טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentFarid Maor
SubjectTuned Pendulum as Nonlinear Energy Sink for
Broad Energy Range
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

Nonlinear Energy Sinks (NES) are widely studied as possible engineering solution for mitigation of steady-state, impulsive, transient and broadband excitations. Current work is devoted to applicability of common pendulum as the NES for mitigation of impulsive excitations. It turns out that if the pendulum is tuned at linear frequency of the primary mass, it can overcome one of main shortcomings of traditional NES designs and efficiently absorb energy in a wide range of energies. The reason is that for small energies the pendulum responds as tuned mass damper; at higher energies the pendulum acts as rotational NES. Thus, relatively broad diapason of energies can be covered.

. The model of the eccentric NES is presented in Figure 1.



Text Box: Figure 1- Scheme of primary mass with attached eccentric rotator




We demonstrate numerically that the properly tuned pendulum can be used as the NES and indeed has broader energy range than regular rotational NES. We study analytically and numerically the dynamics of such pendulum NES and explore corrections to a structure of its slow invariant manifold caused by presence of the gravity. Besides, we discuss the relationship between the pendulum NES performance and variation of its initial conditions, as one can see in Figure 2- the mean time for sufficient energy absorbance and its standard deviation for different values of initial energy, given by different values of initial[U1]  conditions, under gravity significances.


?????: C:\Documents and Settings\???? ????\????? ??????\???????\???\????\3-11-13\figures\means_std_for_different_betas.bmp




Text Box: Figure 2 - The average characteristic time of energy dissipation and its standard deviation for different values of initial energy, with account of different values of initial conditions.






As one can conclude from Figure 2, the most efficient design coefficient for energy absorbance, both for low energy values and for higher ones, was found, b=1. It describes an internal resonance in the NES system, between the natural frequency of the main mass's translations, and the natural frequency of the secondary smaller mass's rotations.

This efficient energy absorbance is in essence that a rapid, efficient TET occurs for a broad energy range.



 [U1]Some response curves would be of interest