Volume 19, Issue 9 (September 2019)                   Modares Mechanical Engineering 2019, 19(9): 2203-2213 | Back to browse issues page

XML Persian Abstract Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Torkan E, Pirmoradian M, Hashemian M. Dynamic Instability Analysis of Moderately Thick Rectangular Plates Influenced by an Orbiting Mass Based on the First-order Shear Deformation Theory. Modares Mechanical Engineering 2019; 19 (9) :2203-2213
URL: http://mme.modares.ac.ir/article-15-18525-en.html
1- Young Researchers & Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
2- Mechanical Engineering Department, Mechanical Engineering Faculty, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran , pirmoradian@iaukhsh.ac.ir
3- Mechanical Engineering Department, Mechanical Engineering Faculty, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
Abstract:   (4892 Views)
In this paper, the dynamic stability of a moderately thick rectangular plate carrying an orbiting mass and lying on a visco-elastic foundation is studied. Considering all inertial terms of the moving mass and using plate first-order shear deformation theory, the governing equations on the dynamic behavior of the system are derived. The Galerkin’s method on the basis of trigonometric shape functions is applied to change the coupled governing partial differential equations to a system of ordinary differential equations. Due to the alternative motion of the mass along the circular path over the plate’s surface, the governing equations are the equations with the periodic constant. Applying the semi-analytical incremental harmonic balance method, the influences of the relative thickness of the plate, radius of the motion path, and stiffness and damping of the visco-elastic foundation on the instability conditions of the system are investigated. A good agreement can be observed by comparing the predicted results of the incremental harmonic balance method with the numerical solution results. Based on the findings, increasing the radius of the motion path broadens the instability regions. Moreover, increasing the stiffness and damping of the foundation cause the system more stable.
Full-Text [PDF 962 kb]   (2230 Downloads)    
Article Type: Original Research | Subject: Aerospace Structures
Received: 2018/04/5 | Accepted: 2019/02/7 | Published: 2019/09/1

1. Reissner E. On the theory of transverse bending of elastic plates. International Journal of Solids and Structures. 1976;12(8):545-554. [Link] [DOI:10.1016/0020-7683(76)90001-9]
2. Mindlin RD. Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics. 1951;18:31-38. [Link]
3. Nateghi Babagi P, Navayi Neya B, Dehestani M. Three dimensional solution of thick rectangular simply supported plates under a moving load. Meccanica. 2017;52(15):3675-3692. [Link] [DOI:10.1007/s11012-017-0653-x]
4. Chen G, Meng Z, Yang D. Exact nonstationary responses of rectangular thin plate on Pasternak foundation excited by stochastic moving loads. Journal of Sound and Vibration. 2018;412:166-183. [Link] [DOI:10.1016/j.jsv.2017.09.022]
5. Rahimzadeh Rofooei F, Enshaeian AR, Nikkhoo A. Dynamic response of geometrically nonlinear, elastic rectangular plates under a moving mass loading by inclusion of all inertial components. Journal of Sound and Vibration. 2017;394:497-514. [Link] [DOI:10.1016/j.jsv.2017.01.033]
6. Enshaeian AR, Rahimzadeh Rofooei F. Geometrically nonlinear rectangular simply supported plates subjected to a moving mass. Acta Mechanica. 2014;225(2):595-608. [Link] [DOI:10.1007/s00707-013-0983-2]
7. Nikkhoo A, Rahimzadeh Rofooei F. Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass. Acta Mechanica. 2012;223(1):15-27. [Link] [DOI:10.1007/s00707-011-0547-2]
8. Nikkhoo A, Ebrahimzadeh Hassanabadi M, Eftekhar Azam S, Vaseghi Amiri J. Vibration of a thin rectangular plate subjected to series of moving inertial loads. Mechanics Research Communications. 2014;55:105-113. [Link] [DOI:10.1016/j.mechrescom.2013.10.009]
9. Pirmoradian M, Torkan E, Karimpour H. Parametric resonance analysis of rectangular plates subjected to moving inertial loads via IHB method. International Journal of Mechanical Sciences. 2018;142-143:191-215. [Link] [DOI:10.1016/j.ijmecsci.2005.09.005]
10. Gbadeyan JA, Dada MS. Dynamic response of a Mindlin elastic rectangular plate under a distributed moving mass. International Journal of Mechanical Sciences. 2006;48(3):323-340. [Link] [DOI:10.1016/j.ijmecsci.2005.09.005]
11. Vaseghi Amiri J, Nikkhoo A, Davoodi MR, Ebrahimzadeh Hassanabadi M. Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method. Thin Walled Structures. 2013;62:53-64. [Link] [DOI:10.1016/j.tws.2012.07.014]
12. Homayoun Sadeghi M, Lotfan S. Stability and bifurcation analysis of a beam-mass-spring-damper system under primary and one-to-three internal resonances. Modares Mechanical Engineering. 2017;17(2):166-176. [Persian] [Link]
13. Torkan E, Pirmoradian M, Hashemian M. On the parametric and external resonances of rectangular plates on an elastic foundation traversed by sequential masses. Archive of Applied Mechanics. 2018;88(8):1411-1428. [Link] [DOI:10.1007/s00419-018-1379-5]
14. Nelson HD, Conover RA. Dynamic stability of a beam carrying moving masses. Journal of Applied Mechanics. 1971;38(4):1003-1006. [Link] [DOI:10.1115/1.3408901]
15. Pirmoradian M, Keshmiri M, Karimpour H. Instability and resonance analysis of a beam subjected to moving mass loading via incremental harmonic balance method. Journal of Vibroengineering. 2014;16(6):2779-2789. [Link]
16. Pirmoradian M, Keshmiri M, Karimpour H. On the parametric excitation of a Timoshenko beam due to intermittent passage of moving masses: Instability and resonance analysis. Acta Mechanica. 2015;226(4):1241-1253. [Link] [DOI:10.1007/s00707-014-1240-z]
17. Pirmoradian M, Karimpour H. Nonlinear effects on parametric resonance of a beam subjected to periodic mass transition. Modares Mechanical Engineering. 2017;17(1):284-292. [Persian] [Link]
18. Torkan E, Pirmoradian M, Hashemian M. Occurrence of parametric resonance in vibrations of rectangular plates resting on elastic foundation under passage of continuous series of moving masses. Modares Mechanical Engineering. 2017;17(9):225-236. [Persian] [Link]
19. Torkan E, Pirmoradian M, Hashemian M. Instability inspection of parametric vibrating rectangular Mindlin plates lying on Winkler foundations under periodic loading of moving masses. Acta Mechanica Sinica. 2019;35(1):242-263. [Link] [DOI:10.1007/s10409-018-0805-9]
20. Lau SL, Cheung YK, Wu SY. A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems. Journal of Applied Mechanics. 1982;49(4):849-853. [Link] [DOI:10.1115/1.3162626]

Add your comments about this article : Your username or Email:

Send email to the article author

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.