A model for an extensional mode resonator used as a frequency-adjustable vibration energy harvester

In an effort to identify techniques for harvesting energy from ambient vibrations, a prototype device that utilizes stretching piezoelectric film to support a proof mass, with an adjustable support that allows the resonant frequency of the device to be easily altered, has been developed. This extensional mode resonator (XMR) device is described by a model developed in this paper that predicts the power that is harvested as a function of the frequency and amplitude of the external vibration, the elastic and piezoelectric materials properties, and the device geometry. The model provides design guidelines for the effects of device geometry and applied tension through an adjustable support that suggest a strong dependence on mechanical damping and a weak dependence on frequency, as opposed to a bending cantilever device. The model predictions are compared to experimental measures from a prototype device for frequencies between 120 and 180 Hz, and at accelerations between 0.1 and 10 m/s². Up to 9 mW is generated from a device with a mass of ∼82 g, and over the range of frequencies tested the power harvested at 4 m/s² is between 3 and 4 mW.     

Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral and vertical whole-body vibration

It is currently assumed that the same frequency weightings, derived from studies of vibration discomfort, can be used to evaluate the severity of vibration at all vibration magnitudes from the threshold of vibration perception to the vibration magnitudes associated with risks to health. This experimental study determined equivalent comfort contours for the whole-body vibration of seated subjects over the frequency range 2-315 Hz in each of the three orthogonal axes (fore-and-aft, lateral and vertical). The contours were determined at vibration magnitudes from the threshold of perception to levels associated with severe discomfort and risks to health.At frequencies greater than 10 Hz, thresholds for the perception of vertical vibration were lower than thresholds for fore-and-aft and lateral vibration. At frequencies less than 4 Hz, thresholds for vertical vibration were higher than thresholds for fore-and-aft and lateral vibration. The rate of growth of sensation with increasing vibration magnitude was highly dependent on the frequency and axis of vibration. Consequently, the shapes of the equivalent comfort contours depended on vibration magnitude. At medium and high vibration magnitudes, the equivalent comfort contours were reasonably consistent with the frequency weightings for vibration discomfort in current standards (i.e. W_b and W_d). At low vibration magnitudes, the contours indicate that relative to lower frequencies the standards underestimate sensitivity at frequencies greater than about 30 Hz. The results imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of whole-body vibration.     

The vibration discomfort of standing persons: 0.5-16-Hz fore-and-aft, lateral, and vertical vibration

To minimise the discomfort of standing people caused by vibration of a floor, it is necessary to know how their sensitivity to vibration depends on the frequency of the vibration. This study was designed to determine how the discomfort of standing people exposed to horizontal and vertical vibration depends on vibration frequency over the range 0.5-16 Hz. Using the method of magnitude estimation, sixteen subjects judged the discomfort caused by fore-and-aft, lateral, and vertical sinusoidal vibration at each of the sixteen preferred one-third octave centre frequencies from 0.5 to 16 Hz at each of nine magnitudes. Subjects also reported the main cause of their discomfort. Equivalent comfort contours were constructed, reflecting the effect of frequency on subject sensitivity to vibration acceleration. With horizontal vibration, at frequencies between 0.5 and 3.15 Hz the discomfort was similar when the vibration velocity was similar, whereas at frequencies between 3.15 and 16 Hz the discomfort was similar when the vibration acceleration was similar. At frequencies less than 3.15 Hz, the subjects experienced problems with their stability, whereas at higher frequencies vibration discomfort was mostly experienced from sensations in the legs and feet. With vertical vibration, discomfort was felt in the lower-body and upper-body at all frequencies. The frequency weightings in current standards for predicting the vibration discomfort of standing persons have been greatly influenced by the findings of studies with seated subjects: the weightings are consistent with the experimentally determined frequency-dependence of discomfort caused by vertical vibration but inconsistent with the experimentally determined frequency-dependence of discomfort caused by horizontal vibration. The results suggest that the responses of seated and standing people are similar for vertical vibration, but differ for horizontal vibration, partly due to greater instability in standing persons.     

