Nonlinear Absorber Research Articles

Influence of Boundary Impedance of 3D Cavity on Targeted Energy Transfer between a Damped Acoustic Mode and a Nonlinear Membrane Absorber

In order to apply the nonlinear energy sink (NES) to reduce the low-frequency noise inside a 3D acoustic cavity with an impedance boundary, a two degrees-of-freedom (DOF) dynamic model of the coupled system of one damped acoustic mode of a regular 3D acoustic cavity and a nonlinear membrane absorber as the NES is established. The damping coefficient of the acoustic mode is obtained based on the finite element analysis method and the relationship of the boundary impedance and the absorption coefficient of the cavity. Based on the set-up of the system, the damping coefficient of the acoustic mode is determined. The frequency responses and the targeted energy transfer (TET) phenomenon of the coupled system are analyzed, and the theoretical and numerical results of the frequency responses of the system are in good agreement with the experimental ones. The effects of the wall impedance of the cavity on the optimal TET are discussed. With the increase in the impedance ratio of the wall, the amplitude of the acoustic displacement plateau decreases, and the frequency bandwidth of the plateau and the two thresholds of the optimal TET interval of the excitation increase. It provides a comprehensive theoretical model and experimental basis for the application of NES in the actual complex structure and provides a reliable design method and control strategy for controlling vehicle interior low-frequency broadband noise.

Internal resonance analysis of bio-inspired X-shaped structure with nonlinear vibration absorber

In this paper, a vibration isolation system based on bio-inspired structure with a nonlinear absorber is proposed. The nonlinear vibration properties and complex dynamical characteristics are explored elaborately in the presence of internal resonance. Lagrange’s principle is employed to derive the governing equations, which can describe the coupled nonlinear vibration system. The method of multiple scales is utilized to obtain the steady-state responses of the coupled system. It is found that the frequency-amplitude relationships reveal the typical nonlinear phenomena including jumping and multi-value. The influences of parameters on the dynamical characteristics are discussed in detail. Numerical integrations are directly implemented on the vibration equations to verify the aforementioned analytical results. And furthermore, bifurcations and chaotic motions are detected in the bifurcation diagrams via the Poincare section techniques. The proposed system and the corresponding researches would be of significance for the design and practical applications of the passive vibration control.

Random vibration analysis of nonlinear structure with pounding tuned mass damper

To mitigate the undesired vibrations of the structure, a cost-effective approach is to set up the nonlinear dynamic vibration absorber (NLDVA) on the structure. As an alternative NLDVA, the Pounding Tuned Mass Damper (PTMD) gathered extensively attention in recent years. However, the random vibration analysis of structure coupled with PTMD still poses a challenge. Besides, there remains an urgent need to construct a more comprehensive recovery coefficient (RC) for the two-stage damping mechanism of PTMD. To fill in this gap, this work involves the nonlinear random vibration of a type of two degree-of-freedom system composing of a main structure (MS) coupled to a PTMD device, in which the collision process of the system is portrayed by a segmented recovery coefficient (RC) model. Specifically, an equivalent system of structure-PTMD is firstly constructed by coordinate transformation. Then, the approximate probability density function (PDF) of equivalent system is performed by combining non-smooth conversion and stochastic averaging method (SAM). Further, the approximate PDF solution of the structure-PTMD can be determined by resorting to Jacobi transformation and verified numerically. Remarkably, the approximate PDF solutions of the system can also be applied to estimate the power spectral density of the system response. Being analytical, the analysis in this work yields results in the closed-form expressions that enable one to acquire new insight into the dynamic features of the structure-PTMD system. Moreover, the proposed scheme will promote the design and application of PTMD in practical projects from a theoretical point of view.

