Mass-spring Resonator Research Articles

A novel frog-like meta-structure with linkage mechanism for low-frequency vibration isolation

Structures with linkage mechanism, which could be widely seen in engineering, usually need to bear a certain load and exhibit ideal vibration isolation performance. One of the key factors affecting the mechanical and vibration properties is the connection behavior of the linkage mechanism. To clarify its influence on the vibration characteristics, a novel frog-like meta-structure by introducing a linkage mechanism into the conventional locally resonant metamaterial with a mass-spring resonator is proposed in the present paper, in which the linkage connection is considered as three types of hinged, fixed and elastic, respectively. The equivalent dynamic model of the meta-structure is established theoretically to calculate the effective material properties, which is then validated numerically through band gap and vibration analysis. The results show that the hinged linkage offers equivalent mass and free vertical displacement, while the fixed linkage provides supporting stiffness, shifting the band gap towards higher frequencies. An appropriate elastic connection can enhance the ‘spring-vibrator’ effect, which in turn can significantly expand the low-frequency vibration suppression range of the structure. Experiments are also conducted corresponding to the different linkage mechanisms, and the dynamic model is verified. This study could provide a new idea for promoting the application of the locally resonant meta-structure with a linkage mechanism in the field of low-frequency vibration isolation.

A novel lever-type elastic metamaterial model for low-frequency wave attenuation

Elastic metamaterials have received extensive attention due to their proven track record in wave attenuation. In this study, a novel one-dimensional lever-type elastic metamaterial model is designed to achieve low-frequency wave attenuation by introducing an adjustable lever mechanism in a conventional mass-spring resonator. The dispersion relation and effective mass expression of the proposed metamaterial are theoretically derived. Then, the band structure characteristics and the effect of parameters on the band gap are analyzed in detail. The results show that by selecting appropriate lever ratio and initial rotation angle, a low frequency band gap can be obtained and the wave attenuation capability within the band gap can be enhanced. Finally, the dynamic response of the proposed structure is calculated by direct numerical integration method to verify the analytical results. Furthermore, the application potential of the proposed elastic metamaterial in shock wave attenuation is demonstrated by analyzing the spatial propagation of wave packets along the proposed structure. This study provides a meaningful reference for the design of other tunable elastic metamaterials to attenuate waves.

Broadband low-frequency sound insulation performance of quasi-zero stiffness local resonant acoustic metamaterial plate

For realizing the effective broadband insulation of sound at low frequencies, a novel local resonant acoustic metamaterial plate having quasi-zero stiffness is proposed. Based on the classical mass-spring local resonance model, a metastructure is constructed by introducing additional inclined springs with negative stiffness. First, the normalized equivalent stiffness of the quasi-zero stiffness structure is derived from the perspective of dynamics. Then, by employing the method of equivalent medium, a sound insulation model of the metastructure is established theoretically. For validation, numerical simulations as well as experimental measurements are carried out. It is demonstrated that in the positive (equivalent) stiffness regime, increasing either the stiffness ratio or pre-compression can significantly reduce the local resonance frequency of the metastructure, which exhibits the great insulation performance around the local resonance frequency. For a typical example, the proposed metastructure can achieve a transmission loss of 30 dB around 10 Hz. In contrast, within the negative stiffness regime, the metastructure does not exhibit local resonance, thus avoiding sound insulation valley caused by the “coincidence effect”. Compared with traditional materials or similar metamaterials, the proposed metastructure has significant advantages in sound insulation (e.g. more than 30 dB drop over a wide frequency band of 53－1500 Hz). By analyzing the equivalent mass density, reflection coefficient, and acoustic impedance ratio of the metastructure, the physical mechanism behind its superior insulation performance is further explored. The equivalent mass density changes from positive to negative and tends to infinity at the insulation peak. The insulation peak is attributed to a nearly perfect total reflection of sound wave caused by impedance mismatch, while the insulation valley is caused by low-frequency “coincidence effect” originating from the local resonance band gap. The using of the quasi-zero stiffness local resonance to achieve low-frequency broadband sound insulation overcomes the disadvantages of traditional metamaterials such as reduced stiffness or additional mass, thus becoming vastly attractive for constructing low-frequency broad band sound insulation structures.

