural reliability, uncertainty in structural responses must be quantified. There is not a reported research in the literature studying free vibration of composite plate with spatially stochastic material properties. In this research, physical and mechanical properties of composite plate including tensile and shear modulus and density of the plate are modeled as stochastic Gaussian fields. Assuming exponential auto covariance kernels for aforementioned stochastic fields, they are discretized to two parts, including deterministic and stochastic parts employing Karhunen-Loeve theorem. Assuming linear form of strains, mechanical strains are defined applying first order shear deformation theory. Kinetic and potential energy of the composite plate is extracted using finite element formulation. Stochastic finite element formulation is derived employing Hamilton’s principle and Euler-Lagrange and equations are verified with the results in the literature for deterministic case. After verification of formulation, material uncertainty effects on uncertainty of natural frequencies are investigated using Monte Carlo simulation. Results show that there is a linear relation between coefficient of variation of uncertain properties and coefficient of variation of stochastic natural frequencies.

Keywords

Main Subjects

References

[1] S. Salim, D. Yadav, N.J.M.R.C. Iyengar, Analysis of composite plates with random material characteristics, 20(5) (1993) 405-414.
[2] B. Navaneetha Raj, N. Iyengar, D.J.A.C.M. Yadav, Response of composite plates with random material properties using FEM and Monte Carlo simulation, 7(3) (1998) 219-237.
 [3] A.K. Noor, J.H. Starnes Jr, J.M.J.C.S. Peters, Uncertainty analysis of stiffened composite panels, 51(2) (2001) 139- 158.
[4]A.K. Noor, J.H. Starnes Jr, J.M.J.C.m.i.a.m. Peters, engineering, Uncertainty analysis of composite structures, 185(2-4) (2000) 413-432.
[5] C.C. António, L.N.J.R.E. Hoffbauer, S. Safety, Uncertainty analysis based on sensitivity applied to angle-ply composite structures, 92(10) (2007) 1353- 1362. [6] P. Gayathri, K. Umesh, R.J.R.E. Ganguli, S. Safety, Effect of matrix cracking and material uncertainty on composite plates, 95(7) (2010) 716-728.
[7] S.J.I.j.o.s. Lin, structures, Buckling failure analysis of random composite laminates subjected to random loads, 37(51) (2000) 7563-7576.
[8] A. Lal, B. Singh, R.J.C. Kumar, Structures, Effects of random system properties on the thermal buckling  analysis of laminated composite plates, 87(17-18) (2009) 1119-1128.
[9] V.K. Verma, B.J.I.J.o.S.S. Singh, Dynamics, Thermal buckling of laminated composite plates with random geometric and material properties, 9(02) (2009) 187-211.
[10] P.M. Pawar, S. Nam Jung, B.P.J.A.E. Ronge, A. Technology, Fuzzy approach for uncertainty analysis of thin walled composite beams, 84(1) (2012) 13-22.
[11] B.N. Singh, N. Iyengar, D.J.J.o.e.m. Yadav, Effects of random material properties on buckling of composite plates, 127(9) (2001) 873-879.
[12] P. Sasikumar, R. Suresh, S.J.A.M. Gupta, Stochastic finite element analysis of layered composite beams with spatially varying non-Gaussian inhomogeneities, 225(6) (2014) 1503-1522.
 [13] R. Rafiee, F. Reshadi, S.J.M. Eidi, Design, Stochastic analysis of functional failure pressures in glass fiber reinforced polyester pipes, 67 (2015) 422-427.
[14] A.K. Onkar, D.J.C.S. Yadav, Forced nonlinear vibration of laminated composite plates with random material properties, 70(3) (2005) 334-342.
[15] B. Singh, A. Bisht, M. Pandit, K.J.J.o.s. Shukla, vibration, Nonlinear free vibration analysis of composite plates with material uncertainties: A Monte Carlo simulation approach, 324(1-2) (2009) 126-138.
