High Frequency Vibration Responses Research Articles

Magnetic coupling and amplitude truncation based bistable energy harvester

We present a two-degree-of-freedom bistable piezoelectric energy harvester (PEH) combining both magnetic coupling and amplitude truncation mechanisms to improve the electrical response when installed within compact spaces. The PEH processes a time-varying potential well and each beam has two electrical responses due to the interaction between two magnets. The collision-induced amplitude truncation behavior leads to high-frequency vibration responses, which reduces the matching impedance of the PEH. The Hamilton's principle and the Galerkin method was applied to establish the distributed parameter model for the system. By numerical calculations, the influence of the magnet distance and beam stiffness ratio on the static potential well, as well as the influence of excitation acceleration and stop gap on the voltage and power response were explored. A series of experiments were conducted to validate the voltage and power responses under sweep and fixed frequency excitations. The experimental and simulation results agree with each other. Due to the effect of magnetic coupling, the response frequency bandwidth of the cantilever beam widens by more than 7 Hz. The frequency-up effect generated by collision increases the response power of the system with the maximum of 307.8 mW at 103.6 Ω in experiments, and the combination of the two widens the impedance matching range of the system. This broadband structure with a wide impedance matching range and limited motion is more suitable for practical applications.

Error analysis and modeling of the racetrack magnetohydrodynamic linear motion sensor

Micro-vibration measurement methods for spacecraft structures mainly include the use of an accelerometer, laser, and magnetohydrodynamic (MHD) measurement methods. The micro-vibration measurement sensor developed based on the MHD measurement method has no mechanical wear between internal components, a fast high-frequency vibration response, and strong anti-interference properties. To reduce the measurement error of the racetrack MHD linear motion sensor developed in the laboratory, this paper investigated the sensor error, analysed the error source, combined the BP neural network optimized by particle swarm optimization (PSO) with variational mode decomposition (VMD), used the VMD-PSO-BP neural network to establish the error compensation model of the racetrack MHD linear motion sensor, and combined the PSO-BP neural network with wavelet threshold de-noising (WTD). The WTD-PSO-BP and RBF neural networks were used to develop the error compensation model of the racetrack MHD linear motion sensor. Comparing the three models, the experimental results show that the VMD-PSO-BP model has the best compensation effect. The mean absolute error of the output signal of the racetrack MHD linear motion sensor compensated by the VMD-PSO-BP neural network model was 1–2 times lower than that before compensation, the signal-to-noise ratio was 10 times higher on average, and the correlation coefficient was more than 0.95.

Prediction of structural high-frequency vibration with considering uncertainty in measurement

The concept of statistical energy analysis (SEA) was proposed in the early 1960′s. The word ‘statistical’ emphasizes that the studied systems are presumed to be drawn from similar design and construction that have the known distributions of their dynamical parameters. The word ‘energy’ denotes the primary variable of interest. SEA method can well be used to predict the structural high-frequency vibration energy, and it has widely been used in many engineering fields such as aerospace, shipping and machinery. In the previous studies, the effect of uncertainty caused by measurement errors of SEA parameters was not considered. In this paper, the uncertain parameters are expressed in the form of interval variables, and the interval decomposition method is applied to predict the high-frequency vibration responses. An experimental research on vibration of complex structure is carried out, and the result from experimental research is compared with that from theoretical analysis.

Radiative energy transfer model for high frequency vibration of functionally graded beams in thermal environment

A simple and efficient energy flow model is developed by radiative energy transfer method (RETM) to predict the high frequency vibration response of functionally graded(FG) beams in thermal environment. The Timoshenko beam theory is applied to derive the motion governing equations. Thermal effects are incorporated into the dynamic model through the temperature dependent material properties and the thermal stresses. The wavenumber and group velocity associated with thermal stress are included in the energy governing equation. By introducing the artificial springs to simulate different boundary conditions, the energy conversion relationship of the two waves at boundaries are deduced. The response of FG beam loaded by a high-frequency harmonic force is described by energy density and energy flow intensity. They are composed of energy rays from the real source at the load point and energy rays reflected from the imaginary sources at the boundaries. Numerical simulations are performed in various forms of thermal environments to verify the proposed model. The RETM results are compared with those obtained by the wave propagation approach under different parameters, and good consistencies are observed. Numerical results show that the vibrational energy density of FG beams are affected by thermal effects and can be reduced by optimising the gradient factors.

