Vibration Cycle Research Articles

Some factors affecting the loosening failure of bolted joints under vibration using finite element analysis

Finite element analysis has been regarded as an effective research method for analyzing the loosening failure of bolted joints under vibration. However, there exist some factors, which influence the accuracy and reliability of loosening results, thus determining the explanations of the loosening mechanism. In this study, a 3D finite element model of a typical bolted joint was built to investigate the effects of several different factors on the loosening under transverse vibration loading. These influencing factors include preload generation, vibration parameter, and material model. Based on the simulation results, it was found that applying the method of pretension element to generate preload instead of the actual method of torque was reliable and efficient. For the vibration parameter, it showed that the decrease rate in preload was higher for a larger vibration amplitude. But once the bearing surface reached complete slip, the loosening rate would keep constant. This was because the thread surface at that time reached a sticking state. Vibration frequency was proved to have no effect on the loosening behavior. This result demonstrated that the quasi-static assumption for vibration frequency was reasonable. Additionally, it also indicated that plastic material models only affected the preload loss in the initial several vibration cycles and had no influence on the loosening rate of preload after several vibration cycles. Finally, experiments were conducted to confirm qualitatively the results obtained based on finite element analysis.

An alternative representation of the receptance: The ‘elliptical plane’ and its modal properties

Abstract Modal Identification from Frequency Response Functions (FRFs) has been extensively investigated up to the point its research reached a stagnation state. Yet, a new approach to determine the modal damping factors from FRFs was recently proposed, showing that there still is scope for new findings in the field. Contrary to other modal identification methods which are based on the dynamic motion governing equations, the method used the dissipated energy per cycle of vibration as a starting point. For lightly damped systems with conveniently spaced modes, it produced quite accurate results, especially when compared to the well-known method of the inverse. The method used a plot of the sine of the phase of the receptance against its amplitude, whereby damping was determined from the slope of a linear fit to the resulting plot. In this paper, it is shown that this plot has other (perhaps more important) special properties that were not explored before. Near resonant frequencies, its shape is elliptical, whereby the real and imaginary parts of the modal constants can be determined from numerical curve-fitting. This finding allowed developing a new method which formulation is presented in this paper. The method is discussed through numerical and experimental examples. Although the intention is not to present a new modal identification method that is superior to other existing ones (like the method of the inverse or those based on the Nyquist plot), the authors believe that this new representation of the receptance and its properties may bring valuable insights for other researchers in the field.

Vibration damage rate curves for quantifying abrasion of printed packaging in accelerated random vibration test

Some vibration‐based damages in packaged products, such as surface abrasion and bruising of fruits, are not necessarily caused by vibration stresses at resonant frequencies. They are often nonfatigue damages resulting from the accumulation of low stress vibrations. This study introduces a new concept and methodology of vibration damage rate curves, which describes the relationship between damage rate, Grms, and vibration cycles, N. The vibration damage rate curves for quantifying the abrasion of a column stacked printed packaging was developed on the basis of ASTM D 4169 truck profile level 1, 2, and 3, as well as the field test. The abrasion rate in the laboratory was then compared to that in the equivalent time of road transportation per accelerated random vibration test formula. This study recommends that the accelerated random vibration formula can be used when vibration damage rate curves for printed packaged products are developed, to effectively reproduce the damage in the laboratory that is equivalent to the field.

Experimental travelling waves identification in mechanical structures

Vibrations are often represented as a sum of standing waves in space, i.e. normal modes of vibration. While this can be mathematically accurate, the representation as travelling waves can be compact and more appropriate from a physical point of view, in particular when the energy flux along the structure is meaningful. The quantification of travelling waves assists in computing the energy being transferred and propagated along a structure. It can provide local as well as global information about the structure through which the mechanical energy flows. Presented in this paper is a new method to quantify the fraction of mechanical power being transmitted in a vibration cycle at a specific direction in space using measured data. It is shown that the method can detect local defects causing slight non-uniformity of the energy flux. Equivalence is being made with the electrical power factor and electromagnetic standing waves ratio, commonly employed in such cases. Other methods to perform experiment based wave identification in one-dimension are compared with the power flow based identification. Including a signal processing approach that fits an ellipse to the complex amplitude curve and Hilbert transform for obtaining the local phase and amplitude. A new representation of the active and reactive power flow is developed and its relationship to standing waves ratio is demonstrated analytically and experimentally.