Sound transmission loss of multi-layered infinite micro-perforated plates

In this paper, the sound transmission loss (STL) of multi-layered infinite micro-perforated plates (MPPs) is studied. A prediction model for the STL of the multi-layered infinite MPPs is developed, where each MPP may or may not have a perforation, and the number of MPPs is arbitrary. When the frequency of interest is well below the critical frequency of the plate such that the effect of flexural vibration can be neglected compared to that of the inertia term, the mass is replaced by an equivalent complex mass. For numerical examples, single-, double- and triple-layered MPPs are studied. As the perforation ratio increases, the magnitude of the equivalent complex mass decreases rapidly, which in turn results in a decrease of the STL. It is observed that for very small perforation ratios, the mass-spring resonance frequencies in double- and triple-layered MPPs move toward a higher frequency as the perforation ratios increase. In addition, the dips at the resonance frequencies become blunt with increases in the perforation ratios due to the artificial damping induced by micro-perforations. It is also found that at a high frequency, the STL shows dips regardless of the perforation ratios when the wavenumber and air gap depths satisfy certain conditions.

Band-Gap Properties of Elastic Metamaterials With Inerter-Based Dynamic Vibration Absorbers

In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.

Broadband low-frequency sound isolation by lightweight adaptive metamaterials

Blocking broadband low-frequency airborne noises is highly desirable in lots of engineering applications, while it is extremely difficult to be realized with lightweight materials and/or structures. Recently, a new class of lightweight adaptive metamaterials with hybrid shunting circuits has been proposed, demonstrating super broadband structure-borne bandgaps. In this study, we aim at examining their potentials in broadband sound isolation by establishing an analytical model that rigorously combines the piezoelectric dynamic couplings between adaptive metamaterials and acoustics. Sound transmission loss of the adaptive metamaterial is investigated with respect to both the frequency and angular spectrum to demonstrate their sound-insulation effects. We find that efficient sound isolation can indeed be pursued in the broadband bi-spectrum for not only the case of the small resonator's periodicity where only one mode relevant to the mass-spring resonance exists, but also for the large-periodicity scenario, so that the total weight can be even lighter, in which the multiple plate-resonator coupling modes appear. In the latter case, the negative spring stiffness provided by the piezoelectric stack has been utilized to suppress the resonance-induced high acoustic transmission. Such kinds of adaptive metamaterials could open a new approach for broadband noise isolation with extremely lightweight structures.

Design of a Maglev Vibration Test Platform for the Research of Maglev Vehicle-girder Coupled Vibration Problem

The maglev vehicle-girder coupled vibration problem has been encountered in many maglev test or commercial lines, which significantly degrade the performance of the maglev train. In previous research on the principle of the coupled vibration problem, it has been discovered that the fundamental model of the maglev girder can be simplified as a series of mass-spring resonators of different but related resonance frequencies, and that the stability of the vehicle-girder coupled system can be investigated by separately examining the stability of each mass-spring resonator – electromagnet coupled system. Based on this conclusion, a maglev test platform, which includes a single electromagnetic suspension control system, is built for experimental study of the coupled vibration problem. The guideway of the test platform is supported by a number of springs so as to change its flexibility. The mass of the guideway can also be changed by adjusting extra weights attached to it. By changing the flexibility and mass of the guideway, the rules of the maglev vehicle-girder coupled vibration problem are to be examined through experiments, and related theory on the vehicle-girder self-excited vibration proposed in previous research is also testified.

Nonlinear secondary noise sources for passive defect detection using ultrasound sensors

This paper introduces the concept of secondary noise sources for passive defect detection and localization in structures. The proposed solution allows for the exploitation of the principle of Green's function reconstruction from noise correlation, even in the absence of an adequate ambient noise. The main principle is to convert a part of low-frequency modal vibrations into high-frequency noise by exploiting the frictional contact nonlinearities. The device consists of a mass-spring resonator coupled to a flexible beam by a rough frictional interface. The extremity of the beam, attached to the surface of a plate, excites efficiently flexural waves in the plate up to 30kHz when the primary resonator vibrates around its natural frequency, i.e. a few dozens Hz. A set of such devices is placed at random positions on the plate surface, and low-frequency excitation is provided by a shaker. The generated high-frequency noise is recorded by an array of eight piezoelectric transducers attached to the plate. A differential correlation matrix is constructed by subtracting correlation functions computed from noise signals at each sensor pairs, before and after the introduction of a local heterogeneity mimicking a defect. A simple array processing then allows for the detection and estimation of the defect location from this differential correlation matrix. Beyond the successful proof of concept, influence of experimental parameters, such as the number of secondary sources or the variability of the position of the shaker application point, is also investigated.