Energy Flow Analysis Model of High-Frequency Vibration Response for Plates with Free Layer Damping Treatment

The energy flow analysis (EFA) model is developed for predicting the vibrational response of plates with free layer damping (FLD) treatment under high-frequency excitation. For the plate with fully free layer damping (FFLD) treatment, the energy density equation of the laminated plate with high damping is deduced by combining the equivalent complex stiffness method with the EFA theory. For the plate with partially free layer damping (PFLD) treatment, the relationship between energy density and energy intensity is obtained based on the wave theory of coupled plate by analyzing the energy transfer relationship at the damping boundary. The high-frequency energy density response of the structure with FLD treatment is solved through the energy finite element analysis (EFEA) method. To verify the developed EFEA model, several numerical analyses are performed for the plate with FFLD and PFLD treatments. The numerical results demonstrate that the obtained EFEA solutions consistently converge to the time-averaged modal analytical solutions at various analysis frequencies. Finally, the influences of the loss factor and the thickness of the damping layer on the resulting energy density are investigated in detail.

Research status and development trend of energy finite element analysis: a review

Compared with finite element method (FEA) and statistical energy method (SEA), the energy finite element method (EFEA) is a promising and more suitable method to predict the high-frequency vibration response and radiated noise of mechanical structures, due to its advantages of both computational efficiency and ability to get detail information. In recent years, researchers have made great progress in EFEA, due to the urgency of engineering application. This paper aims to comprehensively summarize historical and latest development of energy finite element analysis from two aspects of theory and engineering, to furtherly promote its application in the engineering field. Firstly, the development history of EFEA in basic structures is summarized, and the theoretical development direction of energy finite element in recent years is further analyzed. After that, the application of EFEA in aerospace, ship and vehicle engineering are summarized. Finally, the problems that need to be furtherly studied in EFEA are presented, and it is pointed out that it is an urgent research work to continue to improve the energy finite element analysis theory and software and apply it to engineering.

An analytical investigation into the vibration behavior of an orthotropic steel deck

Due to advantages such as small weight, large load capacity, and easy manufacturing, orthotropic steel decks (OSDs) are widely used in many steel bridges. As an important component of steel bridge decks that bear vehicle loads, OSDs may produce excessive vibrations and corresponding noise due to low dead loads. Therefore, it is important to study the vibration behavior of OSDs to guide the design to reduce vibration and noise in steel bridges. In this paper, the vibration response of an OSD with simply supported boundary conditions is calculated using the modal expansion method. The input mobility and insertion loss are selected as indices to evaluate the vibration response and suppression performance of the bridge. The results of calculations were compared with those of the finite element method to verify their accuracy. They showed that the input mobility of the OSD was affected primarily by the bending stiffness of the corresponding top plate and longitudinal ribs. The vibration energy of the OSD had both frequency-dependent and excitation location-dependent characteristics. When a source acted on the longitudinal rib or was close to it (within a distance of ¼ of the wavelength), the high-frequency vibration response of the OSD could still be greatly suppressed, with an average vibration reduction of approximately 15 dB. Reducing the spacing between the longitudinal ribs is one of the best ways to reduce the vibration response of the OSD. The frequency of the positive insertion loss ranged from 160 to 500 Hz when the longitudinal rib spacing was reduced from 0.8 to 0.4 m. The frequency-related vibration response of the OSD can be further reduced by adding transverse ribs, especially in the high-frequency range.

Energy Flow Analysis of High-Frequency Flexural Vibration of Wedge Beam Structures

