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Journal of Applied Nonlinear Dynamics 9(1) (2020) 115--128 | DOI:10.5890/JAND.2020.03.010

B. Chabsang, S. J. Fariborz, J. P. Vafa

Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Avenue, Tehran, Iran

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Abstract

The structural response of a slender beam subjected to impact by several rigid particles is investigated. A higher-order shear deformation beam model and the von-Karman geometric measure are employed. The equations of motion, continuity conditions at the points of impact by particles, and geometric and natural boundary conditions for the beam are derived by means of Hamilton’s principle. The generalized differential quadrature and Newmark time integration methods are utilized to carry out the numerical solution of the system of nonlinear partial differential equations comprised of the equations of motion and stress resultants. The durations of contact, displacements, and stress resultants are obtained for beams with various types of boundary conditions.

References

1. [1]	Boettcher, R., Russell, A., and Mueller, P. (2017), Energy dissipation during impacts of spheres on plates: Investigation of developing elastic flexural waves, International Journal of Solids and Structures, 106, 229- 239.

2. [2]	Kelly, J.M. (1967), The impact of a mass on a beam, International Journal of Solids and Structures, 3, 191-196.

3. [3]	Goldsmith, W. (1960), Impact, the Theory and Physical Behavior Colliding Solids, Edward Arnold: London.

4. [4]	Sun, C.T. and Huang, S.N. (1975), Transverse impact problems by higher order beam finite element, Computers & Structures, 5, 297-303.

5. [5]	Lam, K.Y. and Sathiyamoorthy, T.S. (1999), Response of composite beam under low-velocity impact of multiple masses, Composite Structures, 44, 205-220.

6. [6]	Stronge, W.J. (2000), Impact Mechanics, Cambridge University Press: Cambridge.

7. [7]	Pashah, S., Massenzio, M., and Jacquelin, E. (2008), Prediction of structural response for low velocity impact, International Journal of Impact Engineering, 35, 119-132.

8. [8]	Wang, H., Yin, X., Qi, X., Deng, Q., Yu, B., and Hao, Q. (2017), Experimental and theoretical analysis of the elastic-plastic normal repeated impacts of a sphere on a beam, International Journal of Solids and Structures, 109, 131-142.

9. [9]	Liu, J.H. and Jones, N. (1988), Dynamic Response Of A Rigid Plastic Clamped Beam Struck By A Mass At Any Point On The Span, International Journal of Solids and Structures, 24(3), 251-270.

10. [10]	Shu, C. andWang, C.M. (1999), Treatment of mixed and non-uniform boundary conditions in GDQ vibration analysis of rectangular plates, Engineering Structures, 21, 125-134.

11. [11]	Newmark, M.N.(1959), A method of computation for structural dynamics, ASCE Journal of the Engineering Mechanics Division, 85, 67-94.

12. [12]	Hilber, H.M., Hughes, T.J.R., and Taylor, R.L. (1977), Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engineering and Structural Dynamics, 5, 283-292.