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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-a8f77d03-b6d9-46fc-ac76-24960cb98a62

Czasopismo

Diagnostyka

Tytuł artykułu

Linear and geometrically non-linear frequencies and mode shapes of beams carrying a point mass at various locations. An analytical approch and a parametric study

Autorzy Adri, A.  Benamar, R. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In the present paper, the frequencies and mode shapes of a clamped beam carrying a point mass, located at different positions, are investigated analytically and a parametric study is performed. The dynamic equation is written at two intervals of the beam span with the appropriate end and continuity conditions. After the necessary algebraic transformations, the generalised transcendental frequency equation is solved iteratively using the Newton Raphson method. Once the corresponding program is implemented, investigations are made of the changes in the beam frequencies and mode shapes for many values of the mass and mass location. Numerical results and plots are given for the clamped beam first and second frequencies and mode shapes corresponding to various added mass positions. The effect of the geometrical non-linearity is then examined using a single mode approach in order to obtain the corresponding backbone curves giving the amplitude dependent non-linear frequencies.
Słowa kluczowe
PL drgania nieliniowe   zasada Hamiltona   metoda Newtona-Raphsona   analiza modalna  
EN non-linear vibration   Hamilton’s principle   Newton-Raphson method   backbone curve   second formulation  
Wydawca Polskie Towarzystwo Diagnostyki Technicznej
Czasopismo Diagnostyka
Rocznik 2017
Tom Vol. 18, No. 2
Strony 13--21
Opis fizyczny Bibliogr. 29 poz., rys., tab., wykr.
Twórcy
autor Adri, A.
  • Laboratoire de Mécanique Productique & Génie Industriel (LMPGI) École Supérieure de Technologie Hassan II University in Casablanca, ahmedadri@gmail.com
autor Benamar, R.
  • Equipe des Etudes et Recherches en Simulation et Instrumentation Ecole Mohammadia des Ingénieurs; Mohammed V University in Rabat, rhali.benamar@gmail.com
Bibliografia
1. Adri A, Beidouri Z, El Kadiri M, Benamar R. Geometrically nonlinear free vibration of a beam carrying concentrated masses international. Journal of Engineering Research & Technology (IJERT),2016, ISSN: 2278-0181.Vol. 5 Issue 01.
2. De Rosa MA, Auciello NM, Maurizi MJ. The use of Mathematica in the dynamics analysis of a beam with a concentrated mass and dashpot. Journal of Sound and Vibration, 2003;263:219-226.
3. Nagules Waran S. Transverse vibrations of an EulerBernoulli uniform beam carrying several particles, International Journal of Mechanical Science, 2002; 44:2463-2478.
4. Chang CH. Free vibration of a simply supported beam carrying a rigid mass at the middle, Journal of Sound and Vibration, 2000;237(4):733-744.
5. De Rosa MA, Franciosi C, Maurizi MJ. On the dynamics behaviour of slender beams with elastic ends carrying a concentrated mass, Computers and Structures, 1995;58(6):1145-1159.
6. Laura PAA, Filipich CP, Cortinez VH. Vibrations of beams and plates carrying concentrated masses, 1987, Journal of Sound and Vibration 117 (3) 45965.
7. M. Gûrgôze, On the vibration of restrained beams and rods with heavy masses, Journal of Sound and Vibration,1985, 100 (4) 588-589.
8. Gûrgôze M. A note on the vibrations of restrained beams and rods with point masses, Journal of Sound and Vibration,1984;96(4):461-468.
9. Laura PAA, Pombo JL,. Susemihl EL. A note on the vibration of a clamped-free beam with a mass at the free end. Journal of Sound and Vibration, 1974; 37:161-168.
10. Chen Y. On the vibration of beams or rods carrying a concentrated mass, Journal of Applied Mechanics, 1963;30:310-311.
11. EL Kadiri M, Benamar R, White RG. Improvement of the semi-analytical method, based on Hamilton's principle and spectral analysis, for determination of the geometrically non-linear free response of thin straight structures. Part I: Application to C-C and SSC beams. of Journal Sound and Vibration, 2002; 249(2):263-305.
12. Azrar RL, Benamar R, White RG. A semi-analytical approach to the non-linear dynamic response problem of S-S and C-C beams at the large vibration amplitudes part1: General theory and application to the single mode approach to free and forced vibration analysis. Journal of Sound and Vibration, 1999;224(2): 183-207.
13. Benamar R, Bennouna M, White RG. The effects of large vibration amplitudes on the fundamental mode shape of thin elastic structures, part I: Simply supported and clamped-clamped beams. Journal of Sound and Vibration, 1991;149:179-195.
14. Benamar R. Non-linear dynamic behavior of fully clamped beams and rectangular isotropic and laminated plates Ph.D. thesis, University of Southampton. 1990.
15. Bennouna M, White RG. The effects of large vibration amplitude on the fundamental mode shape of a clamped-clamped beam. Journal of Sound and vibration,1984;(3):309-331.
16. El Kadiri M. Contribution à l’analyse modale non linéaire des structures minces droites : réponses libres et forcées des poutres et des plaques rectangulaires aux grandes amplitudes de vibrations. Ph.D. thesis, Université Mohammed V-Agdal, Ecole Mohammadia des Ingénieurs. 2001.
17. Hai-Ping Lin, Chang SC. Free vibration analysis of multi-span beams with intermediate flexible constraints. of Journal Sound and Vibration, 2995;281:155-169.
18. Yozo M. Orthogonality condition for a multi-span beam, and its application to transient vibration of two span beam. Of Journal Sound and Vibration, 2008;314:851-866.
19. Hsien-Yuan Lin, Ying-Chien Tsai. Free vibration analysis of uniform multi-span beam carrying multiple spring-mass systems. of Journal Sound and Vibration,2007;302:442-456.
20. Yesilce Y, Demirdag O. Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems. International Journal of Mechanical Sciences, 2008;50:995-1003.
21. Laura PAA, Maurizi MJ, Pombo JL. A note on the dynamics analysis of an elastically restrained-free beam with a mass at the free end. Journal of Sound and Vibration,1975;41:397 05.
22. Dowell EH. On some general properties of combined dynamical systems, Transactions of the ASME, 1979;46:206-209.
23. Laura PAA, Verniere de Irassar PL, Ficcadenti GM. A note of transverse vibration of continuous beams subjected to an axial force and carrying concentrated masses, Journal of Sound and Vibration, 1983;86(2):279-284.
24. Liu WH, Wu JR, Huang CC. Free vibrations of beams with elastically restrained edges and intermediate concentrated masses. Journal of Sound and Vibration, 1988;122(2):193-207.
25. Register AH. A note on the vibration of generally restrained end loaded beams, Journal of Sound and Vibration, 1994;172(4):561-571.
26. Kukla S, Posiadala B. Free vibrations of beams with elastically mounted masses. Journal of Sound and Vibration, 1994;175(4):557-564.
27. Gûrgôze M. On the eigenfrequencies of cantilevered beams carrying tip mass and a spring mass in span, International Journal ofMechanical Engineering Sciences, 1996;38(12):1295-1306.
28. Rossit CA, Laura PAA. Transverse vibrations of a cantilever beam with a spring mass system attached on the free end. cean Engineering, 2001;28:933-939.
29. Volterra E, Zachmanoglou EC. Dynamics of Vibrations, Charles E. Merrill Books, Inc., Columbus, OH, 1965.
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