Author
Abstract
The present work studies the performance of linear and nonlinear dynamic vibration absorbers mounted on Euler–Bernoulli beams subjected to moving loads. Absorbers used in this work consist of one mass, two springs and one linear damper.The springs may be considered either linear or non-linear. The objective is to compare the performance of these absorbers with classical dynamic and nonlinear absorbers. The partial differential equations governing the problem are reduced to a set of ordinary differential equations by means of Galerkin–Bubnov method. The performance of the dynamic absorbers in reduction of the beams’ vibration is estimated through the maximum amplitude of vibration and the portion of energy dissipated by the dynamic damper. Finally, after optimizations, the effectiveness of the dynamic absorbers is determined for different conditions and applications.
Keywords
1. Gendelman, O. V., “Transition of Energy to Nonlinear Localized Mode in Highly Asymmetric System of Nonlinear Oscillators”, Nonlinear Dynamics, Vol. 25, pp. 237-253, 2001.
2. Vakakis, A. F., “Inducing Passive Nonlinear Energy Sinks in Linear Vibrating Systems”, Journal of Vibration and Acoustics, Vol. 123, No. 3, pp. 324-332, 2001.
3. Gendelman, O. V., Vakakis, A. F., Manevitch, L. I., and McCloskey, R., “Energy Pumping in Nonlinear Mechanical Oscillators I: Dynamics of the Underlying Hamiltonian System”, Journal of Applied Mechanics, Vol. 68, No. 1, pp. 34-41, 2001.
4. Vakakis, A. F., and Gendelman, O.V., “Energy Pumping in Nonlinear Mechanical Oscillators II: Resonance Capture”, Journal of Applied Mechanics, Vol. 68, No. 1, pp. 42-48, 2001.
5. Gendelman, O. V., Gorlov, D. V., Manevitch, L. I., and Musienko, A. I., “Dynamics of Coupled Linear and Essentially Nonlinear Oscillators with Substantially Different Masses”, Journal of Sound and Vibration, Vol. 286, pp. 1-19, 2005.
6. Timoshenko, S., Young, D. H., and Weaver, W., Vibration Problems in Engineering, Fourth ed., Wiley, New York, 1974.
7. Esmailzadeh, E., and Ghorashi, M., “Vibration Analysis of Beams Traversed by Uniform Partially Distributed Moving Mass”, Journal of Sound and Vibration, Vol. 184, No. 1, pp. 9-17, 1995.
8. Den Hartog, J. P., Mechanical Vibrations, McGraw-Hill, New York, 1985.
9. Wu, J. J., “Study on the Inertia Effect of Helical Spring of the Absorber on Suppressing the Dynamic Responses of a Beam Subjected to a Moving Load”, Journal of Sound and Vibration, Vol. 297, pp. 981-999, 2006.
10. Greco, A., and Santini, A., “Dynamic Response of a Flexural Non-Classically Damped Continuous Beam under Moving Loadings”, Computers and Structures, Vol. 80, pp. 1945-1953, 2002.
11. Lee, Y. S., Kerschen, G., Vakakis, A. F., Panagopoulos, P. N., Bergman L. A., and Farland, D. M. Mc, “Complicated Dynamics of a Linear Oscillator with a Light, Essentially Nonlinear Attachment”, Physica D, Vol. 204, pp. 41-69, 2005.
12. Kwon, H.-C., Kim, M.-C., and Lee I.-W., “Vibration Control of Bridges under Moving Loads”, Computers and Structures, Vol. 66, pp. 473-480, 1998.
13. Muserosa, P., and Martinez- Rodrigo, M. D., “Vibration Control of Simply Supported Beam Sunder Moving Loads using Fluid Viscous Dampers”, Journal of Sound and Vibration, Vol. 300, pp. 292-315, 2007.
14. Wang, J. F., Lin, C. C., and Chen, B. L., “Vibration Suppression for High-Speed Railway Bridges using Tuned Mass Dampers”, International Journal of Solids and Structures, Vol. 40, pp. 465-491, 2003.