Effect of the mass-spring resonance of a slab covered with carpets on the sound insulation performance

It is well known that the overall sound insulation performance between two adjacent rooms in actual buildings is not so much increased even if a high spec wall is used for the partition because of several flanking sound transmission paths. In recent years, the phenomena that a slab covered with carpets increases the sound transmission through the floor have been found. This is caused by the resonance with the mass of the carpets and the spring of those underlying materials, and consequently the sound insulation performance significantly decreases in the mid-low frequency range. The resonance frequency can be shifted to higher frequencies using formed plastic sheets of higher stiffness for the underlying materials. Although this would usually be one of countermeasures to increase the overall sound insulation performance, it is not a fundamental solution for noise control engineering. In the present work, in order to control the mass-spring resonance itself, a method of focusing on permeability of the carpets is proposed. The resonance is expected to be damped with the flow resistance, which is caused by setting an appropriate permeability. It is theoretically investigated using a simple model, and an experimental validation is also carried out.

Passive defect detection in plate from nonlinear conversion of low-frequency vibrational noise

It is known that, under the assumption of diffuse noise, the cross-correlation of acoustic signals recorded at two points of a medium allows to passively estimate the impulse response between these points. This principle, associated with coherent array processing, has been successfully applied to defect detection and localization in reverberant plates subject either to distributed noise sources or friction noise. In order to extend the applicability of this principle even in the absence of an adequate ambient noise, we have introduced the concept of secondary noise sources based on the conversion of low-frequency modal vibrations into high-frequency noise by exploiting frictional contact nonlinearities. The device consists of a mass-spring resonator coupled to a flexible beam by a rough frictional interface. The extremity of the beam, attached to the surface of a plate, excites efficiently flexural waves in the plate in the ultrasound range when the primary resonator vibrates around its natural frequency....

Direct determination of dynamic properties of railway tracks for flexural vibrations

Abstract The vertical vibration of rails constrained and supported by fastening systems occurs due to moving dynamic loads induced from rotating train wheels. The dynamic stiffness and damping capability of the railway track on the viscoelastic medium are essential to evaluate their performance on minimizing rail vibration and environmental noise generation. In this study, a new experimental method to measure the viscoelastic properties of the railway track for flexural vibration was proposed using the wave propagation approach. The proposed method was used to analyze the generation and transfer of vertical rail vibration at frequencies of rolling noise generation and to test actual track models. A slab track model and embedded railway tracks were used in the experiments. The rail was excited by a shaker or an impact hammer, and the resulting acceleration responses were measured at two locations. The flexural wave propagation was found to occur only at frequencies higher than the mass-spring resonance frequency of the rails. After obtaining the wavenumber from the transfer function between the measured responses, the frequency-dependent stiffness and loss factor of the track structures were calculated. The viscoelastic properties of different railway tracks of finite length were measured accurately in the laboratory setups. Then, for validation of the proposed method, the field test was performed using the infinitely long embedded tracks used for a tramway. The measured dynamic stiffness from the finite embedded tracks in the laboratory was very similar to the field test results. The proposed method enables direct determination of the dynamic properties and comparison of flexural wave propagation characteristics of different railway tracks.

A Design of Mechanical Frequency Converter Linear and Non-linear Spring Combination for Energy Harvesting

In this study, the improvement of energy harvesting from wideband vibration with random change by using a combination of linear and nonlinear spring system is investigated. The system consists of curved beam spring for non-linear buckling, which supports the linear mass-spring resonator. Applying shock acceleration generates a snap through action to the buckling spring. From the FEM analysis, we showed that the snap through acceleration from the buckling action has no relationship with the applied shock amplitude and duration. We use this uniform acceleration as an impulse shock source for the linear resonator. It is easy to obtain the maximum shock response from the uniform snap through acceleration by using a shock response spectrum (SRS) analysis method. At first we investigated the relationship between the snap-through behaviour and an initial curved deflection. Then a time response result for non-linear springs with snap through and minimum force that makes a buckling behaviour were obtained by FEM analysis. By obtaining the optimum SRS frequency for linear resonator, we decided its resonant frequency with the MATLAB simulator.

Vibration Analysis of Railway Tracks Forced by Distributed Moving Loads

The purpose of this study was to develop a theoretical model to analyze the vibration of finite railways forced by distributed moving loads. The vibration characteristics of compliantly supported beam utilizing compressional damping model were investigated through the Rayleigh-Ritz method. The distributed moving load was analyzed as the cross correlation function on railways. This allowed the use of statistical characteristics for simulation of the moving train wheels on the rail. The results showed there is a critical velocity inducing resonant vibration of the rail. The mass spring resonance from the rail fastening systems exhibited significant influence on the resulting vibration response. In particular, the effect of the viscoelastic core damping was investigated as an efficient method for minimizing rail vibration. The decrease of the averaged vibration and rolling noise generation by the damping core was maximized at the mass-stiffness-mass resonance frequency.

