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Stochastic Vibration Analyses of Laminated Composite Plates via a Statistical Moments-Based Methodology

  • Abdullah Seçgin
  • Murat Kara
Original Paper
  • 6 Downloads

Abstract

Purpose

In the present study, stochastic vibration analyses of a symmetrically laminated composite plate having uncertain input parameters are performed via a probabilistic methodology. Here, uncertain input parameters are selected as plate thickness, specific volume (inverse of density) and structural damping. These parameters are modeled statistically as a normal distribution.

Methods

The methodology carries out the closed form solution of stochastic partial differential equation governing a structural vibration by discrete singular convolution (DSC) method in terms of its first two statistical moments: mean and standard deviation.

Results

The effects of uncertain parameters (combined in six different cases) on modal and vibration displacement response due to a harmonic excitation force are investigated. In this manner, firstly, mean and standard deviation of natural frequencies of the composite plate are obtained by solving its partial differential equation using discrete singular convolution method. After that, statistics of vibration frequency response are obtained by predicted natural frequencies’ statistics. Monte Carlo simulations are also performed to test the proposed methodology.

Conclusion

It is shown that the methodology is more reliable in higher frequencies where the uncertainty is much more considerable. Besides, the computation time is very efficient when comparing with Monte Carlo simulations.

Keywords

Uncertainty propagation Statistical moments Stochastic vibration analyses Laminated composite plates Discrete singular convolution 

Notes

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

References

  1. 1.
    Ramaiah BP, Rammohan B, Kumar SV, Babu DS, Raghuatnhan R (2009) Aero-elastic analysis of stiffened composite wing structure. Adv Vib Eng 8:255–264Google Scholar
  2. 2.
    Fahy FJ (1994) Statistical energy analysis: a critical overview. Philos Trans R Soc Lond A Math Phys Eng Sci 346:431–447CrossRefGoogle Scholar
  3. 3.
    Elishakoff I, Haftka RT, Fang J (1994) Structural design under bounded uncertainty—optimization with anti-optimization. Comput Struct 53:1401–1405CrossRefGoogle Scholar
  4. 4.
    Evans M, Swartz T (2000) Approximating integrals via Monte Carlo and deterministic methods. OUP Oxford, New YorkzbMATHGoogle Scholar
  5. 5.
    Rubinstein RY, Kroese DP (2016) Simulation and the Monte Carlo method. Wiley, Hoboken, New JerseyCrossRefGoogle Scholar
  6. 6.
    Ji L (2013) A case study on simplifying the resound/hybrid theory. Adv Vib Eng 12:391–399Google Scholar
  7. 7.
    Ghanem RG, Spanos PD (2003) Stochastic finite elements: a spectral approach. Courier Corporation, New YorkzbMATHGoogle Scholar
  8. 8.
    Sepahvand K, Marburg S, Hardtke H-J (2007) Numerical solution of one-dimensional wave equation with stochastic parameters using generalized polynomial chaos expansion. J Comput Acoust 15:579–593MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sepahvand K, Marburg S, Hardtke H-J (2010) Uncertainty quantification in stochastic systems using polynomial chaos expansion. Int J Appl Mech 2:305–353CrossRefGoogle Scholar
  10. 10.
    Sepahvand K, Marburg S (2014) Identification of composite uncertain material parameters from experimental modal data. Probab Eng Mech 37:148–153CrossRefGoogle Scholar
  11. 11.
    Sepahvand K, Scheffler M, Marburg S (2015) Uncertainty quantification in natural frequencies and radiated acoustic power of composite plates: analytical and experimental investigation. Appl Acoust 87:23–29CrossRefGoogle Scholar
  12. 12.
    Sepahvand K (2017) Stochastic finite element method for random harmonic analysis of composite plates with uncertain modal damping parameters. J Sound Vib 400:1–12CrossRefGoogle Scholar
  13. 13.
    Hien TD, Noh H-C (2017) Stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness. Comput Methods Appl Mech Eng 318:845–863MathSciNetCrossRefGoogle Scholar
  14. 14.
    Chakraborty S, Mandal B, Chowdhury R, Chakrabarti A (2016) Stochastic free vibration analysis of laminated composite plates using polynomial correlated function expansion. Compos Struct 135:236–249CrossRefGoogle Scholar
  15. 15.
    Dey S, Naskar S, Mukhopadhyay T, Gohs U, Spickenheuer A, Bittrich L, Sriramula S, Adhikari S, Heinrich G (2016) Uncertain natural frequency analysis of composite plates including effect of noise—a polynomial neural network approach. Compos Struct 143:130–142CrossRefGoogle Scholar
  16. 16.
    Naskar S, Mukhopadhyay T, Sriramula S, Adhikari S (2017) Stochastic natural frequency analysis of damaged thin-walled laminated composite beams with uncertainty in micromechanical properties. Compos Struct 160:312–334CrossRefGoogle Scholar
  17. 17.
    Nayak AK, Satapathy AK (2016) Stochastic damped free vibration analysis of composite sandwich plates. Proc Eng 144:1315–1324CrossRefGoogle Scholar
  18. 18.
    Venini P, Mariani C (1997) Free vibrations of uncertain composite plates via stochastic Rayleigh-Ritz approach. Comput Struct 64:407–423CrossRefGoogle Scholar
  19. 19.
    Wei GW (1999) Discrete singular convolution for the solution of the Fokker-Planck equation. J Chem Phys 110:8930–8942CrossRefGoogle Scholar
  20. 20.
    Wei GW (2001) Discrete singular convolution for beam analysis. Eng Struct 23:1045–1053CrossRefGoogle Scholar
  21. 21.
    Wei GW (2001) Vibration analysis by discrete singular convolution. J Sound Vib 244:535–553MathSciNetCrossRefGoogle Scholar
  22. 22.
    Wei GW (2001) A new algorithm for solving some mechanical problems. Comput Methods Appl Mech Eng 190:2017–2030MathSciNetCrossRefGoogle Scholar
  23. 23.
    Civalek Ö (2007) Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach. J Comput Appl Math 205:251–271MathSciNetCrossRefGoogle Scholar
  24. 24.
    Civalek Ö (2007) Free vibration and buckling analyses of composite plates with straight-sided quadrilateral domain based on DSC approach. Finite Elem Anal Des 43:1013–1022CrossRefGoogle Scholar
  25. 25.
    Seçgin A, Sarıgül AS (2008) Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: algorithm and verification. J Sound Vib 315:197–211CrossRefGoogle Scholar
  26. 26.
    Seçgin A, Sarıgül AS (2009) A novel scheme for the discrete prediction of high-frequency vibration response: discrete singular convolution–mode superposition approach. J Sound Vib 320:1004–1022CrossRefGoogle Scholar
  27. 27.
    Seçgin A (2013) Numerical determination of statistical energy analysis parameters of directly coupled composite plates using a modal-based approach. J Sound Vib 332:361–377CrossRefGoogle Scholar
  28. 28.
    Whitney JM (1987) Structural analysis of laminated anisotropic plates. Technomic Publishing, Lancaster, PennsylvaniaGoogle Scholar
  29. 29.
    Timoshenko S, Woinowsky-Kreiger S (1959) Theory of plates and shells, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  30. 30.
    Goodman LA (1960) On the exact variance of products. J Am Stat Assoc 55:708–713MathSciNetCrossRefGoogle Scholar

Copyright information

© KrishteleMaging Solutions Private Limited 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringDokuz Eylül UniversityBucaTurkey

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