A Comparison Between the Linear and Nonlinear Dynamic Vibration Absorber for a Timoshenko Beam
الموضوعات :
H Kouhi
1
,
R Ansari
2
,
E Salahshoor
3
,
B Miripour Fard
4
1 - Department of Mechanical Engineering, University of Guilan, Rasht, Iran
2 - Department of Mechanical Engineering, University of Guilan, Rasht, Iran
3 - Department of Mechanical Engineering, Izeh Branch, Islamic Azad University, Izeh, Iran
4 - Department of Mechanical Engineering, University of Guilan, Rasht, Iran
الکلمات المفتاحية: Robustness, Uncertainty, Timoshenko beam, Optimization, Dynamic Vibration Absorber,
ملخص المقالة :
Dynamic vibration absorbers (DVAs) play an important role in the energy dissipation of a vibrating system. Undesirable vibrations of structures can be reduced by using the absorbers. This paper investigates the effect of an attached energy sink on the energy dissipation of a simply supported beam subjected to harmonic excitation. The aim is to design an optimal linear energy sink (LES) and a nonlinear energy sink (NES) and then compare them with each other. Each absorber includes a spring, a mass, and a damper. For each absorber, the optimum mass, stiffness, and damping coefficients are obtained in order to minimize the beam’s maximum amplitude at the resonant frequencies. The optimization problem is minimizing the maximum amplitude of the beam subjected to an arbitrary harmonic force excitation. For consideration of the effects of rotary inertia and shear deformation, the Timoshenko beam theory is used. The mathematical model of beam with DVA is verified by using the ANSYS WORKBENCH software. Finally, by considering the uncertainty on the DVA parameters it was observed that the LES is more robust than the NES.
[1] Ahmadabadi Z.N., Khadem S., 2012, Nonlinear vibration control of a cantilever beam by a nonlinear energy sink, Mechanism and Machine Theory 50: 134-149.
[2] Avramov K., Gendelman O., 2010, On interaction of vibrating beam with essentially nonlinear absorber, Meccanica 45: 355-365.
[3] Chen J., Zhang W., Yao M., Liu J., Sun M., 2020, Thermal effect on dynamics of beam with variable-stiffness nonlinear energy sink, International Journal of Nonlinear Sciences and Numerical Simulation 21: 1-10.
[4] Chen Y.-H., Hiang Y.-H., 2004, Timoshenko beam with tuned mass dampers and its design curves, Journal of Sound and Vibration 278: 873-888.
[5] Esmailzadeh E., Jalili N., 1998, Optimum design of vibration absorbers for structurally damped Timoshenko beams, Journal of Vibration and Acoustics 120(4): 833-841.
[6] Georgiades F., Vakakis A.F., 2007, Dynamics of a linear beam with an attached local nonlinear energy sink, Communications in Nonlinear Science and Numerical Simulation 12: 643-651.
[7] Huang T., 1961, The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions, Journal of Vibration and Acoustics 28(4): 579-584.
[8] Kani M., Khadem S., Pashaei M. Dardel M., 2016a, Vibration control of a nonlinear beam with a nonlinear energy sink, Nonlinear Dynamics 83: 1-22.
[9] Kani M., Khadem S.E., Pashaei M. H., Dardel M., 2016b, Design and performance analysis of a nonlinear energy sink attached to a beam with different support conditions, Proceedings of the Institution of Mechanical Engineers Part C, Journal of Mechanical Engineering Science 230: 527-542.
[10] Moghaddas M., Esmailzadeh E., Sedaghati R., Khasravi P., 2012, Vibration control of Timoshenko beam traversed by moving vehicle using optimized tuned mass damper, Journal of Vibration and Control 18: 757-773.
[11] Parseh M., Dardel M., Ghasemi M. H., 2015, Investigating the robustness of nonlinear energy sink in steady state dynamics of linear beams with different boundary conditions, Communications in Nonlinear Science and Numerical Simulation 29: 50-71.
[12] Samani F. S., Pellicano F. Masoumi A., 2013, Performances of dynamic vibration absorbers for beams subjected to moving loads, Nonlinear Dynamics 73: 1065-1079.
[13] Starosvetsky Y., Gendelman O., 2008, Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber, Nonlinear Dynamics 51: 47.
[14] Vakakis A. F., Manevitch L., Gendelman O., Bergman L., 2003, Dynamics of linear discrete systems connected to local, essentially non-linear attachments, Journal of Sound and Vibration 264: 559-577.
[15] Younesian D., Nankali A., Motieyan E., 2011, Optimal nonlinear energy sinks in vibration mitigation of the beams traversed by successive moving loads, Journal of Solid Mechanics 3:321-323.
[16] Zang J., Zhang Y.-W., Ding H., Yang T.-Z., Chen L.-Q., 2019, The evaluation of a nonlinear energy sink absorber based on the transmissibility, Mechanical Systems and Signal Processing 125: 99-122.
