Abstract
Targeted energy transfer (TET) refers to the spatial transfer of energy between a primary structure of interest and isolated oscillators called the energy sink (ES). In this work, the primary structure of interest is a slender beam modeled by the Euler-Bernoulli theory, and the ES is a single-degree-of-freedom oscillator with either linear or cubic nonlinear stiffness property. The objective of this study is to characterize the TET and the effectiveness of ES under impact and periodic excitations. By using the scientific computation package, MATLAB, numerical simulations are carried out based on excitations of various strength and locations. Both time and frequency domain characterizations are used. For the impact excitation, the ES with the cubic nonlinear stiffness property is more superior to the linear oscillator in that larger percentage of the impact energy can be dissipated there. The main energy transfer was found to be due to a 3- to-1 frequency coupling between the first bending mode and the ES. For the periodic excitation, however, both linear and nonlinear ES exhibit generally poorer performance than the case with the impact excitation. Future works should focus on the frequency-energy relationship of the periodic solution of the underlying Hamiltonian, as well as using finite element model to verify the simulation results.
Highlights
This thesis describes the investigation on the Targeted EnergyTransfer (TET) from a multimodal beam vibration to the Energy Sink (ES)
R1, which measures the ratio of the dissipated energy by energy sink (ES) and the total beam energy can drop significantly (Figures 4.1c~4.5c). (Note that the results shown in these figures are in logarithmic scale.) For example, R1 drops significantly in the frequency neighborhoods around f 7.5 Hz and f 21 Hz at D1 = 0.3
Discussions and Conclusion Numerical results of the targeted energy transfer between the Euler-Bernoulli beam and ES are presented. Both nonlinear energy sink (NES) and linear energy sink (LES) are considered for the beam under impact and periodic excitations
Summary
Transfer (TET) from a multimodal beam vibration to the Energy Sink (ES). The beam can experience various external disturbances such as impact loading, periodic or random excitation. The purpose of the ES is to absorb or dissipate the unwanted vibration of the beam due to the disturbance. An ES is normally modelled with a nonlinear or linear stiffness term and a linear viscous damping term. It can be categorized as nonlinear energy sink (NES) or linear energy sink (LES). The main energy transfer mechanism is contributed by “mode locking” of specific frequency of vibration of the beam and the ES. The energy is channeled through a kind of resonance mechanism or resonant modal interaction to ES [2, 3]. The attachment of the ES can be grounded or ungrounded and it can be single-degree-of-freedom (SDOF) or multi-degree-of-freedom (MDOF) system depending on the design and use
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