Wedge members with variable thickness are widely used in ship structures, aerospace structures, and building structures. Considering their application scenarios, their high-frequency vibration characteristics have important research value. Energy finite element analysis (EFEA) is a powerful tool to predict high-frequency vibration response. EFEA is essentially applying finite element analysis to solve the energy density governing equation. However, the equation for wedge beam is missing. Energy flow analysis aims to obtain energy density governing equation. The energy flow model of wedge beam with variable thickness is established in this paper. Firstly, according to the geometric acoustic approximation method, the general displacement solution of the bending deformation equation for a wedge beam is deduced. Furthermore, the wave dispersion relation of bending deformation of wedge beam is derived. Then, the relationship between the time-averaged vibration energy density and energy flow of the wedge beam is also derived. Also, the governing equation taking energy density as a variable of the wedge beam structure is derived through the energy balance relationship in the microelement body. The governing equation is numerically solved, and the energy density distribution on the wedge beam structure is calculated. Finally, the energy density distribution of uniform beam and wedge beam under the same excitation is analyzed and summarized; the influence of different excitation frequencies and power exponent of thickness change on the performance of wedge beam structure is also summarized. Geometrically, the wedge beam satisfies the one-dimensional acoustic black hole structure. The calculation results show that the energy density on the beam structure increases with the decrease of thickness and reaches its maximum near the tip. The wedge acoustic black hole beam structure has a good energy absorption effect with a frequency between 250 Hz and 2000 Hz. With the further increase of excitation frequency, the energy absorption effect of the wedge beam structure has dropped significantly.

Non-Contact Damage Detection under Operational Conditions with Multipoint Laservibrometry.

Scanning laser–Doppler vibrometry (SLDV) can localize and visualize damages in mechanical structures. In order to enable scanning, it is necessary to repeat the vibration. Therefore, this technique is not suited to detect emerging hazards in working machinery that change the vibration behavior. A common technique for such cases is monitoring the vibration excited by machine operation with accelerometers. This technique requires mechanical coupling between sensors and the measurement object, which influences the high-frequency vibration responses. However, in the low-frequency range, local damages do not shift resonances or distort operational deflection shapes (ODS) significantly. These alterations in the vibration behavior are tiny and hard to detect. This paper shows that multipoint laservibrometry (MPV) with laser excitation can measure these effects efficiently, and it further demonstrates that damages influence ODSs at frequencies above 20 kHz much stronger than at frequencies below 20 kHz. In addition, ODS-based damage indices are discussed; these are highly sensitive to minute visible changes of the ODSs. In order to enhance the sensitivity of hazard detection, the response vector assurance criterion value is computed and evaluated during operation. The capabilities and limitations of the methodology on the example of a cantilever with manually emerging damage are demonstrated.

High-speed vehicle–slab track coupled vibration analysis of the viscoelastic-plastic dynamic properties of rail pads under different preloads and temperatures

The viscoelastic-plastic dynamic properties of rail pads were are not adequately accounted for in the traditional vehicle–track coupled dynamic model. To investigate the influence of the viscoelastic-plastic dynamic properties of rail pads on the high-speed vehicle–track coupled vibrations, we obtained the viscoelastic-plastic dynamic properties of rail pads first by a series of laboratory tests, after which we described these properties theoretically by a modified Fractional Derivative Zener (FDZ) model and a traditional Berg friction model. A modified vertical vehicle–slab track coupled dynamic model was established by introduction of the modified FDZ and traditional Berg models for rail pads to investigate the influence of the viscoelastic-plastic dynamic properties of the rail pads on the high-speed vehicle–slab track coupled vibration responses under various preloads and temperatures. The FDZ and Berg models for rail pads improved the calculation accuracy of the high-speed vehicle–slab track coupled vibration responses, compared with the traditional KV model for rail pads, especially in the dominant high frequency range. The dynamic plastic properties of the rail pads effectively suppressed the high-frequency wheel-rail forces and yet increased the high-frequency vibration responses of the track substructures under the rail. Low temperatures and increased preloads on rail pads had a similar effect on the vehicle–track coupled vibrations. Increasing the preload on rail pads or decreasing the temperature increased the wheel-rail random excitation energy and its dominant frequencies, increased the vibration responses of the wheel-set and the track substructure under the rail, and decreased the vibrations of the rail at nearly all frequencies. Highlights The dynamic viscoelasticity and plasticity of rail pad under preloads and temperatures were tested. A modified FDZ model for the dynamic viscoelastic properties of rail pads was proposed. The dynamic plastic properties of rail pads can decrease the high-frequency wheel-rail forces. The dynamic plastic properties of rail pads can increase the high-frequency vibration under the rail. Low temperatures and increased preloads on rail pads had a similar effect on vehicle/track vibration.