Comparison study of the dynamic behavior of a generally restrained beam structure attached with two types of nonlinear vibration absorbers

Beam structures with nonlinear vibration absorbers (NVAs) are attracting great research attention. Nonlinear vibration absorbers can more effectively suppress the vibration response of beam structures over the traditional vibration absorbers. The existing studies mainly focus on the dynamic behavior of beam structures with NVAs and boundary rotational restraints of beam structures are typically ignored. Additionally, it is difficult to adjust the stiffness of NVAs, limiting their engineering applications. Motivated by such limitations, the dynamic model of a generally restrained beam attached with two types of NVAs is established. Stiffness coefficients of NVAs can be adjusted by changing the initial length of horizontal springs. Dynamic behavior of the beam structure is predicted via the Galerkin truncated method (GTM). Results calculated by the GTM are verified by the harmonic balance method. Based on this, the influence of these two types of NVAs on dynamic behavior and vibration suppression of the beam structure is investigated. Appropriate parameters of the NVA beneficially affect the vibration suppression of the beam structure. With the same varying range of parameters belonging to NVAs, dynamic responses of the beam structure are more sensitive to the type-A NVA.

Data-driven optimization for flutter suppression by using an aeroelastic nonlinear energy sink

Aeroelastic systems are at risk of flutter instabilities which can lead to structural failure. Recently, an innovative design of nonlinear energy sink (NES) has been introduced to suppress flutter instabilities by adding a NES to the flap control surface as a nonlinear energy absorber resulting in a flap-NES. Optimal choice of flap-NES parameters, however, requires a comprehensive characterization of the nonlinear response of the system in the design space. Performing this nonlinear analysis using traditional approaches demands massive theoretical and computational efforts. This work is a foundational study of flap-NES-based flutter control of a typical pitch–plunge section and focuses on obtaining flap-NES parameters using a data-driven optimization algorithm. The optimization is based on a genetic algorithm combined with a recently introduced data-driven bifurcation forecasting method that allows constructing the bifurcation diagram of the system dynamics using limited time series data. Results of this study show that an optimal design of the flap-NES system results in an increased linear flutter speed, reduced post-flutter limit cycle oscillation amplitudes, and improved nature of the bifurcation diagram from subcritical to supercritical.

Shock-Induced Vibration of Composite Truss Core Sandwich Plates with Distributed Nonlinear Absorbers by Optimal Locations

In order to solve the problems of limited installation space and strict additional quality, the effects of internal distributed nonlinear energy sinks (NES) considering optimal locations on a composite truss core sandwich plate are investigated in this paper. Choose five NESs here and inset them in the different places of the sandwich plate to suppress the vibration of the plate, which is excited by a half-wave shock. The coupled dynamic equations of the system are derived by the principle of conservation of energy. Then, the vibration-control performances of five NESs are discussed by numerical simulation. The distributions of the five NESs are analyzed, and the optimal position distributions are obtained. Based on the optimal location, the transient responses of the system are studied. Moreover, the performances of five NESs and a single NES are compared in different dimensions. Finally, it is found that the selection of parameters has a great impact on the effectiveness of the five NESs. The new distribution way is introduced to improve the suppression effects of the five NESs in the sandwich plate.

A Comparative Study of Parameter Identification Methods for Asymmetric Nonlinear Systems with Quadratic and Cubic Stiffness

Understanding the nonlinear dynamic characteristics of engineering structures is challenging, especially for the systems that exhibit asymmetric nonlinear behavior. This paper compared four parameter identification methods for asymmetric nonlinear systems incorporating quadratic and cubic stiffness nonlinearities. Hilbert transform, zero-crossing, direct quadrature, and wavelet transform were used to obtain the backbone, envelope, and restoring force curves from the free vibration time history. A nonlinear curve-fitting method was then applied to estimate the stiffness parameters of the asymmetric systems, and a linear least square fitting approach was utilized to estimate the damping parameters of the asymmetric systems. We used the Helmholtz–Duffing oscillator as a numerical example and a nonlinear vibration absorber with geometric imperfections to verify the feasibility and accuracy of these methods. The advantages and disadvantages of these methods and the deviations in estimated results are discussed.

A New Way to Predict the Efficiency of Optical Limiters without Providing an Experiment: Processing of TDDFT Calculations for the Case of Pure Two-Photon Absorption.