Ultrasound frame rate requirements for cardiac elastography: experimental and in vivo results

Cardiac elastography using radiofrequency echo signals can provide improved 2D strain information compared to B-mode image data, provided data are acquired at sufficient frame rates. In this paper, we evaluate ultrasound frame rate requirements for unbiased and robust estimation of tissue displacements and strain. Both tissue-mimicking phantoms under cyclic compressions at rates that mimic the contractions of the heart and in vivo results are presented. Sinusoidal compressions were applied to the phantom at frequencies ranging from 0.5 to 3.5 cycles/sec, with a maximum deformation of 5% of the phantom height. Local displacements and strains were estimated using both a two-step one-dimensional and hybrid two-dimensional cross-correlation method. Accuracy and repeatability of local strains were assessed as a function of the ultrasound frame rate based on signal-to-noise ratio values.The maximum signal-to-noise ratio obtained in a uniformly elastic phantom is 20 dB for both a 1.26 Hz and a 2 Hz compression frequency when the radiofrequency echo acquisition is at least 12 Hz and 20 Hz respectively. However, for compression frequencies of 2.8 Hz and 4 Hz the maximum signal-to-noise ratio obtained is around 16 dB even for a 40 Hz frame rate. Our results indicate that unbiased estimation of displacements and strain require ultrasound frame rates greater than ten times the compression frequency, although a frame rate of about two times the compression frequency is sufficient to estimate the compression frequency imparted to the tissue-mimicking phantom. In vivo results derived from short-axis views of the heart acquired from normal human volunteers also demonstrate this frame rate requirement for elastography.     

Integration of shock absorption and energy harvesting using a hydraulic rectifier

Hydraulic shock absorbers have been widely used to dissipate kinetic energy of the shocks into surrounding environment. By employing oscillatory motion to drive power generator, the shock energy can be converted into electricity for harvesting. However, the frequent bidirectional oscillation of the generator can cause a large impact force. This further leads to deteriorated energy harvesting performance, moving parts fatigue, and even system failure. As such, this study introduces four check values to form a hydraulic rectifier to integrate the shock absorption and energy harvesting functionalities. The bidirectional oscillation of the shock and the vibration is converted into unidirectional rotation to drive the generator. Following the proposed concept, a prototype energy-harvesting shock absorber has been designed and fabricated. An electromechanical model has also been developed to examine the response behavior of the prototype device. The prototype performance has been characterized based on the experimental results from three test setups. Both mechanical and electrical parameters of the electromechanical model have been identified based on our cyclic loading experiments. The results have shown that the developed energy-harvesting shock absorber is capable of harvesting the energy and absorbing the shock simultaneously. In our experiments, a maximum of 248.8 W instantaneous power (a maximum of 114.1 W on average) has been captured and a maximum of 38.81% energy harvesting efficiency has been achieved via harmonic excitation with an amplitude of 8 mm and a frequency of 2 Hz, when the load resistance is tuned to 7.5 Ω.     

High-beam-quality, 5.1 J, 108 Hz diode-pumped Nd:YAG rod oscillator-amplifier laser system

A high efficiency, high beam quality diode-pumped Nd:YAG master oscillator power-amplifier (MOPA) laser with six amplifier stages is demonstrated. The oscillator with two-rod birefringence compensation was designed as a thermally determined near hemispherical resonator, which presents a pulse energy of 223 mJ with a beam quality value of M² = 1.29 at a repetition rate of 108 Hz. The MOPA system delivers a pulse energy of 5.1 J with a pulse width of 230 μs, a M² factor of 3.6 and an optical-to-optical efficiency of 38.5%. To the best of our knowledge, this is the highest pulse energy for a diode-pumped Nd:YAG rod laser operation with a high beam quality and a pulse width of hundreds of microseconds at a repetition rate of over 100 Hz.     

