Frequency Of Harmonic Excitation Research Articles

Experimental study to measure the sound transmission loss of natural fibers at tonal excitations

In this paper, the acoustical sound absorbing property such as Insertion Loss (IL) or sound transmission loss (STL) of natural fibers is measured experimentally. The STL is measured for tonal acoustic excitations (one-third octave band harmonic frequencies). The tonal acoustic excitations are generated by using acoustic transducer (loudspeaker) and passed through the various natural fiber samples. The primary objective of this work is to measure the absorption properties of available natural fibers so that they may be replaced with glass material or other synthetic fibers (such as glass, carbon, graphite etc.) for various engineering and architectural applications. The natural fibers used in this study are banana fibers, coconut coir fibers, hemp fibers, jute fibers and kenaf fibers. The diameter and the thickness of the natural fiber specimens are 0.160 m and 0.03 m respectively. It is observed from this experimental study that the sound absorption by the kenaf fibers is more as compared to other natural fibers at tonal one third-octave band harmonic acoustic excitation frequencies.

Frequency domain identification of the fractional Kelvin-Voigt’s parameters for viscoelastic materials

In this work, a new innovative method is used to identify the parameters of fractional Kelvin-Voigt constitutive equation. These parameters are: the order of fractional derivation operator, 0 ≤ α ≤ 1, the coefficient of fractional derivation operator, CV, and the stiffness of the model, KV. A particular dynamic test setup is developed to capture the experimental data. Its outputs are time histories of the excitation and excited accelerations. The investigated specimen is a polymeric cubic silicone gel material known as α-gel. Two kinds of experimental excitations are used as random frequencies and constant frequency harmonic excitations. In this study, experimental frequency response functions confirm that increasing the static preload changes the behavior of the investigated viscoelastic material and the fractional Kelvin-Voigt model loses its validity by increasing the precompression. It is shown that, for a random frequencies excitation, by transforming from the time domain to the frequency domain the mentioned parameters can be identified. Using the identified parameters, analytical frequency response functions are so close to their experimental counterparts. Also, analytically produced time histories of the test setup’s output for steady-state experimental tests are so close to the captured time histories. The mentioned results validate the procedure of identification.

Passive vibration control in a civil structure: Experimental results

The problem of vibrations in civil structures is common; nevertheless, its negative effects can be significantly reduced using structural control methods with intention of maintaining structural welfare as much as possible. This work deals with the study of structural vibration control in a model of a civil-like structure, which consists of three-level building with a tuned mass damper implemented as a passive vibration absorber, mounted on the top of the structure, to attenuate the harmonic vibrations provided by an electromagnetic actuator connected at the base of the primary system. The action of the tuned mass damper is evaluated from an energy approach. The dissipation of energy in the overall system is conducted in an experimental way, where the passive control technique is designed to minimize the undesirable forced dynamic response of the main structure via the tuned mass damper. Experimental results are provided to show the effective performance of the proposed passive vibration absorption scheme to suppress resonant frequency harmonic excitations disturbing the primary system, evaluating the performance energy and contribution of the dissipative device for the energy release in the overall system.

Numerical Delineation of 3D Unsteady Flow Fields in Side Channel Pumps for Engineering Processes

Side channel pumps are important machines for handling toxic, explosive or other dangerous liquids in various engineering processes. However, the operational reliability of these pumps is directly affected by the intensity of the pressure and velocity fluctuations, thus the flow fluctuations existing within the pump cannot be neglected because of their direct influence on the noise, vibration and harshness performance. Therefore, describing precisely the zones of highly unsteady and turbulent flow fields is a key research topic. Moreover, the size of the wrapping angle strongly affects the levels of pressure and velocity fluctuations, thus numerical calculations of the pressure and velocity fluctuation intensities in side channel pump models with different wrapping angles were conducted in this work. The results indicated that the pressure fluctuation coefficient increased gradually from the inflow to the outflow. At the interrupter, the flow experienced the most irregular flow patterns in the pump. The flow at the inflow region in both the impeller and side channel passage rendered weak pressure fluctuation intensities. All three pump cases operated with 24 blades but after one complete circulatory cycle, cases 1, 2 and 3 revealed 21, 20 and 19 regular pressure fluctuations respectively in the impeller flow passage. On the other hand, the side channel flow passage rather produced 24 regular pressure fluctuations. Furthermore, the main frequency harmonic excitations for all studied monitoring points in the impeller and side channel flow passages of the three pump cases occurred at 600 Hz (24 × fn), 1200 Hz (48 × fn), and 1800 Hz (72 × fn). For this reason, exchanged flow times between the impeller and side channel is mainly responsible for the pressure fluctuation which subsequently affects the noise and vibration generation in the side channel pump. Hence, the results could be used as a reference for Noise-Vibration-Harshness (NVH) study in turbomachinery especially modifying the side channel pump in order to improve the operational reliabilities for many engineering processes.