Laser-power-limiting devices play a predominant role in photonics because of their potential for protecting human eyes and optical devices that are sensitive to intense laser beams. This paper describes a new methodology for predicting the efficiency of optical limiting based on electric-field-induced changes in absorption spectra calculated with the TDDFT quantum-chemical method. Analytical equations are derived to evaluate the optical thresholds and speed of switching on, the dynamic range, and the degree of nonlinear attenuation of the radiation fluxes for the case of two-photon absorption. Thus, the researcher does not need to conduct costly experiments to evaluate the suitability of nonlinear absorbers for the creation of optical limiters. The possibility of developing a forecasting model is demonstrated by an example of a series of stable slipped-cofacial phthalocyanine J-type dimers, which were synthesized and investigated previously.

A non-traditional variant nonlinear energy sink for vibration suppression and energy harvesting

In this article, an apparatus is proposed for simultaneous vibration suppression and energy harvesting in a broad frequency band. Traditionally, both the spring and the damper of a vibration absorber are directly connected to a primary system. Alternatively, a non-traditional way is to place the damper of the vibration absorber between the absorber mass and the base. A nonlinear energy sink (NES) is a type of nonlinear vibration absorber with an essential nonlinearity. When a strong nonlinear oscillator with a small linear stiffness is weakly coupled to a primary system, it behaves similarly to the NES, which is termed “variant NES”. In the proposed apparatus, a variant NES is arranged in the non-traditional way in which a cantilever beam is placed between a pair of continuous-contact blocks which force the beam to deflect nonlinearly. An electromagnetic energy harvester, which also acts as a damper in the non-traditional variant NES, is formed by attaching a pair of permanent magnets to the free end of the beam and fixing a pair of coils to the base. The transient performances of the developed apparatus are investigated in terms of vibration suppression and energy harvesting using numerical simulation and compared with those of an optimum non-traditional vibration absorber. The simulation results are validated by an experimental study. It is found that the proposed non-traditional variant NES exhibits typical NES characteristics such as 1:1 resonance, targeted energy transfer (TET), and an initial energy threshold. With the prerequisite of TET being established under high-level initial energy, the best trade-off between vibration suppression and energy harvesting is achieved when the NES’s oscillation decays slowly under low electrical damping or quickly under high electrical damping.

Evaluation of a robust dynamic vibration absorber based on negative stiffness and internal resonance against seismic excitation

In this study, a nonlinear absorber that works with a negative stiffness is introduced to control vibration and its effect on reducing earthquake damage is investigated. Negative stiffness increases structural softness and damping. Also, due to its inherent nonlinear nature, negative stiffness can cause internal resonance and transfer vibration energy from a directly excited vibrating mode to a higher frequency mode. Using these features can be effective in reducing vibration. First, to investigate the dynamic behavior in conditions without internal resonance and with 1:3 internal resonance, the proposed absorber is added to a nonlinear main system and when the system is under external resonance due to harmonic excitation, the negative stiffness parameter of the absorber for conditions with and without Internal resonance is adjusted. The mathematical model of the system is presented and the governing differential equations are derived. The governing equations are solved by the Multiple Scale method, the answers and their stability are examined, discussed and compared. Then, by generalizing the absorber ability to structures with general nonlinear behavior, the effect of the proposed absorber on reducing the damage caused by near and far from the fault earthquakes is studied by numerical simulation and for cases where under an earthquake record, The absorber intensifies the damage to the structure and loses its reliability, an active control loop is proposed and its effect is investigated.

Stable and tunable multi-wavelength erbium-doped fiber lasers using saturable absorbent tungsten disulfide

A multi-wavelength erbium-doped fiber laser using tungsten disulfide (WS2) as a nonlinear saturable absorber is proposed. The laser structure consists of a Lyot filter and a WS2 film in a ring cavity. The WS2 film attached to the end of the fiber jumper can suppress the mode competition phenomenon caused by erbium-doped fiber due to its good nonlinear optical properties. In addition, it can suppress mode contention and stabilize multi-wavelength output. The number of wavelengths can be tuned by adjusting the length of the polarization-maintaining fiber (PMF). In the Lyot filter, the PMF of 4, 8 and 12 m excite 5, 9 and 13 wavelengths with 1.38, 0.7 and 0.42 nm intervals, respectively. The experimental results show that in the range of 1528–1536 nm, the side-mode suppression ratio is 42 dB. After 60 min of continuous excitation, the output wavelength of the structure remains stabilization. It can be used as a light source in distributed sensing and wavelength division multiplexing systems.

