JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Stochastic elastic wave analysis of angled beams
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Stochastic elastic wave analysis of angled beams
Bai, Changqing; Ma, Hualin; Shim, Victor P.W.;
 Abstract
The stochastic finite element method is employed to obtain a stochastic dynamic model of angled beams subjected to impact loads when uncertain material properties are described by random fields. Using the perturbation technique in conjunction with a precise time integration method, a random analysis approach is developed for efficient analysis of random elastic waves. Formulas for the mean, variance and covariance of displacement, strain and stress are introduced. Statistics of displacement and stress waves is analyzed and effects of bend angle and material stochasticity on wave propagation are studied. It is found that the elastic wave correlation in the angled section is the most significant. The mean, variance and covariance of the stress wave amplitude decrease with an increase in bend angle. The standard deviation of the beam material density plays an important role in longitudinal displacement wave covariance.
 Keywords
elastic wave;stochastic finite element;angled beam;impact;random parameter;uncertainty;
 Language
English
 Cited by
 References
1.
Abd-Alla, A.M., Abo-Dahab, S.M. and Bayones, F.S. (2015), "wave propagation in fibre-reinforced anisotropic thermo-elastic medium subjected to gravity field", Struct. Eng. Mech., 53(2), 277-296. crossref(new window)

2.
Benaroya, H. and Rehak, M. (1988), "Finite element methods in probabilistic structural analysis: A selective review", Appl. Mech. Rev., 41, 201-213. crossref(new window)

3.
Countreras, H. (1980), "The stochastic finite element method", Comput. Struct., 12, 341-348. crossref(new window)

4.
Elishakoff, I., Ren, Y.J. and Shinozuka, M. (1997), "New formulation of FEM for deterministic and stochastic beams through generalization of Fuchs' approach", Comput. Meth. Appl. Mech. Eng., 144, 235-243. crossref(new window)

5.
Ghanem, R.G. and Spanos, P.D. (1991), Stochastic finite elements: a spectral approach, Springer -verlag, New York, USA

6.
Gibson, L.J. and Ashby, M.F. (1997), Cellular solids: Structure and properties, Cambridge University Press, Cambridge, UK.

7.
Guo, Y.B., Shim, V.P.W. and Yeo, A.Y.L. (2010), "Elastic wave and energy propagation in angled beams", Acta Mech., 214, 79-94. crossref(new window)

8.
Gupta, S. and Manohar, C.S. (2002), "Dynamic stiffness method for circular stochastic Timoshenko beams: response variability and reliability analysis", J. Sound Vib., 253, 1051-1085. crossref(new window)

9.
Hosseini, S.A.A. and Khadem, S.E. (2005), "Free vibration analysis of rotating beams with random properties", Struct. Eng. Mech., 20, 293-312. crossref(new window)

10.
Hosseini, S.A.A. and Khadem, S.E. (2007), "Vibration and reliability of a rotating beam with random properties under random excitation", Int. J. Mech. Sci., 49, 1377-1388. crossref(new window)

11.
Hosseini, S.M. and Shahabian, F. (2014), "Stochastic analysis of elastic wave and second sound propagation in media with Gaussian uncertainty in mechanical properties using a stochastic hybrid mesh-free method", Struct. Eng. Mech., 49(1), 41-64. crossref(new window)

12.
Hughes, T.J.R. (1987), The finite element method, Prentice-Hall, N.J.

13.
Ishida, R. (2001), "Stochastic finite element analysis of beam with stochastical uncertainties", AIAA J., 39, 2192-2197. crossref(new window)

14.
Lee, J.P. and Kolsky, H. (1972), "The generation of stress pulses at the junction of two noncollinear rods", ASME J. Appl. Mech., 39, 809-813. crossref(new window)

15.
Liu, M. and Gorman, D.G. (1995), "Formulation of Rayleigh damping and its extension", Comput. Struct., 57, 277-285. crossref(new window)

16.
Nouy, A. and Clement, A. (2010), "Extended stochastic finite element method for the numerical simulation of heterogeneous materials with random material interfaces", Int. J. Numer. Meth. Eng., 83, 1312-1344. crossref(new window)

17.
Papadopoulos, V., Papadrakakis, M. and Dodatis, G. (2006), "Analysis of mean and mean square response of general linear stochastic finite element systems", Comput. Meth. Appl. Mech. Eng., 195, 5454-5471. crossref(new window)

18.
Sankaran, M. and Achintya, H. (1991), "Reliability-based optimization using SFEM", Lec. Note. Eng., 61, 241-250. crossref(new window)

19.
Simha, K.R.Y. and Fourney, W.L. (1984), "Investigation of stress wave propagation through intersection bars", ASME J. Appl. Mech., 51, 345-353. crossref(new window)

20.
Yamazaki, F., Shinozuka, M. and Dasgupta, G. (1985), "Neumann expansion for stochastic finite element analysis", ASCE J. Eng. Mech., 114, 1335-1354.

21.
Young, K.H. and Atkins, K.J. (1983), "Generation of elastic stress waves at a T-junction of square rods", J. Sound Vib., 88, 431-436. crossref(new window)

22.
Zhong, W.X., Zhu, J.N. and Zhong, X.X. (1996), "On a new time integration method for solving time dependent partial differential equations", Comput. Meth. Appl. Mech. Eng., 130, 163-178. crossref(new window)

23.
Zhong, W.X., Zhu, J.P. and Zhong, X.X. (1994), "A precise time integration algorithm for non-linear systems", Proc. 3rd World Congress on Computational Mechanics, Chiba, Japan.