Effect of pulse frequency on the microstructure, phase composition and corrosion performance of a phosphate-based plasma electrolytic oxidation coated AM50 magnesium alloy

An AM50 magnesium alloy was plasma electrolytic oxidation treated using a pulsed DC power supply at three different pulse frequencies viz., 10 Hz, 100 Hz and 1000 Hz with a constant pulse ratio for 15 min in an alkaline phosphate electrolyte. The resultant coatings were characterized by X-ray diffraction, energy dispersive spectroscopy and scanning electron microscopy for their phase composition and microstructural features. The 10 Hz condition yielded relatively thick and rough coatings, which was attributed to the higher energy input per individual pulse during the PEO processing. The phase composition was also found to be influenced by the processing frequency. Electrochemical impedance spectroscopy studies performed in 0.1 M NaCl solutions revealed that the coatings produced at 10 Hz condition had a better corrosion resistance, which was attributed to the higher thickness, more compact microstructural features and a relatively stable phase composition.     

A Fabry-Perót type resonator tunable below 2 GHz for use in time domain rotational spectroscopy: Application to the measurement of the radio frequency spectra of bromobenzene and iodobenzene

Two aluminum mirrors with radii of 203.2 mm and radii of curvature also of 203.2 mm have been used to construct a tunable Fabry-Perót type resonator with Q values of ∼200 at frequencies as low as 500 MHz. The resonator has been incorporated into a pulsed nozzle, Fourier transform, Balle-Flygare spectrometer typically used for recording pure rotational spectra in the microwave region. The resonator design allows the instrument to access the radio frequency region (?3 GHz) of the electromagnetic spectrum. The spectrometer is of use in (i) recording low J transitions of large asymmetric molecules where the spectra are often greatly simplified compared to higher frequency regions; (ii) measuring hyperfine constants for heavy molecules with higher accuracy than may be obtained at higher frequencies where hyperfine structure may not be resolvable; and (iii) provides further synchronicity between laboratory based measurements and radio astronomy in the 30 cm region. The resonators use is illustrated by recording the rotational spectra of bromobenzene and iodobenzene. The lowest ΔJ = +1 transition for iodobenzene has been observed at 1130.5292(10) MHz.     

Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral, and vertical vibration at the foot for seated persons

Vibration at the feet can contribute to discomfort in many forms of transport and in some buildings. Knowledge of the frequency-dependence of discomfort caused by foot vibration, and how this varies with vibration magnitude, will assist the prediction of discomfort caused by vibration. With groups of 12 seated subjects, this experimental study determined absolute thresholds for the perception of foot vibration and quantified the discomfort caused by vibration at the foot. The study investigated a wide range of magnitudes (from the threshold of perception to levels associated with severe discomfort) over a wide range of frequencies (from 8 to 315 Hz in one-third octave steps) in each of the three orthogonal translational axes (fore-and-aft, lateral, and vertical). The effects of gender and shoes on absolute thresholds for the perception of vertical vibration at the foot were also investigated. Within each of the three axes, the vibration acceleration corresponding to the absolute thresholds for the perception of vibration, and also all contours showing conditions producing equivalent discomfort, were highly frequency-dependent at frequencies greater than about 40 Hz. The acceleration threshold contours were U-shaped at frequencies greater than 80 Hz in all three axes of excitation, suggesting the involvement of the Pacinian channel in vibration perception. At supra-threshold levels, the frequency-dependence of the equivalent comfort contours in each of the three axes was highly dependent on vibration magnitude. With increasing vibration magnitude, the conditions causing similar discomfort across the frequency range approximated towards constant velocity. Thresholds were not greatly affected by wearing shoes or subject gender. The derived frequency weightings imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of foot vibration.     

Experimental identification of pedestrian-induced lateral forces on footbridges

This paper presents a comprehensive experimental analysis of lateral forces generated by single pedestrians during continuous walking on a treadmill. Two different conditions are investigated; initially the treadmill is fixed and then it is laterally driven in a sinusoidal motion at varying combinations of frequencies (0.33-1.07 Hz) and amplitudes (4.5-48 mm). The experimental campaign involved 71 male and female human adults and covered approximately 55 km of walking distributed between 4954 individual tests. When walking on a laterally moving surface, motion-induced forces develop at the frequency of the movement and are herewith quantified through equivalent velocity and acceleration proportional coefficients. Their dependency on the vibration frequency and amplitude is presented, both in terms of mean values and probabilistically to illustrate the randomness associated with intra- and inter-subject variability. It is shown that the motion-induced portion of the pedestrian load (on average) inputs energy into the structure in the frequency range (normalised by the mean walking frequency) between approximately 0.6 and 1.2. Furthermore, it is shown that the load component in phase with the acceleration of the treadmill depends on the frequency of the movement, such that pedestrians (on average) subtract from the overall modal mass for low frequency motion and add to the overall modal mass at higher frequencies.     