Stiff light composite panels for duct noise reduction

Low-frequency duct noise reduction using stiff light composite panels is developed and tested. Since these composite panels are made of lightweight and stiff materials, this actuation strategy will enable the creation of composite panels for duct noise control without using traditional heavy structural mass. The results suggest that the mass-spring resonance absorption in the case of a comparatively stiff thick panel with a thin flexible plate is more efficient with minimum weight, verifying that when subjected to low-frequency (<500 Hz). The efficiency of the panel absorber depends on the mass of the thin flexible plate and the stiffness of the panel.

Development of a Compact and Tuneable Vibration Compensator for Hydraulic Systems

AbstractThis publication is about vibration compensators for the attenuation of fluid flow pulsations in hydraulic systems. After a problem definition and an overview of conventional devices, a compact and adjustable mass-spring resonator featuring a hydraulic spring will be presented. The main advantages of this design are: simple and compact design, excellent noise attenuation characteristics, suitability for all pressure levels through mean pressure compensation and the possibility to alter the resonance frequency of the device in both a semi-active and active manner.Besides the description of the working principle, the discussion of some phenomena occurring at high frequencies, the treatment of some design aspects, such as the optimisation of the sealing gap geometry, dimensioning etc. and a section devoted to compactness of vibration compensators, experimental results will be presented which prove the usefulness of the concept.

A boron etch-stop assisted lateral silicon etching process for improved high-aspect-ratio silicon micromachining and its applications

High-aspect-ratio micromachining (HARM) developed in recent years has made many devices more versatile compared to the surface micromachining process, but it has also met some challenges which have not occurred before. Those issues made many restrictions on HARM structure design, including structure thickness/width limitations, anchor-induced design problems, thickness uniformity and sidewall conductivity problems, which are discussed in this paper. Accordingly, we propose a novel boron etch-stop assisted lateral silicon etching (BELST) process which employs the (111) wafer process and heavy boron diffusion. Many design constraints have been reduced through some delicate designs of the BELST process. Furthermore, the process is capable of various applications, and has been applied in fabricating a dual mass-spring resonator and a micro vibrating gyroscope in this work. In summary, the developed BELST process can possess most existing merits as well as reducing many design constraints in the existing HARM process, and is expected to contribute in making HARM more competitive and convenient.

A simple neutrally buoyant sensor for direct measurement of particle velocity and intensity in water

Acoustic particle velocity is commonly inferred from measurement of pressure or pressure gradient; however, in water, direct measurement is simple. A moving-coil sensor embedded in a neutrally buoyant package produces a voltage directly proportional to the particle velocity in the surrounding fluid for frequencies above the mass-spring resonance. Leslie et al. [J. Acoust. Soc. Am. 28, 711–715 (1956)] built such a sensor by mounting a moving-coil element inside a hollow brass sphere. The sensor described in this paper is identical in principle but is considerably easier to fabricate. Useful from tens of hertz to several kilohertz, this sensor consists of a glass- microballoon-and-epoxy composite cast around a small, commercial geophone. The sensor is inexpensive, rugged, and has good immunity to interference. In conjunction with a pressure hydrophone, acoustic intensity can be measured without the errors associated with subtraction of nearly equal signals (as in the two-hydrophone method).

A fiber-optic interferometric seismometer

A fiber-optic interferometric sensor has been developed which consists of a seismic mass of 520 gm supported by two rubber mandrels, each wound with a single layer of single-mode optical fiber 6.5 m long. One end of each fiber is cleaved to enhance reflection. The other ends are interconnected via a fiber-to-fiber 3-dB coupler, forming a Michelson interferometer. When the case of the sensor is displaced, the fiber around one mandrel extends in length while the other contracts. The resulting "push-pull" mechanical operation of the sensor allows both legs of the interferometer to be active, providing good common mode rejection of spurious effects, as a reference leg is not required. This, together with the fact that the light traverses each leg of a Michelson interferometer twice due to reflection, provides the sensor with four times the sensitivity of a conventionally constructed interferometric sensor. Sensitivities of 8500 rad of optical phase shift per micrometer of case displacement have been measured above the mass-spring resonance, where the sensor operates as a seismometer. Below resonance the sensor operates as an accelerometer with a measured sensitivity of 10 500 rad/g, the highest reported to date. Including both thermodynamic and demodulator noise sources ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\approx 10 \mu</tex> rad/ <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sqrt{Hz}</tex> ), below resonance the sensor has a detection threshold of 1 ng/ <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sqrt{Hz}</tex> , a 20- dB improvement over the best existing conventional low noise vibration sensors.