Simultaneous Suspension Control and Energy Harvesting Through Novel Design and Control of a New Nonlinear Energy Harvesting Shock Absorber

Simultaneous vibration control and energy harvesting of vehicle suspensions have attracted significant research attention over the past decades. However, existing energy harvesting shock absorbers (EHSAs) are mainly designed based on the principle of linear resonance, thereby compromising suspension performance for high-efficiency energy harvesting and being only responsive to narrow bandwidth vibrations. In this paper, we propose a new EHSA design -- inerter pendulum vibration absorber (IPVA) -- that integrates an electromagnetic rotary EHSA with a nonlinear pendulum vibration absorber. We show that this design simultaneously improves ride comfort and energy harvesting efficiency by exploiting the nonlinear effects of pendulum inertia. To further improve the performance, we develop a novel stochastic linearization model predictive control (SL-MPC) approach in which we employ stochastic linearization to approximate the nonlinear dynamics of EHSA that has superior accuracy compared to standard linearization. In particular, we develop a new stochastic linearization method with guaranteed stabilizability, which is a prerequisite for control designs. This leads to an MPC problem that is much more computationally efficient than the nonlinear MPC counterpart with no major performance degradation. Extensive simulations are performed to show the superiority of the proposed new nonlinear EHSA and to demonstrate the efficacy of the proposed SL-MPC.

Passive suppression of flow-induced vibrations of a cantilevered pipe discharging fluid using non-linear vibration absorbers

This paper addresses the problem of passive suppression of vibrations induced by flow in a cantilevered pipe discharging fluid. The suppressor utilized, called rotative non-linear vibration absorber (NVA, for short), is composed of a mass connected to the extremity of a rigid bar linked to the pipe by means of a hinge and a rotational damper. The NVA is defined by its mass, radius and damping coefficient. The suppressor may affect the pipe dynamics in two different ways, which are the inherent mass addition to the system, and the fact that the device can rotate and thus can dissipate energy through its damper. The former is characterized by its mass and position along the pipe while the latter is also a function of other design parameters, such as damping coefficient and radius. It is shown that while mass additions play an important role in the pipe stability, the energy dissipation associated with the relative motion between the device and the pipe is capable of alleviating the pipe vibrations. Considering a fixed set of parameters for the pipe, a parametric study is carried out with the objective of identifying a proper set of parameters for the NVA, which leads to a robust and effective vibration mitigation. It is shown that the methodology adopted herein allows for such identification to be made and that the suppression achieved with the selected NVA is one of the best among the results presented, even if supercritical internal flow velocities are considered.

A nonlinear absorber for the reflection of travelling waves in bars

A nonlinear absorber for the reflection of travelling waves in bars

Low-Temperature PECVD Growth of Germanium for Mode-Locking of Er-Doped Fiber Laser.

A low-temperature plasma-enhanced chemical vapor deposition grown germanium (Ge) thin-film is employed as a nonlinear saturable absorber (SA). This Ge SA can passively mode-lock the erbium-doped fiber laser (EDFL) for soliton generation at a central wavelength of 1600 nm. The lift-off and transfer of the Ge film synthesized upon the SiO2/Si substrate are performed by buffered oxide etching and direct imprinting. The Ge film with a thickness of 200 nm exhibits its Raman peak at 297 cm−1, which both the nanocrystalline and polycrystalline Ge phases contribute to. In addition, the Ge thin-film is somewhat oxidized but still provides two primary crystal phases at the (111) and (311) orientations with corresponding diffraction ring radii of 0.317 and 0.173 nm, respectively. The nanocrystalline structure at (111) orientation with a corresponding d-spacing of 0.319 nm is also observed. The linear and nonlinear transmittances of the Ge thin-film are measured to show its self-amplitude modulation coefficient of 0.016. This is better than nano-scale charcoal and carbon-black SA particles for initiating the mode-locking at the first stage. After the Ge-based saturable absorber into the L-band EDFL system without using any polarized components, the narrowest pulsewidth and broadest linewidth of the soliton pulse are determined as 654.4 fs and 4.2 nm, respectively, with a corresponding time–bandwidth product of 0.32 under high pumping conditions.