The horizontal apparent mass of the standing human body

The driving-point dynamic responses of standing people (e.g. their mechanical impedance or apparent mass) influence their dynamic interactions with structures on which they are supported. The apparent mass of the standing body has been reported previously for vertical excitation but not for lateral or fore-and-aft excitation. Twelve standing male subjects were exposed to fore-and-aft and lateral random vibration over the frequency range 0.1-5.0 Hz for 180 s at four vibration magnitudes: 0.016, 0.0315, 0.063, and 0.125 m s⁻² rms. With lateral excitation at 0.063 m s⁻² rms, subjects also stood with three separations of the feet. The dynamic forces measured at the driving-point in each of the three translational axes (i.e. fore-and-aft, lateral and vertical) showed components not linearly related to the input vibration, and not seen in previous studies with standing subjects exposed to vertical vibration or seated subjects exposed to vertical or horizontal vibration. A principal peak in the lateral apparent mass around 0.5 Hz tended to decrease in both frequency and magnitude with increasing magnitude of vibration and increase with increasing separation of the feet. The fore-and-aft apparent mass appeared to peak at a frequency lower than the lowest frequency used in the study.     

光学系统受迫振动的激光测量方法

将激光信号与高帧频CCD结合,解决了光学系统中振动信号和激光信号之间的转换问题,不仅能够测量振动对系统光束指向稳定性的影响,而且能够得到振动信号本身的频率特性。利用该方法对振源为150 Hz和200 Hz两种条件下的光学系统受迫振动进行测量,得到了与输入信号相吻合的振动信号属性。通过实验与分析得知:时域振幅测量精度为6.25 m,频域分辨力为2 Hz,方法简便高效,测量结果准确,已应用于角多路准分子激光主振荡功率放大器系统打靶试验平台光束指向稳定性的研究中。     

Long distance real-time measurement of multi-points micro-vibration in region by digital holography

Many applications require micro-vibration measurement, especially multi-points detection at long distance in real-time. In this paper, a micro-vibration measurement approach based on digital holographic interferometry is proposed for middle-low frequency detection. It can be used to monitor irregular frequency/amplitude vibration in selected region over 10 m away simultaneously and synchronously. A series of experiments were conducted including real-time measurement of 300 Hz, 1 kHz, 2 kHz and 3 kHz constant frequency/amplitude periodic vibration, precision and frequency response tests with calibration of LDV, 1 kHz irregular amplitude vibration, irregular frequency/amplitude vibration as well as the real-time measurement and simultaneous display of multi-points vibration. The experimental results demonstrate the feasibility of the proposed method and reveal its unique advantages.     

Large aperture tapered fiber phase conjugate mirror in MOPA laser systems with high repetition rate and high pulse energy

A large aperture tapered fused silica fiber phase conjugate mirror with a maximum 50.7% stimulated Brillouin scattering (SBS) reflectivity is presented, which is operated with 400 Hz pulse repetition rate and 36.5 mJ input pulse energy. To the best of our knowledge, it is the first time that over 50% SBS reflectivity is achieved by using solid-state phase conjugate mirror under such high pulse repetition rate and high pulse energy. With much higher pulse repetition rate of 500 and 1000 Hz, the maximum SBS reflectivity is 41.2% and 33.3%, respectively. A single-longitudinal-mode Nd:YAG laser is experimentally studied with master oscillator power amplifier (MOPA) scheme using such a tapered fiber as a phase conjugate mirror. A 101 mJ pulse energy is achieved at 400 Hz repetition rate, with a pulse width of 6 ns and a M² factor of less than 2. The corresponding peak power reaches 16.8 MW.     