[16] M.T. Piovan, J.M. Ramirez, R.J.C.S. Sampaio, Dynamics of thin-walled composite beams: Analysis of parametric uncertainties, 105 (2013) 14-28.
[17] M.K. Pandit, B.N. Singh, A.H.J.J.o.A.E. Sheikh, Stochastic free vibration response of soft core sandwich plates using an improved higher-order zigzag theory, 23(1) (2009) 14-23.
[18] S. Dey, T. Mukhopadhyay, H.H. Khodaparast, S.J.A.M. Adhikari, Stochastic natural frequency of composite conical shells, 226(8) (2015) 2537-2553.
 [19] S. Dey, T. Mukhopadhyay, S. Sahu, G. Li, H. Rabitz, S.J.C.P.B.E. Adhikari, Thermal uncertainty quantification in frequency responses of laminated composite plates, 80 (2015) 186-197.
[20] A. Lal, B.J.C.M. Singh, Stochastic nonlinear free vibration of laminated composite plates resting on elastic foundation in thermal environments, 44(1) (2009) 15-29.
[21] A. Lal, M.V. Tadvi, R. Kumar, Stochastic Thermal Free Vibration Response of Laminated Composite Plates Resting on Elastic Foundation with Uncertain Material Properties, in: 2008 First International Conference on Emerging Trends in Engineering and Technology, IEEE, 2008, pp. 754-757.
 [22] A. Lal, B. Singh, R.J.I.J.o.M.S. Kumar, Nonlinear free vibration of laminated composite plates on elastic foundation with random system properties, 50(7) (2008) 1203-1212.
 [23] K. Sepahvand, S. Marburg, On uncertainty quantification in sandwich structures with spatial random damping behavior, in: International Conference on Structural Dynamic, EURODYN, 2014.
[24] S. Adhikari, A.S.J.A.J. Phani, Random eigenvalue problems in structural dynamics: experimental investigations, 48(6) (2010) 1085-1097.
[25] S. Adhikari, Free vibration analysis of angle-ply composite plates with uncertain properties, in: 17th AIAA Non-Deterministic Approaches Conference, 2015, pp. 1146.
[26] S. Murugan, D. Harursampath, R.J.A.j. Ganguli, Material uncertainty propagation in helicopter nonlinear aeroelastic response and vibratory analysis, 46(9) (2008) 2332-2344.
[27] S. Murugan, R. Chowdhury, S. Adhikari, M.J.A.S. Friswell, Technology, Helicopter aeroelastic analysis with spatially uncertain rotor blade properties, 16(1) (2012) 29-39.  
[28] A. Shaker, W.G. Abdelrahman, M. Tawfik, E.J.C.M. Sadek, Stochastic finite element analysis of the free vibration of laminated composite plates, 41(4) (2008) 493-501.
[29] K. Sepahvand, S. Marburg, H.-J.J.J.o.S. Hardtke, Vibration, Stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion, 331(1) (2012) 167-179.
[30] K. Sepahvand, M. Scheffler, S.J.A.A. Marburg, Uncertainty quantification in natural frequencies and radiated acoustic power of composite plates: Analytical and experimental investigation, 87 (2015) 23-29.
[31] K. Umesh, R.J.M.o.A.M. Ganguli, Structures, Material uncertainty effect on vibration control of smart composite plate using polynomial chaos expansion, 20(7) (2013) 580-591.
 [32] S. Sriramula, M.K.J.S.S. Chryssanthopoulos, An experimental characterisation of spatial variability in GFRP composite panels, 42 (2013) 1-11.
 [33] R.G. Ghanem, P.D. Spanos, Stochastic finite element method: Response statistics, in: Stochastic finite elements: a spectral approach, Springer, 1991, pp. 101- 119.
[34] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, CRC press, 2004.
[35] H.-S. Shen, J.-J. Zheng, X.-L.J.C.S. Huang, Dynamic response of shear deformable laminated plates under thermomechanical loading and resting on elastic foundations, 60(1) (2003) 57-66.
[36] B. Singh, D. Yadav, N.J.A.C.M. Iyengar, AC° element for free vibration of composite plates with uncertain material properties, 11(4) (2002) 331-350.
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 12
March 2021
Pages 3503-3520

Files

Share

How to cite

Statistics