Shock response mitigation of a large-scale structure by modal energy redistribution facilitated by a strongly nonlinear absorber

Shock response mitigation of a large-scale structure by modal energy redistribution facilitated by a strongly nonlinear absorber

Vibration attenuation and energy harvesting in metastructures with nonlinear absorbers conserving mass and strain energy

Vibration attenuation and energy harvesting in metastructures with nonlinear absorbers conserving mass and strain energy

Online Frequency Estimation on a Building-like Structure Using a Nonlinear Flexible Dynamic Vibration Absorber

The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system using solely available measurement signals of position, velocity, or acceleration are presented. Fast algebraic frequency estimation can, thus, be implemented to tune online a semi-active dynamic vibration absorber to obtain a high attenuation level of undesirable vibrations affecting the main mechanical system. A semi-active vibration absorber can be tuned for application where variations of the excitation frequency can be expected. Adaptive vibration absorption for forced harmonic vibration suppression for operational scenarios with variable excitation frequency can be then performed. Analytical, numerical, and experimental results to demonstrate the effectiveness and efficiency of the operating frequency estimation, as well as the acceptable attenuation level achieved by the tunable flexible vibration absorber, are presented. The algebraic parametric estimation approach can be extended to add capabilities of variable frequency vibration suppression for several configurations of dynamic vibration absorbers.

Bound-State Soliton and Noise-like Pulse Generation in a Thulium-Doped Fiber Laser Based on a Nonlinear Optical Loop Mirror

We demonstrate a thulium-doped, mode-locked, all-fiber laser capable of operating in two generation regimes: dispersion-managed soliton and noise-like pulse (NLP). Employing a nonlinear optical loop mirror as an artificial saturable absorber, the oscillator generated optical pulses with a fundamental pulse repetition frequency of ~15.795 MHz. The total net dispersion of the laser cavity had a slightly anomalous group delay dispersion value of −0.016 ps2. After appropriate adjustment of a polarization controller, bound states of a dispersion-managed soliton composed of three pulses with fixed soliton separations were also observed. NLP generation, tunable over 35 nm from 1943.5 to 1978 nm, was also presented in the same laser setup. To our knowledge, this is the first report of the generation of tunable NLPs in a mode-locked thulium-doped fiber laser based on a nonlinear loop mirror saturable absorber.

Bi2Te3/Graphene Heterostructure as the Saturable Absorber for ~1.0 μm Passively Q-switched Solid State Pulsed Laser

Due to the tunable nonlinear optical properties of the Bi2Te3/graphene heterostructure, stable solid state pulsed lasers based on the Bi2Te3/graphene saturable absorber have attracted intensive attention. In this work, the Bi2Te3/graphene heterostructure with good nonlinear absorption characteristics was synthesized by a self-assembly solvothermal route, and the optical saturable absorption properties of the saturable absorber were investigated. Owing to the large modulation depth of Bi2Te3 nanosheets and the high thermal conductivity of graphene, the Bi2Te3/graphene heterostructure saturable absorber shown good nonlinear saturable absorber performance and contributed the improved passively Q-switched Yb3+: GdAl3(BO3)4 pulsed laser when compared with that of the pure Bi2Te3 based Yb3+: GdAl3(BO3)4 laser, no matter pulse width or pulse energy. Our work demonstrates that the Bi2Te3/graphene heterostructure was a promising saturable absorber in ~1 μm solid-state pulsed lasers.