Apparent mass of the human body in the vertical direction: Inter-subject variability

The biodynamic responses of the seated human body to whole-body vibration vary considerably between people, but the reasons for the variability are not well understood. This study was designed to determine how the physical characteristics of people affect their apparent mass and whether inter-subject variability is influenced by the magnitude of vibration and the support of a seat backrest. The vertical apparent masses of 80 seated adults (41 males and 39 females aged 18-65) were measured at frequencies between 0.6 and 20 Hz with four backrest conditions (no backrest, upright rigid backrest, reclined rigid backrest, reclined foam backrest) and with three magnitudes of random vibration (0.5, 1.0 and 1.5 m s^-2 rms). Relationships between subject physical characteristics (age, gender, weight, and anthropometry) and subject apparent mass were investigated with multiple regression models. The strongest predictor of the modulus of the vertical apparent mass at 0.6 Hz, at resonance, and at 12 Hz was body weight, with other factors having only a marginal effect. After correction for other variables, the principal resonance frequency was most consistently associated with age and body mass index. As age increased from 18 to 65 years, the resonance frequency increased by up to 1.7 Hz, and when the body mass index was increased from 18 to 34 kg m⁻² the resonance frequency decreased by up to 1.7 Hz. These changes were greater than the 0.9-Hz increase in resonance frequency between sitting without a backrest and sitting with a reclined rigid backrest, and greater than the 1.0-Hz reduction in resonance frequency when the magnitude of vibration increased from 0.5 to 1.5 m s⁻² rms. It is concluded that the effects of age, body mass index, posture, vibration magnitude, and weight should be taken into account when defining the vertical apparent mass of the seated human body.     

The effect of magnetic stress and stiffness modulus on resonant characteristics of Ni-Mn-Ga ferromagnetic shape memory alloy actuators

The prospect of using ferromagnetic shape memory alloys (FSMAs) is promising for a resonant actuator that requires large strain output and a drive frequency below 1 kHz. In this investigation, three FSMA actuators, equipped with tetragonal off-stoichiometric Ni₂MnGa single crystals, were developed to study their frequency response and resonant characteristics. The first actuator, labeled as A1, was constructed with low-k bias springs and one Ni-Mn-Ga single crystal. The second actuator, labeled as A2, was constructed with high-k bias springs and one Ni-Mn-Ga crystal. The third actuator, labeled as A3, was constructed with high-k bias springs and two Ni-Mn-Ga crystals connected in parallel. The three actuators were magnetically driven over the frequency range of 10 Hz-1 kHz under 2 and 3.5 kOe magnetic-field amplitudes. The field amplitude of 2 kOe is insufficient to generate significant strain output from all three actuators; the maximum magnetic-field-induced strain (MFIS) at resonance is 2%. The resonant MFIS output improves to 5% under 3.5-kOe amplitude. The frequency responses of all three actuators show a strong effect of the spring k constant and the Ni-Mn-Ga modulus stiffness on the resonant frequencies. The resonant frequency of the Ni-Mn-Ga actuator was raised from 450 to 650 Hz by increasing bias spring k constant and/or the number of Ni-Mn-Ga crystals. The higher number of the Ni-Mn-Ga crystals not only increases the magnetic force output but also raises the total stiffness of the actuator resulting in a higher resonant frequency. The effective modulus of the Ni-Mn-Ga is calculated from the measured resonant frequencies using the mass-spring equation; the calculated modulus values for the three actuators fall in the range of 50-60 MPa. The calculated effective modulus appears to be close to the average modulus value between the low twinning modulus and high elastic modulus of the untwined Ni-Mn-Ga crystal.     

The effects of floating slab bending resonances on the vibration isolation of rail viaduct

This paper compared the performance of several isolation designs to control vibration transmissions from concrete rail viaducts. The isolation systems analysed includes medium- and short-length floating slabs, and floating ladders. The vibration was measured in Japan, Korea and Hong Kong. The study aimed to assess the effects of bending resonances of the floating slab systems. Simple formulae of estimating the significant bending resonance frequency and support passage frequency of a floating slab system are proposed. The resonance peaks obtained in site measurement are found to be in agreement with the calculation results. The results show that other than the vertical rigid body resonances for the isolation systems, the bending resonances of slabs have significant effects on vibration isolation performance. In particular, bending resonance frequencies should not coincide with the vertical isolator resonance and support passage frequency. According to the in-situ measurement results, a mini-type concrete floating slab can reduce the vibration level by more than 30 dB in the frequency range of 63-200 Hz. This should be achieved by designing the first bending resonances of the floating slab to be out of the dominant frequency range of concrete rail viaduct vibration.     