A novel high temperature eddy current damper with enhanced performance by means of impedance matching

When an electrically conductive material is exposed to time-varying magnetic fields, eddy currents are generated inside the conductor which oppose the change in the magnetic field. When eddy currents circulate through the conductor they are dissipated in form of heat due to the resistivity of the material. For low frequency vibrations, eddy current damping force is proportional to the vibration speed. Therefore, damping of vibrations at low frequencies or displacement amplitudes becomes increasingly difficult using this technology. Typical damping densities of eddy current dampers range between 0.1 for most devices and 2 MN s m−4 for best-in-class prototypes. Those values are relatively low compared with, for examples, hydraulic dampers that can reach up to 4 MN s m−4. This low density limits potential applications of the technology. In addition, certain applications like vibration isolation of aircraft engines may require the damper to operate at high temperatures. However, most of current damping solutions are rarely effective at temperature higher than 100 °C because they frequently use NdFe magnets. In this paper, a passive eddy current damper with enhanced performance for use in high temperatures is presented. The Z-Damper takes advantage from impedance matching inside a magnetic linear gear to amplify the input vibration motion, maximizing the effectiveness of an integrated eddy current damper. SmCo magnets and high temperature components are used in the Z-Damper, potentially enabling operation in a wide temperature range. A theoretical model describing the dynamic behavior of the Z-Damper is presented and a set of experiments were conducted to evaluate its performance. A prototype of the Z-Damper has been designed, manufactured and experimentally demonstrated in a temperature range from 25 °C to 200 °C under low frequency (up to 60 Hz) harmonic excitations. A maximum equivalent viscous damping coefficient of 35 Ns mm−1, measured at 200 °C, has been achieved. A damping density of 8.4 MN s m−4 is calculated.

A Study of shape/layout design of piezoelectric energy harvesting skin considering harvesting power and skin volume

Piezoelectric energy harvesting skin (EH Skin) is a device which is attached on the surface of a vibrating plate to harvest electric power. This study discusses shape/layout design of the EH skin from the view of two-objective design problem to maximize harvesting power and to minimize skin volume. Characteristics found for optimal solution are: system resonance frequency close to harmonic excitation frequency for large vibration amplitude, and second, EH skin limited for the area with large surface strain.

Analytical solution and energy harvesting from nonlinear vibration of an asymmetric bimorph piezoelectric plate and optimizing the plate parameters by genetic algorithm

In this article, harvesting of electrical power from nonlinear vibration of an asymmetric bimorph piezoelectric plate is presented based on the classical plate theory with von Kármán strain–displacement nonlinear relations in the presence of temperature change effect. Two piezoelectric layers with different thicknesses cover top and bottom layers of a substructure. The structure has been excited under harmonic transverse forces in case of primary resonance. Two coupled ordinary differential equations for displacement and voltage have been derived and solved via multiple time scales method. The voltage equation has been defined by electric displacement and Gauss’s law. Analytic relations for voltage and harvested electrical power have been derived. The analytic relation for power is based on different parameters of the plate such as thicknesses of the layers, dimensions of plate, load resistance, frequency of harmonic excitation, and mechanical properties of structure. The parameters are optimized using genetic algorithm method with consideration of power relation as cost function. To harvest the maximum energy from the plate, the thicknesses of two piezoelectric layers, load resistance, and detuning parameter have been optimized. To illustrate the effectiveness of the optimization, results are depicted in three different simulations.