An energy flow model for high-frequency vibration analysis of two-dimensional panels in supersonic airflow

Many energy flow models have been proposed for high-frequency forced vibration analysis of structures. In this paper, a novel energy flow model is developed to predict the high-frequency vibration response of panels in supersonic airflow and quantify the effects of supersonic airflow on high-frequency forced vibration characteristics. The additional damping due to supersonic airflow is derived from the motion equation of a two-dimensional panel. The relationship between the wavenumber and the group velocity is introduced to describe the energy transmission property considering the effects of supersonic airflow. Then the energy density governing equation (i.e. energy flow model) is established and solved by the energy flow analysis (EFA) and the energy finite element method (EFEM). Finally, comparing the vibration responses obtained by the present energy flow model with the corresponding exact analytical solutions, the developed energy flow model is verified to be effective for high-frequency vibration analysis of panels in supersonic airflow. Furthermore, the numerical simulations indicate that supersonic airflow can affect the equivalent damping of the propagating elastic waves, and thus change the energy density distribution of the panel.

An energy finite element method for high frequency vibration analysis of beams with axial force

In order to predict the high frequency vibration response of beams with axial force, an energy finite element method (EFEM) is developed. An Euler–Bernoulli beam with constant axial force is considered. The energy density and energy intensity of the beam with axial force are introduced, and the relationship between the wavenumber and group velocity is derived, then the energy density governing equation is established. In addition, the impedance of beam with axial force is derived to calculate the input power, and the energy density is evaluated by solving the governing equation using finite element method. Finally, the feasibility and correctness of the present EFEM are verified by comparing the results obtained by the EFEM with the corresponding exact solutions. The effects of axial force on the energy density response and the limitations of EFEM are also discussed.

Bolt loosening analysis and diagnosis by non-contact laser excitation vibration tests

In this paper, a vibration testing and health monitoring system based on an impulse response excited by laser ablation is proposed to detect bolted joint loosening. A high power Nd: YAG pulse laser is used to generate an ideal impulse on a structural surface which offers the potential to measure high frequency vibration responses on the structure. A health monitoring apparatus is developed with this vibration testing system and a damage detecting algorithm. The joint loosening can be estimated by detecting fluctuations of the high frequency response with the health monitoring system. Additionally, a finite element model of bolted joints is proposed by using three-dimensional elements with a pretension force applied and with contact between components taken into account to support the bolt loosening detection method. Frequency responses obtained from the finite element analysis and the experiments using the laser excitation are in good agreement. The bolt loosening can be detected and identified by introducing a damage index by statistical evaluations of the frequency response data using the Recognition-Taguchi method. The effectiveness of the present approach is verified by simulations and experimental results, which are able to detect and identify loose bolt positions in a six-bolt joint cantilever.

보강재가 평판 진동 및 음향 특성에 미치는 영향

The purpose of this study was to analyze the vibro-acoustic characteristics of a stiffened rectangular plate at high frequencies. The stiffeners attached along the plate surface were assumed to have rotational and translational stiffness and inertia. The harmonic response of the stiffened plate were predicted and compared using the Rayleigh-Ritz method with two different trial functions - polynomial and beam functions. The variation of the spatially averaged mean square velocity and the modal characteristics with the number of stiffeners were obtained. The use of the beam function ensured fast convergence which was essential for analyzing the high frequency vibration responses. Using the calculated modal characteristics and the Rayleigh-integral, the radiated sound power was predicted, and the effects of stiffeners were investigated. The proposed model can be applied to study optimal layout of stiffeners for minimal noise generation of the stiffened structures.

Loose Bolt Detection by High Frequency Vibration Measurement with Non-Contact Laser Excitation

This paper proposes a vibration testing and health monitoring system based on an impulse response excited by a laser ablation. High power YAG pulse laser is used for producing an ideal impulse force on structural surface. It is possible to measure high frequency vibration responses in this system. A health monitoring system is constructed by this vibration testing system and a damage detecting algorithm. A microscopic damage of structures can be extracted by detecting fluctuations of high frequency vibration response with the present health monitoring system. In this study, loosening of bolt tightening torques is defined as the damage of the system. The damage is detected and identified by statistical evaluations of measured frequency response data with Recognition-Taguchi method. The effectiveness of the present approach is verified by experiment to detect and identify the loosening of bolts installed on an aluminum block structure.

