Exploring 1:3 internal resonance for broadband piezoelectric energy harvesting

Aravindan, M.; Ali, Shaikh Faruque

doi:10.1016/j.ymssp.2020.107493

Cited by 35 publications

(10 citation statements)

References 49 publications

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“…The frequency stabilization allows for MEMS to be used in time-keeping devices and paves the way for further miniaturization of clocks. Other applications exploiting nonlinear internal resonance are for example, improved mass sensing [19] or broadband piezoelectric energy harvesting [20]. Internal resonance can also be found in a single cantilever beam due to its third and fourth bending modes being naturally close to a ratio of 1:2.…”

Section: Possible Use Of Internal Resonance In Structural Dynamicsmentioning

confidence: 99%

Internal resonance in nonlinear structures—and what it can be used for

Tatzko

2023

Proc Appl Math and Mech

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In vibrating structures, nonlinear effects can play a decisive role. For example, stiffening responses can occur in integral components with low damping, but softening effects with a shift of the resonance to lower values by an increase of the vibration energy can be observed. Often these systems are considered only in a characteristic nonlinear vibration mode, allowing well‐known phenomena to be investigated. However, it may be the case that more than one nonlinear mode has a significant effect on the structural response of multi‐degree‐of‐freedom systems. If these modes take on integer multiples of frequency values, we speak of an internal resonance. In this work, the phenomenon of internal resonance is explained on the basis of a two‐mass oscillator. For this purpose, nonlinear modal analysis (NMA) is used to determine the amplitude‐dependent behavior of the resonant frequencies, referred to as nonlinear modes. These nonlinear modes already display the internal resonance in the form of characteristic trajectories, which are examined and explained in more detail here. A computational framework consisting of harmonic balance and continuation is used to calculate the nonlinear mode curves. In addition, nonlinear frequency responses are determined and their trajectories and properties in the internal resonance region are shown. To further understand the oscillatory behavior time plots are considered. Finally, a possible use for the observed properties is discussed as well and current approaches in research for the use of internal resonances are pointed out.

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Section: Possible Use Of Internal Resonance In Structural Dynamicsmentioning

confidence: 99%

Internal resonance in nonlinear structures—and what it can be used for

Tatzko

2023

Proc Appl Math and Mech

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“…Substituting equation (24) into equations ( 19) and (20), and separating the real and imaginary parts, the modulation equations of the Cartesian form are obtained as…”

Section: J Stat Mech (2022) 023204mentioning

confidence: 99%

“…It revealed that the internal resonance can broaden the frequency band and enhance the output performance. Aravindan et al [20] investigated the nonlinear dynamics of a 1:3 internally resonant piezoelectric cantilever beam with a lumped mass. They revealed that the strong modal interaction can make the structure easily realize the effect of broadband vibration under the primary resonance of the second mode.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

Nie¹,

Gao²,

Wang³

et al. 2022

J. Stat. Mech.

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The nonlinear behaviors of the L-shaped beam structure based on 1:2 internal resonance are investigated. The governing equations considering quadratic and cubic nonlinearity of the L-shaped beam structure are verified by the transient dynamic analysis of the finite element model. The approximate analytical solution for this system is derived by the method of multiple scales, and verified by the numerical solution. The Jacobian matrix of the modulation equation is employed to determine the equilibrium stability of the vibration response. The effects of the excitation frequency, amplitude and cubic nonlinear terms on the nonlinear responses of the primary resonance of the first and second modes are discussed. The bifurcation diagram, spectrum, phase plane and Poincaré section are applied to investigate the nonlinear vibration response. The results reveal that many nonlinear phenomena are observed, such as double-jump, hysteresis, Hopf bifurcation, modal saturation, multiple solutions, multi-softening and so on. The influence of cubic nonlinear term on internal resonance response should be considered. The broadband characteristics of internal resonance system are broadened by the nonlinear softening and hardening in the frequency response curve. In the primary resonance of the second mode, the hardening region in the frequency response curve becomes the softening region with the increase of excitation amplitude. The double-jump phenomenon is found in this newly formed softening region, and up to five solutions are observed in this region, including three sink points and two saddle-nodes. The broadband characteristics of the system is of great benefit to the application of broadband piezoelectric vibration energy harvesting.

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“…Jiang et al (2022) explored a novel one-to-one internal resonance to scavenge flow energy from vortex-induced vibrations, the mechanism of synchronous oscillations was introduced by the amplitude-frequency relationship. Aravindan and Ali (2021) analyzed the nonlinear dynamics behaviors and harvesting performance of a one-to-three internally resonant piezoelectric cantilever beam with a lumped mass under harmonic excitation and showed that the higher mode invoked through internal resonance plays a significant role in broadband power generation. Fan et al (2022b) presented an internal resonance piezoelectric energy harvester with three-dimensional coupled bending and torsional modes and shown that the fine-tuned system leverages a two-to-one internal resonance between its first torsion and second bending modes to enhance the power output.…”

Section: Introductionmentioning

confidence: 99%

Broadband energy harvesting in a two-degree-of-freedom nonlinear system without internal resonance

Zhang,

Yang,

Jiang

et al. 2023

Journal of Intelligent Material Systems and Structures

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In this paper, we propose a novel two-degree-of-freedom (TDOF) nonlinear energy harvester without internal resonance to realize broadband harvesting characteristic. To show the performance, a TDOF nonlinear electromagnetic harvester is designed. The electromechanical coupling system is established and solved by adopting the harmonic balance method. The modulation equations are constructed, the first-order harmonic solutions of the system are obtained and the frequency response curves of the displacement and current are plotted. The advantage of the proposed harvester is compared to the conventional single-degree-of-freedom (SDOF) nonlinear model and the corresponding TDOF linear system, the results achieve that the proposed scheme can enhance the bandwidth of the harvesting energy. Furthermore, the influences of system parameters on the response are discussed. The accuracy of the first-order harmonic results is revealed by numerical simulations. To further demonstrate the accuracy of analytical solutions, the finite element simulation is constructed in ANSYS finite element analysis (FEA) software. The performance predictions from the analytical solutions are compared with results from FEA. It is convincingly demonstrated that periodic solutions have a degree of good consistency for the behavior of frequency response curves.

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Exploring 1:3 internal resonance for broadband piezoelectric energy harvesting

Cited by 35 publications

References 49 publications

Internal resonance in nonlinear structures—and what it can be used for

Internal resonance in nonlinear structures—and what it can be used for

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

Broadband energy harvesting in a two-degree-of-freedom nonlinear system without internal resonance

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