Structural control and biomechanical tremor suppression: Comparison between different types of passive absorber

Active and semi-active control devices can be used as advanced and accurate controllers to reduce the undesired vibration of a structure. However, some of these controllers may have a complex design, especially for systems excited with multi-degree-of-freedom frequencies, which demand the use of high anti-fatigue material properties, and others that may require a large power source. So, improvements in the design of passive controllers are of high interest for researchers. These controllers have a very simple design and aim to counteract vibration with no power requirements. In this paper, six different passive controllers were designed to analyze and compare their performance. The performance is considered in terms of the percentage of reduction in the primary system’s displacement amplitude and the bandwidth of each designed passive controller. The system of interest is taken as the three-degree-of-freedom dynamic hand system reflecting the behavior of Parkinsonian patients. Four joint muscles operating at two resonance harmonic excitation frequencies are considered to produce movements. Each controller was attached to the forearm of the hand set in the horizontal plane to analyze their capability in reducing the rest tremor (3–7 Hz) at the proximal joint. The dual series elastic–viscous absorber is shown to be a very effective controller. It is formed from a series connection between an elastic absorber (mass–spring) and a viscous absorber (mass–dashpot). It causes about 80% reduction in tremor amplitude with 4 Hz wide frequency band at the shoulder, elbow and wrist joints. This range of operational frequency is close to that of healthy cases, 4.5 Hz.

Dynamics of Microbeams under Multi-Frequency Excitations

This paper presents an investigation of the dynamics of microbeams under multiple harmonic electrostatic excitation frequencies. First, the response of a cantilever microbeam to two alternating current (AC) source excitation is examined. We show by simulations the response of the microbeam at primary resonance (near the fundamental natural frequency) and at secondary resonances (near half, superharmonic, and twice, subharmonic, the fundamental natural frequency). A multimode Galerkin method combined with the Euler-Bernoulli beam equation, accounting for the nonlinear electrostatic force, has been used to develop a reduced order model. The response of the cantilever microbeam to three AC source excitation is also investigated and shown as a promising technique to enhance the bandwidth of resonators. Finally, an experimental study of a clamped-clamped microbeam is conducted, demonstrating the multi-frequency excitation resonances using two, three, and four AC sources.

Optimization of the Vibro-Impact Capsule System

Optimization of the vibro-impact capsule system for the best progression is considered in this paper focusing on the choice of the excitation parameters and the shape of the capsule. Firstly, the fastest and the most efficient progressions are obtained through experimental investigations on a novel test bed. Control parameters, the amplitude and the frequency of harmonic excitation, and one of the system parameter, namely the stiffness ratio, are optimized. The experimental results confirm that the control parameters for the fastest progression are not the same as those for the most efficient progression from the energy consumption point of view. Therefore, the capsule system can be controlled either in a speedy mode or in an energy-saving mode depending on the operational requirements. In the second part of the paper, optimization of the capsule shape is studied using computational fluid dynamics (CFD) simulations. Here the aim of achieving the best progression is addressed through minimizing the drag and the lift forces acting on a stationary capsule positioned in the pipe within a fluid flow. The CFD results indicate that both drag and lift forces are dependent on capsule and arc lengths, and finally, an optimized shape of the capsule is obtained.

Fabrication of a biomimetic piezoelectric polyvinylidene difluoride (PVDF) fibre with a metal core and its application in vibration sensors

The fabrication is described of a vibration sensor based on the structure of the sensitive hair of some insects. The biomimetic hair has a metal core wrapped with a polyvinylidene difluoride (PVDF) layer. Two surface electrodes were coated on the PVDF surface of the fibre. A single SMPF (symmetric electrodes of metal core piezoelectric fibre) pasted on a matrix can be used as a vibration sensor. We propose a theoretical model describing the cantilever beam structure of the vibration sensor. The SMPF can detect both vibration amplitude and direction of the matrix. It can also detect the matrix harmonic excitation frequency and amplitude. We prepared PVDF fibres with metal cores (diameter: 230 µm) with the mould drawing method and used the surface electrodes and the metal core to polarize the PVDF layer. When the SMPF is used as a sensor, we only use the output signal of the two surface electrodes. Our experiments indicate that the SMPF can detect both vibration amplitude and direction of the matrix as well as the harmonic excitation frequency and the vibration direction. Our experimental results are consistent with the theoretical considerations.

Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation**Projects supported by the National Natural Science Foundation of China (Grant Nos. 51475246, 51277098, and 51075215), the Research Innovation Program for College Graduates of Jiangsu Province China (Grant No. KYLX15 0725), and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20131402).

The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc–Wen force–velocity (F–v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system.

Spatially uniform harmonic acoustic radiation force excitation using one-dimensional linear array

Low frequency harmonic force excitation can be used for both imaging and tissue characterization. This type of excitation can be achieved via intersecting two beams that slightly differ in frequency. One requirement of this technique is creating focused intersecting beams using available hardware. Previous studies have suggested different configurations for creating harmonic radiation force using linear arrays. However, these methods rely on identical frequency response assumption across all elements of the aperture. In practice, this assumption can be easily violated, especially if the transmit frequencies are not around the center frequency of the probe. When using electronic steering and focusing at different locations, this can result in a non-uniform radiation force pattern due to frequency changes in the sub-aperture. When used for vibro-acoustography, this manifests as vertical streaks in the final image that can severely degrade the quality of the image. We present a novel technique that minimizes element transmit frequency switching which in turn results in a more uniform excitation intensity. The results of applying this aperture configuration for vibro-acoustography imaging of breast phantoms with hard inclusions show significant improvements over previous methods. [This work was supported by NIH Grant R01 EB17213.]

The effect of subglottal acoustics on vocal fold vibration

Acoustic pressures above and below the vocal folds produce a push-pull action on the vocal folds which can either help or hinder vocal fold vibration. The key variable is acoustic reactance, the energy-storage part of the complex acoustic impedance. For the subglottal airway, inertive (positive) reactance does not help vocal fold vibration, but helps to skew the glottal airflow waveform for high frequency harmonic excitation. Compliant (negative) reactance, on the contrary, helps vocal fold vibration but does not skew the waveform. Thus, the benefit of subglottal reactance is mixed. For supraglottal reactance, the benefit is additive. Inertive supraglottal reactance helps vocal fold vibration and skews the waveform, whereas compliant supraglottal reactance does neither. The effects will be demonstrated with source-filter interactive simulation.

Separation of structural modes and harmonic frequencies in Operational Modal Analysis using random decrement

Operational Modal Analysis (OMA) is used to extract modal parameters of a structure on the basis of their output response measured during operation. OMA, when applied to mechanical engineering structures is often faced with the problem of harmonics present in the output response. A complex structure may have many dominant frequency components in its response frequency spectrum. These may contain frequency components associated with resonant frequencies of the structure, which and the associated mode shapes and the damping factors represent the data of interest, but may also contain frequencies or harmonics associated with the excitation sources. Since in OMA the characteristics of the excitation sources are not known, one of the problems lies in separating the resonant frequencies from the harmonic excitation frequencies. Any error in this regard may lead to an error in modal identification with the consequence that a harmonic may be construed as a structural mode and vice versa. This issue is addressed in this paper and a method is presented for separating resonant frequencies from harmonic excitation frequencies using random decrement of the response. The principle of the method is presented using an analytical study on a single degree of freedom system. The effectiveness of the method is then demonstrated through numerical studies on a lumped parameter multi-degree of freedom system and a simulated plate structure. Detection of single and multiple harmonics in the response that are well separated as well as close to resonant frequencies are considered.

Phase resolved characterization of conical premixed flames near and far from blowoff

A harmonically excited conical bluff body stabilized flame was studied to determine its behavior under strong burning and near blowoff conditions. Chemiluminescence imaging was employed using a high speed camera to characterize the phase resolved flame characteristics for a range of excitation frequencies from 50 to 400Hz. Phase-resolved measurements of strain rate along the flame front were utilized to provide important insights for understanding of flame behavior particularly near blowoff. Phase resolved particle image velocimetry (PIV) was utilized to map the different phases of the velocity field for the harmonically modulated flames. PIV data along the flame front identified from seed density change were utilized to determine the strain rate variations at different phases of the flame oscillation. Oscillations of recirculation zone length were also characterized at all harmonic excitation frequencies accompanied by a cyclically varying strain rate along the flame front. At certain phases of the cycle, the strain rate reaches a maximum just before the phase when the recirculation zone length is a minimum. At this point, flame pinching and vortex breakdown phenomena were observed. This vortex breakdown phenomenon accompanies flame blowoff when the ratio of the minimum recirculation zone length to the convective length scale is in the range between 0.35 and 0.5. Based on these results, a description of flame blowoff phenomenon under externally forced flow is proposed.

