PL EN
The effect of added point masses on the geometrically non-linear vibrations of SCSC rectangular plates
 
Więcej
Ukryj
1
Mohammed V University, Mohammadia School of Engineers, Rabat, Morocco
AUTOR DO KORESPONDENCJI
Mustapha Hamdani   

Mohammed V University, Mohammadia School of Engineers, Rabat, Morocco
Data nadesłania: 10-02-2022
Data ostatniej rewizji: 30-04-2022
Data akceptacji: 04-05-2022
Data publikacji online: 05-05-2022
Data publikacji: 05-05-2022
 
Diagnostyka 2022;23(2):2022206
 
SŁOWA KLUCZOWE
DZIEDZINY
STRESZCZENIE
A point mass added to a plate may have a significant effect on its linear and nonlinear dynamics, including frequencies, mode shapes and the forced response to external loading. In the present paper, a simply supported clamped simply supported clamped rectangular plate (SCSCRP) carrying a point mass is examined. The expressions for the kinetic, linear and non-linear strain energies are derived by taking into account the effect of the added mass on the kinetic energy and the effect of the membrane forces induced by the non-linearity on the strain energy. The discretization of these expressions makes the mass tensor, the linear and non-linear rigidity tensors appear in a non-linear algebraic multimode amplitude equation, the iterative solution of which permit to obtain, in the neighborhood of the first non-linear mode, the basic SCSCRP function amplitude dependent contribution coefficients. Nonlinear frequency response functions have been obtained for the first time, based on an iterative numerical solution in each case of the associated complete set of nonlinear algebraic equations. Such new results are useful for a better qualitative understanding allowing an optimal dynamic design of the rectangular plates with added masses.
 
REFERENCJE (25)
1.
Low KH, Chai GB, Lim TM, Sue SC. Comparisons of experimental and theoretical frequencies for rectangular plates with various boundary conditions and added masses. International Journal of Mechanical Sciences. 1998;40(11), 1119-1131.
 
2.
Boay CG. Free vibration of rectangular isotropic plates with and without a concentrated mass. Computers and structures. 1993;48(3):529-533.
 
3.
Low KH, Chai GB. An improved model for predicting fundamental frequencies of plates carrying multiple masses. 1997.
 
4.
Beidouri Z, Benamar R, El Kadiri M. Geometrically non-linear transverse vibrations of C-S-S-S and C-S-C-S rectangular plates. International Journal of Non-Linear Mechanics. 2006;41(1):57-77.
 
5.
Benamar R, Bennouna MMK, White RG. The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures, Part II: fully clamped rectangular isotropic plates. Journal of Sound and Vibration. 1993;164(2):295-316.
 
6.
El Kadiri M, Benamar R. Improvement of the semi-analytical method, for determining the geometrically non-linear response of thin straight structures: part II-first and second non-linear mode shapes of fully clamped rectangular plates. Journal of Sound and Vibration. 2002;257(1):19-62.
 
7.
Zhou D, Ji T. Free vibration of rectangular plates with attached discrete sprung masses. Shock and Vibration. 2012;19(1):101-112. https://doi.org/10.3233/SAV-20....
 
8.
McMillan AJ, Keane AJ. Shifting resonances from a frequency band by applying concentrated masses to a thin rectangular plate. Journal of Sound and Vibration. 1996;192(2): 549-652.
 
9.
Leissa AW. Vibration of shells. Scientific and Technical Information Office, National Aeronautics and Space Administration. 1973;288.
 
10.
Wu JS, Chou HM, Chen DW. Free vibration analysis of a rectangular plate carrying multiple various concentrated elements. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics. 2003;217(2):171-183. https://doi.org/10.1243/146441....
 
11.
Jacquot RG, Soedel W. Vibrations of elastic surface systems carrying dynamic elements. The Journal of the Acoustical Society of America. 1970;47(5B):1354-1358.
 
12.
Laura PAA, Filipich CP, Cortinez VH. Vibrations of beams and plates carrying concentrated masses. Journal of Sound Vibration. 1987;117(3): 459-465.
 
13.
Der Kiureghian, A, Sackman JL, Nour Omid B. Dynamic response of light equipment in structures. Earthquake Engineering Center, College of Engineering, University of California. 1981.
 
14.
Li QS. An exact approach for free vibration analysis of rectangular plates with line concentrated mass and elastic line-support. International Journal of Mechanical Sciences. 2003;45(4):669-685. https://doi.org/10.1016/S0020-....
 
15.
Fakhreddine H, Adri A, Chajdi M, Rifai S, Benamar R. A multimode approach to geometrically non-linear forced vibration of beams carrying point masses. Diagnostyka. 2020;21(4):23-33. https://doi.org/10.29354/diag/....
 
16.
Wang D, Et Friswell MI. Support position optimization with minimum stiffness for plate structures including support mass. Journal of Sound and Vibration. 2021;499:116003. https://doi.org/10.1016/j.jsv.....
 
17.
Mahadevaswamy P. Et Suresh BS. Optimal mass ratio of vibratory flap for vibration control of clamped rectangular plate. Ain Shams Engineering Journal. 2016;7(1):335-345. https://doi.org/10.1016/j.asej....
 
18.
Martin PA, Et Hull, Andrew J. Dynamic response of an infinite thin plate loaded with concentrated masses. Wave Motion. 2020;98:102643. https://doi.org/10.1016/j.wave....
 
19.
Pang X, Sun J, Zhang Z. FE-holomorphic operator function method for nonlinear plate vibrations with elastically added masses. Journal of Computational and Applied Mathematics. 2022:114156.
 
20.
Whitney JM. Structural Analysis of Laminated Anisotropic Plates (Lancaster, PA: Technomic). 1987.
 
21.
Low KH, Chai GB, Ng CK. Experimental and analytical study of the frequencies of an SCSC plate carrying a concentrated mass. 1993;115(4):391-396. https://doi.org/10.1115/1.2930....
 
22.
Chai GB. Frequency analysis of a SCSC plate carrying a concentrated mass. Journal of sound and vibration. 1995;179(1):170-177.
 
23.
Boay CG. Frequency analysis of rectangular isotropic plates carrying a concentrated mass. Computers and structures. 1995;56(1):39-48.
 
24.
Low KH, Ng CK, Ong YK. Comparative study of frequencies for plates carrying mass. Journal of engineering mechanics. 1993;119(5):917-937.
 
25.
Wądołowski M, Pankiewicz J, Markuszewski D. Application for analysis of the multiple coherence function in diagnostic signal separation processes. Vibrations in Physical Systems. 2020;31(3):2020324. https://doi.org/10.21008/j.086....
 
eISSN:2449-5220