Understanding targeted energy transfer from a symmetry breaking perspective

Targeted energy transfer (TET) represents the phenomenon where energy in a primary system is irreversibly transferred to a nonlinear energy sink (NES). This only occurs when the initial energy in the primary system is above a critical level. There is a natural asymmetry in the system due to the desire for the NES to be much smaller than the primary structure it is protecting. This asymmetry is also essential from an energy transfer perspective. To explore how the essential asymmetry is related to TET, this work interprets the realization of TET from a symmetry breaking perspective. This is achieved by introducing a symmetrized model with respect to the generically asymmetric original system. Firstly a classic example, which consists of a linear primary system and a nonlinearizable NES, is studied. The backbone curve topology that is necessary to realize TET is explored and it is demonstrated how this topology evolves from the symmetric case. This example is then extended to a more general case, accounting for nonlinearity in the primary system and linear stiffness in the NES. Exploring the symmetry-breaking effect on the backbone curve topologies, enables the regions in the NES parameter space that lead to TET to be identified.

Numerical Study Of The Targeted Energy Transfer Between The Euler-Bernoulli Beam And A Nonlinear Energy Sink

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.

Numerical Study Of The Targeted Energy Transfer Between The Euler-Bernoulli Beam And A Nonlinear Energy Sink

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.