15. Das, A. K., and Dey, S. S., “Effects of Tuned Mass Dampers on Random Response of Bridges”, Computers and Structures, Vol. 43, pp. 745-750, 1992.
16. Georgiades, F., and Vakakis, A. F., “Dynamics of a Linear Beam with an Attached Local Nonlinear Energy Sink”, Communications in Nonlinear Science and Numerical Simulation, Vol. 12, pp. 643-651, 2005.
17. Vakakis, A. F., Manevitch, L. I., Gendelman, O., and Bergman, L., “Dynamics of Linear Discrete Systems Connected to Local Essentially Nonlinear Attachments”, Journal of Sound and Vibration, Vol. 264, pp. 559-577, 2003.
18. Gendelman, O. V., “Targeted Energy Transfer in Systems with Non-Polynomial Nonlinearity”, Journal of Sound and Vibration, Vol. 315, pp. 732-745, 2008.
19. Samani, F. S., and Pellicano, F., “Vibration Reduction on Beams Subjected to Moving Loads using Linear and Nonlinear Dynamic Absorbers”, Journal of Sound and Vibration, Vol. 325, pp. 742-754, 2009.
20. Samani, F. S., Pellicano, F., and Masoumi, .A, “Performances of Dynamic Vibration Absorbers for Beams Subjected to Moving Loads”, Nonlinear Dyn, Vol. 73, pp. 1065-1079, 2013.
21. Abu-Alshaikha, I. M., Al-Rabadib, A. N., and Alkhaldi, H. S, “Dynamic Response of Beam with Multi-Attached Oscillators and Moving Mass: Fractional Calculus Approach”, Jordan Journal of Mechanical and Industrial Engineering, Vol. 8 No. 5 pp. 275-288, 2014.
22. Anh, N. D., Nguyen, N. X., and Hoa, L. T., “Design of Three-Element Dynamic Vibration Absorber for Damped Linear Structures”, Journal of Sound and Vibration, Vol. 332, pp. 4482-4495, 2013.
23. Wu, J. J., “Study on the Inertia Effect of Helical Spring of the Absorber on Suppressing the Dynamic Responses of a Beam Subjected to a Moving Load”, Journal of Sound and Vibration, Vol. 297, pp. 981-999, 2006.
24. Ahmadabadi, Z. N., and Khadem, S. E., “Nonlinear Vibration Control of a Cantilever Beam by a Nonlinear Energy Sink”, Mechanism and Machine Theory, Vol. 50, pp. 134-149, 2012.
2. Vakakis, A. F., “Inducing Passive Nonlinear Energy Sinks in Linear Vibrating Systems”, Journal of Vibration and Acoustics, Vol. 123, No. 3, pp. 324-332, 2001.
3. Gendelman, O. V., Vakakis, A. F., Manevitch, L. I., and McCloskey, R., “Energy Pumping in Nonlinear Mechanical Oscillators I: Dynamics of the Underlying Hamiltonian System”, Journal of Applied Mechanics, Vol. 68, No. 1, pp. 34-41, 2001.
4. Vakakis, A. F., and Gendelman, O.V., “Energy Pumping in Nonlinear Mechanical Oscillators II: Resonance Capture”, Journal of Applied Mechanics, Vol. 68, No. 1, pp. 42-48, 2001.
5. Gendelman, O. V., Gorlov, D. V., Manevitch, L. I., and Musienko, A. I., “Dynamics of Coupled Linear and Essentially Nonlinear Oscillators with Substantially Different Masses”, Journal of Sound and Vibration, Vol. 286, pp. 1-19, 2005.
6. Timoshenko, S., Young, D. H., and Weaver, W., Vibration Problems in Engineering, Fourth ed., Wiley, New York, 1974.
7. Esmailzadeh, E., and Ghorashi, M., “Vibration Analysis of Beams Traversed by Uniform Partially Distributed Moving Mass”, Journal of Sound and Vibration, Vol. 184, No. 1, pp. 9-17, 1995.