Health Monitoring Based on High Frequency Vibration Measurement with Laser

This paper proposes a vibration testing and health monitoring system based on an impulse response excited by a laser ablation. High power YAG pulse laser is used in this system for producing an ideal impulse force on structural surface. It is possible to measure high frequency vibration responses in this system. A health monitoring system is constructed by this vibration testing system and a damage detecting algorithm. A microscopic damage of structures can be extracted by detecting fluctuations of high frequency vibration response with the present health monitoring system. In this study, loosening of bolt tightening torques is defined as the damage of the system. The damage is detected and identified by statistical evaluations of measured frequency response data with Recognition-Taguchi method.

656 レーザー加振技術を用いた高周波帯域の特性変動検知に基づくヘルスモニタリング(超音波・熱量の計測および標準,OS-10 機械のための動的計測,総合テーマ「伝統を,未来へ!」)

This paper proposes a vibration testing and health monitoring system based on an impulse response excited by a laser ablation. High power YAG pulse laser is used in this system for producing an ideal impulse force on structural surface. It is possible to measure high frequency vibration responses in this system. A health monitoring system is constructed by this vibration testing system and damage detecting algorithm. A microscopic damage of structures can be extracted by detecting fluctuations of high frequency vibration response with this health monitoring system. Loosening of bolt tightening torques is defined as the damage of the system. The damage is detected by statistical evaluations with Recognition-Taguchi method.

High-Frequency Vibration Response of Metal Honeycomb Sandwich Structure

ARMOR TPS panel is above the whole ARMOR TPS, and the metal honeycomb sandwich structure is the surface of the ARMOR TPS panel. So the metal honeycomb sandwich structure plays an important role in the ARMOR TPS, while it bears the flight dynamic pressure and stands against the flight dynamic calefaction. So the active environment of metal honeycomb sandwich structure is very formidable. We have to discuss any extreme situation, for reason of making sure aerial vehicle is safe. And high-frequency vibration is one of active environment. In this paper we have analyzed high-frequency vibration response of metal honeycomb sandwich structure. We processed high-frequency vibration experiment by simulating true aerial environment. Sequentially we operated high-frequency vibration experiment of metal honeycomb sandwich structure with cracks, notches and holes. Then finite-element analysis was performed by way of validating the experiment results. Haynes214 is a good high temperature alloy material of both face sheet and core at present, so we choose it in this paper.

Reactive oxygen species and inflammatory mediators enhance muscle spindles mechanosensitivity in rats

We tested the hypothesis that reactive oxygen species (ROS) and inflammatory mediators affect transduction properties of muscle spindles. In rats, muscle spindles response to high-frequency vibration (HFV) was recorded before and after (1) injection of hydrogen peroxide (H2O2) in control rats and animals pre-treated with diclofenac (anti-inflammatory substance), (2) injection of bradykinin and (3) fatigue induced by muscle stimulation (MS) in control rats and rats receiving diclofenac, superoxide dismutase (SOD) or H2O2. Muscular oxidative stress and inflammation induced by H2O2 or MS were assessed by measurements of isoprostanes and IL-6 levels. In control rats, H2O2, bradykinin and MS significantly enhanced the HFV response. Pre-treatment with SOD abolished the post-MS-enhanced HFV response whereas diclofenac lowered the peak HFV response to MS and H2O2. H2O2 injection and MS elicited significant and similar increases in isoprostanes and IL-6. We report a direct modulation of muscle spindles mechanosensitivity by ROS and inflammatory mediators.

A novel scheme for the discrete prediction of high-frequency vibration response: Discrete singular convolution–mode superposition approach

This study introduces a novel scheme for the discrete high-frequency forced vibration analysis based on discrete singular convolution (DSC) and mode superposition (MS) approaches. The accuracy of the DSC–MS is validated for thin beams and plates by comparing with available analytical solutions. The performance of the DSC–MS is evaluated by predicting spatial distribution and discrete frequency spectra of the vibration response of thin plates with two different boundary conditions. The frequency spectra of the time-harmonic excitation forces are in the form of ideal and band-limited white noise so that the natural modes in the frequency band are provoked. The solution exposes high-frequency response behaviour definitely. Therefore, it is hoped with this paper to contribute the studies on the treatment of uncertainties in the high-frequency design applications.