A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

An experimental proof of concept of a new semi-passive nonlinear piezoelectric shunt absorber, introduced theoretically in a companion article, is presented in this work. This absorber is obtained by connecting, through a piezoelectric transducer, an elastic structure to a resonant circuit that includes a quadratic nonlinearity. This nonlinearity is obtained by including in the circuit a voltage source proportional to the square of the voltage across the piezoelectric transducer, thanks to an analog multiplier circuit. Then, by tuning the electric resonance of the circuit to half the value of one of the resonances of the elastic structure, a two-to-one internal resonance is at hand. As a result, a strong energy transfer occurs from the mechanical mode to be attenuated to the electrical mode of the shunt, leading to two essential features: a nonlinear antiresonance in place of the mechanical resonance and an amplitude saturation. Namely, the amplitude of the elastic structure oscillations at the antiresonance becomes, above a given threshold, independent of the forcing level, contrary to a classical linear resonant shunt. This paper presents the experimental setup, the designed nonlinear shunt circuit and the main experimental results.

Vibration control through the robust nonlinear absorber with negative stiffness and internal resonance creation

In this study, a nonlinear absorber that works with a negative stiffness mechanism is suggested to mitigate vibration, and its effect on the reduction of vibration is investigated. The negative stiffness, which is inherently nonlinear, creates internal resonance; therefore, the vibration energy can be transmitted from low-frequency to high-frequency vibrating modes, causing vibration suppression. The nonlinear absorber is added to the primary nonlinear system, and when the main system is subjected to external resonance due to harmonic excitation, the negative stiffness parameter of absorber is so adjusted that autoparametric resonance occurs and vibration is reduced. First, the mathematical model of the system is presented and the governing differential equations of the motion are derived, and then, using the multiple scale method, the equations are solved for the case without, and with the 1:3 internal resonance. The responses and their stability are inspected, discussed, and compared. After that, the effect of negative stiffness and damping parameters on vibration amplitude reduction is investigated and the adequacy of the proposed absorber will be demonstrated by numerical analysis. Finally, the energy exchange between the primary system and the absorber will be demonstrated by plotting the responses in the state space and the displacement response Fourier spectrum.

A Study on Nonlinear Dynamic Response of the Large-Span Roof Structure with Suspended Substructure

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on the dynamic performance of the roof structures. In this paper, to explore the dynamic response of a large-span roof structure with a suspended substructure, a real structure model is simplified into a two-degrees-of-freedom system. The essential consideration of nonlinear vibration is elaborated in the equations of motions. Approximate analytical solutions for free and forced vibrations are derived using perturbation methods, while numerical analysis is carried out to validate the solutions. The ratio of linear to nonlinear amplitude is proposed to represent the nonlinear effect of the primary structure, and the nonlinear effect, varying with structural parameters of frequency ratio, mass ratio, excitation ratio, and external force to the primary structure, is investigated. It is shown that internal resonance occurs when the structural frequency ratio is close to 1:2 and that secondary resonance takes place due to certain external excitations; internal resonance and secondary resonance will magnify the amplitude of the primary structure during vibration. Finally, a case of a designed practical dome with a suspended substructure is studied to verify the outcomes from the above research. According to these findings, some design proposals for this type of structure are provided.

Double Antiresonance Fiber Sensor for the Simultaneous Measurement of Curvature and Temperature

Antiresonant hollow core fibers (ARHCFs) have gained some attention due to their notoriously attractive characteristics on managing optical properties. In this work, an inline optical fiber sensor based on a hollow square core fiber (HSCF) is proposed. The sensor presents double antiresonance (AR), namely an internal AR and an external AR. The sensor was designed in a transmission configuration, where the sensing head was spliced between two single mode fibers (SMFs). A simulation was carried out to predict the behaviors of both resonances, and revealed a good agreement with the experimental observations and the theoretical model. The HSCF sensor presented curvature sensitivities of −0.22 nm/m−1 and −0.90 nm/m−1, in a curvature range of 0 m−1 to 1.87 m−1, and temperature sensitivities of 21.7 pm/°C and 16.6 pm/°C, in a temperature range of 50 °C to 500 °C, regarding the external resonance and internal resonance, respectively. The proposed sensor is promising for the implementation of several applications where simultaneous measurement of curvature and temperature are required.

Mode coupling internal resonance characteristics of submerged floating tunnel tether

This study presents the mode coupling internal resonance characteristics of submerged floating tunnel tether. In which, in-plane and out-of-plane coupling of tether is taken into account. And the coupled vibration equations of tether for the in-plane first mode and out-of-plane first mode are obtained. The one-to-one mode coupling internal resonance characteristics of submerged floating tunnel tether are studied by numerical analysis method. It is shown that, when the conditions of modal coupling internal resonance are met, with the increase of the external excitation amplitude of the tether, the mid-span displacement of the tether increases gradually. When the amplitude of external excitation is less than a certain value, the internal resonance of tether will not occur. With the increase of damping ratio, the mid-span displacement of the tether decreases gradually. When the damping ratio increases to a certain value, the internal resonance will not occur. The study is helpful to restrain the vibration of submerged floating tunnel tether.

Performance Enhancing of Galloping-based Piezoelectric Energy Harvesting by Exploiting 1:1 Internal Resonance of Magnetically Coupled Oscillators

In this study, we introduced 1:1 internal resonance in a magnetically coupled 2-degree-of-freedom (2-DOF) galloping-based piezoelectric energy harvester to improve the energy harvesting efficiency. The governing equations for the proposed magnetically coupled aero-electro-mechanical system considering the effect of oscillating wake are established using the extended Hamilton principle, and the method of multiple scale is exploited to obtain approximate analytical solutions. Parameter sweeping numerical calculation is conducted to validate the analytical prediction through comparing with analytical solutions, and the results show a good matching between them. In addition, we investigated the systematic dynamic behaviors under a pure oscillating wake induced 1:1 internal response. Typical nonlinear characteristics such as jump, hysteresis, frequency synchronization under varying design parameters appear in the present system. Especially, cusp bifurcation and synchronization regime of oscillating wake coupled nonlinear oscillator in \(\eta - {\Theta _w}\) plane and \(\sigma - {\Theta _w}\) plan. With an adoption of magnetic force, chaos happens as the gap distance decreases smaller than 5 mm, and a frequency lock-in phenomenon can be strengthened through adjusting the magnet distance. In the perspective of output performance, both of the voltage and power output results shows that the exploiting of 1:1 internal resonance can significantly improve the output performance under a suitable magnet distance.