Rock fragmentation mechanisms and an experimental study of drilling tools during high-frequency harmonic vibration

Resonance drilling is a new technology, still at the laboratory stage. It has great potential to improve rock fragmentation efficiency. We analyzed the amplitude-frequency characteristics of steady-state mechanical vibration excited by harmonic vibration in rocks and an apparatus was built to achieve high frequency vibration of rock. The influence of rock drillability, rotary speed, excitation frequency, and other parameters on the rate of penetration (ROP) in resonance drilling was analyzed. The results show that the rock drillability decreased with an increase in excitation frequency. When drilling with a large size drill bit, the ROP increased with excitation frequency. The ROP reached a maximum value at the resonant frequency of the rock. The ROP of the bit increased linearly with rotary speed when no vibration was applied on the rock and increased approximately exponentially when harmonic vibration was applied. In addition, the resonant frequency of the rock was changing during the process of rock fragmentation, so in order to achieve the desired resonance of the rock, it is necessary to determine an appropriate harmonic vibration excitation frequency.

An experimental study on tuned liquid damper for mitigation of structural response

Abstract This paper investigates the performance of unidirectional tuned liquid damper (TLD) that relies upon the motion of shallow liquid in a rigid tank for changing the dynamic characteristics of a structure and dissipating its vibration energy under harmonic excitation. A series of experimental tests are conducted on a scaled model of structure-tuned liquid damper systems to evaluate their performance under harmonic excitation. One rectangular and one square TLD with various water depth ratios are examined over different frequency ratios, and time histories of accelerations are measured by precisely controlled shaking table tests. The behaviour of TLD is also studied by changing the orientation of the rectangular TLD subjected to the given range of harmonic excitation frequencies. The effectiveness of TLD is evaluated based on the response reduction of the structure. From the study, it is found that for each TLD, there exists an optimum water depth that corresponds to the minimum response amplitude, and the maximum control of vibration is obtained under resonance condition with the attachment of TLD.

The characteristics of a nonlinear vibration neutralizer

This paper concerns an investigation into the use of cubic nonlinearity in a vibration neutralizer to improve its effectiveness. It is assumed that the frequency of the harmonic excitation is well above the resonance frequency of the machine to which the neutralizer is attached, and that the machine acts as a simple mass. It is also assumed that the response of the system is predominantly at the harmonic excitation frequency of the machine. The harmonic balance method is used to analyze the system. It is shown how the nonlinearity has the effect of shifting the resonant peak to a higher frequency away from the tuned frequency of the neutralizer so that the device is robust to mistune. In a linear neutralizer this can only be achieved by adding mass to the neutralizer, so the nonlinearity has a similar effect to that of adding mass. Some characteristic features are highlighted, and the effects of the system parameters on the performance are discussed. It is shown that, for a particular combination of the system parameters, the effect of the nonlinearity is also to increase the bandwidth of the device compared to the linear neutralizer with similar mass and damping. Some approximate expressions are derived, which facilitate insight into the parameters which influence the dynamics of the system. The results are validated by some experimental work.

Efficient path integral solution of Fokker–Planck equation: response, bifurcation and periodicity of nonlinear systems

Response of nonlinear systems subjected to harmonic, parametric, and random excitation is of importance in the field of structural dynamics. The transitional probability density function (PDF) of the random response of nonlinear systems under white or coloured noise excitation (delta-correlated) is governed by both the forward Fokker–Planck (FP) and the backward Kolmogorov equations. This article presents a new approach for efficient numerical implementation of the path integral (PI) method in the solution of the FP equation for some nonlinear systems subjected to white noise, parametric and combined harmonic and white noise excitations. The modified PI method is based on a non-Gaussian transition PDF and the Gauss–Legendre integration scheme. The steady state PDF, jump phenomenon, noise induced state changes of PDF are studied by the modified PI method. Effects of white noise intensity, amplitude and frequency of harmonic excitation and the level of nonlinearity on stochastic jump and bifurcation behaviours of a hardening Duffing oscillator are also investigated.