Abstract
In this paper, a negative stiffness oscillator is modelled and tested to exploit its nonlinear dynamical characteristics. The oscillator is part of a device designed to improve the current collection quality in railway overhead contact lines, and it acts like an asymmetric double-well Duffing system. Thus, it exhibits two stable equilibrium positions plus an unstable one, and the oscillations can either be bounded around one stable point (small oscillations) or include all the three positions (large oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinear dynamics and chaotic motion as well. Furthermore, its design is asymmetrical, and this plays a key role in its dynamic response, as the two natural frequencies associated with the two stable positions differ from each other. The first purpose of this study is to understand the dynamical behavior of the system in the case of linear and nonlinear oscillations around the two stable points and in the case of large oscillations associated with a chaotic motion. To accomplish this task, the device is mounted on a shaking table and it is driven with several levels of excitations and with both harmonic and random inputs. Finally, the nonlinear coefficients associated with the nonlinearities of the system are identified from the measured data.
Highlights
Devices and materials exhibiting a negative stiffness phase are often used as vibration isolators due to their amplified damping properties [1, 2]
A negative stiffness oscillator is modelled and tested to exploit its nonlinear dynamical characteristics. e oscillator is part of a device designed to improve the current collection quality in railway overhead contact lines, and it acts like an asymmetric double-well Duffing system. us, it exhibits two stable equilibrium positions plus an unstable one, and the oscillations can either be bounded around one stable point or include all the three positions
Its design is asymmetrical, and this plays a key role in its dynamic response, as the two natural frequencies associated with the two stable positions differ from each other. e first purpose of this study is to understand the dynamical behavior of the system in the case of linear and nonlinear oscillations around the two stable points and in the case of large oscillations associated with a chaotic motion
Summary
Devices and materials exhibiting a negative stiffness phase are often used as vibration isolators due to their amplified damping properties [1, 2]. A two-fold objective is pursued: first, the dynamical properties of the oscillator are analyzed, replicating experimentally the possible kind of motions it can exhibit (in-well, cross-well, and chaotic); second, nonlinear system identification is performed to extract the model parameters directly from the measurements. 2. A Negative Stiffness Oscillator e device here studied consists in a U-shaped steel frame connected through rods to a central moving mass. With U′′(z±∗ ) being the second derivative of U(z) computed in z∗− or z∗+ It is worth writing the equation of motion considering the oscillations around one of the possible equilibrium points. E advantage of using this formulation instead of equation (4) is that it allows the definition of a stable underlying linear system. is is a crucial requirement for the nonlinear subspace identification method, adopted in Section 4 to perform the nonlinear system identification of the structure under test
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