Vibration transmissibility characteristics of the human hand-arm system under different postures, hand forces and excitation levels

Biodynamic responses of the hand-arm system have been mostly characterized in terms of driving-point force-motion relationships, which have also served as the primary basis for developing the mechanical-equivalent models. The knowledge of localized vibration responses of the hand-arm segments could help derive more effective biodynamic models. In this study, the transmission of z_h-axis handle vibration to the wrist, elbow and the shoulder of the human hand and arm are characterized in the laboratory for the bent-arm and extended arm postures. The experiments involved six subjects grasping a handle subject to two different magnitudes of broad-band random vibration, and nine different combinations of hand grip and push forces. The vibration transmissibility data were acquired in the z_h- and y_h-axis at the wrist and shoulder, and along all the three axes around the elbow joint. The results show that the human hand-arm system in an extended arm posture amplifies the vibration transmitted to the upper-arm and the whole-body at frequencies below 25 Hz, but attenuates the vibration above 25 Hz more effectively than the bent-arm posture, except at the shoulder. The magnitudes of transmitted vibration under an extended arm posture along the y_h-axis were observed to be nearly twice those for the bent-arm posture in the low frequency region. The results further showed that variations in the grip force mostly affect vibration transmissibility and characteristic frequencies of the forearm, while changes in the push force influenced the dynamic characteristics of the entire hand-arm system. The magnitudes of transmitted vibration in the vicinity of the characteristic frequencies were influenced by the handle vibration magnitude.     

Theoretical modeling and experimental realization of dynamically magnified thermoacoustic-piezoelectric energy harvesters

Conventional thermoacoustic-piezoelectric (TAP) harvesters convert thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The input thermal energy generates a steep temperature gradient along a porous medium. At a critical threshold of the temperature gradient, self-sustained acoustic waves are developed inside an acoustic resonator. The associated pressure fluctuations impinge on a piezoelectric diaphragm, placed at the end of the resonator. In this study, the TAP harvester is coupled with an auxiliary elastic structure in the form of a simple spring–mass system to amplify the strain experienced by the piezoelectric element. The auxiliary structure is referred to as a dynamic magnifier and has been shown in different areas to significantly amplify the deflection of vibrating structures. A comprehensive model of the dynamically magnified thermoacoustic-piezoelectric (DMTAP) harvester has been developed that includes equations of motions of the system?s mechanical components, the harvested voltage, the mechanical impedance of the coupled structure at the resonator end and the equations necessary to compute the self-excited frequencies of oscillations inside the acoustic resonator. Theoretical results confirmed that significant amplification of the harvested power is feasible if the magnifier?s parameters are properly chosen. The performance characteristics of experimental prototypes of a thermoacoustic-piezoelectric resonator with and without the magnifier are examined. The obtained experimental findings are validated against the theoretical results. Dynamic magnifiers serve as a novel approach to enhance the effectiveness of thermoacoustic energy harvested from waste heat by increasing the efficiency of their harvesting components.     

A maze structure for sound attenuation

Sonic crystals are periodic arrangement of scatterers made of material with low acoustic impedance or sound hard materials [1]. Sonic crystals have numerous applications such as green belts and sound barriers. Here we showed that a typical maze structure at children playground can attenuate noise effectively for frequencies ranging from 12.5 Hz to 20,000 Hz. The original designer for the maze structure probably does not have that in mind. The maze structure can be viewed as a sonic crystal structure with sound attenuation characteristics. We found that the maze was able to attenuate noise up to 17.9 dBA for frequency range below 1000 Hz and 23 dBA for higher frequency range up to 20,000 Hz. The maze structure was able to mitigate noise at a wide range of frequencies in addition to the center frequency (f_c$f_c$) of 478 Hz which was estimated based on the Bragg’s Law. The periodic effects of the maze was also proven by numerical studies. Our results demonstrated that the maze structure commonly found in children playgrounds was able to attenuate noise covering the whole human hearing range.