8. Den Hartog, J. P., Mechanical Vibrations, McGraw-Hill, New York, 1985.
9. Wu, J. J., “Study on the Inertia Effect of Helical Spring of the Absorber on Suppressing the Dynamic Responses of a Beam Subjected to a Moving Load”, Journal of Sound and Vibration, Vol. 297, pp. 981-999, 2006.
10. Greco, A., and Santini, A., “Dynamic Response of a Flexural Non-Classically Damped Continuous Beam under Moving Loadings”, Computers and Structures, Vol. 80, pp. 1945-1953, 2002.
11. Lee, Y. S., Kerschen, G., Vakakis, A. F., Panagopoulos, P. N., Bergman L. A., and Farland, D. M. Mc, “Complicated Dynamics of a Linear Oscillator with a Light, Essentially Nonlinear Attachment”, Physica D, Vol. 204, pp. 41-69, 2005.
12. Kwon, H.-C., Kim, M.-C., and Lee I.-W., “Vibration Control of Bridges under Moving Loads”, Computers and Structures, Vol. 66, pp. 473-480, 1998.
13. Muserosa, P., and Martinez- Rodrigo, M. D., “Vibration Control of Simply Supported Beam Sunder Moving Loads using Fluid Viscous Dampers”, Journal of Sound and Vibration, Vol. 300, pp. 292-315, 2007.
14. Wang, J. F., Lin, C. C., and Chen, B. L., “Vibration Suppression for High-Speed Railway Bridges using Tuned Mass Dampers”, International Journal of Solids and Structures, Vol. 40, pp. 465-491, 2003.
15. Das, A. K., and Dey, S. S., “Effects of Tuned Mass Dampers on Random Response of Bridges”, Computers and Structures, Vol. 43, pp. 745-750, 1992.
16. Georgiades, F., and Vakakis, A. F., “Dynamics of a Linear Beam with an Attached Local Nonlinear Energy Sink”, Communications in Nonlinear Science and Numerical Simulation, Vol. 12, pp. 643-651, 2005.
17. Vakakis, A. F., Manevitch, L. I., Gendelman, O., and Bergman, L., “Dynamics of Linear Discrete Systems Connected to Local Essentially Nonlinear Attachments”, Journal of Sound and Vibration, Vol. 264, pp. 559-577, 2003.
18. Gendelman, O. V., “Targeted Energy Transfer in Systems with Non-Polynomial Nonlinearity”, Journal of Sound and Vibration, Vol. 315, pp. 732-745, 2008.
19. Samani, F. S., and Pellicano, F., “Vibration Reduction on Beams Subjected to Moving Loads using Linear and Nonlinear Dynamic Absorbers”, Journal of Sound and Vibration, Vol. 325, pp. 742-754, 2009.
20. Samani, F. S., Pellicano, F., and Masoumi, .A, “Performances of Dynamic Vibration Absorbers for Beams Subjected to Moving Loads”, Nonlinear Dyn, Vol. 73, pp. 1065-1079, 2013.
21. Abu-Alshaikha, I. M., Al-Rabadib, A. N., and Alkhaldi, H. S, “Dynamic Response of Beam with Multi-Attached Oscillators and Moving Mass: Fractional Calculus Approach”, Jordan Journal of Mechanical and Industrial Engineering, Vol. 8 No. 5 pp. 275-288, 2014.
22. Anh, N. D., Nguyen, N. X., and Hoa, L. T., “Design of Three-Element Dynamic Vibration Absorber for Damped Linear Structures”, Journal of Sound and Vibration, Vol. 332, pp. 4482-4495, 2013.
23. Wu, J. J., “Study on the Inertia Effect of Helical Spring of the Absorber on Suppressing the Dynamic Responses of a Beam Subjected to a Moving Load”, Journal of Sound and Vibration, Vol. 297, pp. 981-999, 2006.
24. Ahmadabadi, Z. N., and Khadem, S. E., “Nonlinear Vibration Control of a Cantilever Beam by a Nonlinear Energy Sink”, Mechanism and Machine Theory, Vol. 50, pp. 134-149, 2012.
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