The Quasi-static Properties of Natural Marine Clay under Tidal Low Frequency Cyclic Loading in Yangtze Estuary, China

The enclosure engineering of tidal flats behind Changxing Island is taken as the research background. In order to explore the undrained cyclic response of natural marine clay on tidal level periodic changing, the stress-controlled low frequency cyclic tri-axial tests and static creep tests are conducted on natural K0-consolidated Shanghai clay. In the series I tests, samples are cyclically sheared by low-frequency cyclic loading until stability or failure, the accumulative behavior and reversible strain are studied. The effects of confining pressure and stress ratio are also investigated. Significantly, loading frequency is a key factor in controlling the cyclic behavior. In the series II tests, special attention is given to the low frequency cyclic vibration effect on the undrained cyclic tests by comparison with the static creep tests. The critical stress ratio of low frequency cyclic behavior is less than static creep strength.

Development of cutting force prediction model for vibration-assisted slot milling of carbon fiber reinforced polymers

Carbon fiber reinforced polymers (CFRP) have got rapidly increased applications in aerospace/aircraft and other fields due to their attractive properties of high specific strength/stiffness, high corrosion resistance, and low thermal expansion. These materials have also some challenging properties like heterogeneity, anisotropy, and low heat dissipation. Due to these properties, the issues of excessive cutting forces and machining damages (delamination, fiber pull-out, surface/subsurface defects, etc.) are encountered in machining. The cutting forces are required to be minimized for qualified machining with reduced damages. In this research, a novel cutting force prediction model has been developed for vibration-assisted slot milling. The experimental machining has been carried out on CFRP-T700 composite material. The effective cutting time per vibration cycle and the force of friction have been expressed/calculated. The feasibility of vibration-assisted machining for CFRP composites has also been evaluated. The relationships of the axial and feed cutting forces with machining parameters were investigated. The results have shown the variations below 10% among experimental and corresponding simulation values (from the model) of cutting forces. However, the higher variations have been found in some experiments which are mainly due to heterogeneity, anisotropy, and some other properties of such materials. The developed cutting force model then validated through pilot experiments and found the same results. So, the developed cutting force model is robust and can be applied to predict cutting forces and optimization for vibration-assisted slot milling of CFRP composite materials at the industry level.

Active Mechanisms of Vibration Encoding and Frequency Filtering in Central Mechanosensory Neurons

To better understand biophysical mechanisms of mechanosensory processing, we investigated two cell types in the Drosophila brain (A2 and B1 cells) that are postsynaptic to antennal vibration receptors. A2 cells receive excitatory synaptic currents in response to both directions of movement: thus, twice per vibration cycle. The membrane acts as a low-pass filter, so that voltage and spiking mainly track the vibration envelope rather than individual cycles. By contrast, B1 cells are excited by only forward or backward movement, meaning they are sensitive to vibration phase. They receive oscillatory synaptic currents at the stimulus frequency, and they bandpass filter these inputs to favor specific frequencies. Different cells prefer different frequencies, due to differences in their voltage-gated conductances. Both Na+ and K+ conductances suppress low-frequency synaptic inputs, so cells with larger voltage-gated conductances prefer higher frequencies. These results illustrate how membrane properties and voltage-gated conductances can extract distinct stimulus features into parallel channels.

Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

Abstract In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

Study on hydraulic exciting vibration due to flexible valve in pump system with method of characteristics in the time domain

To analyse the flow characteristics of leakage as well as the mechanism of selfexcited vibration in valves, the method of characteristics was used to assess the effect of flexible valve leakage on the self-excited vibration in water-supply pump system. Piezometric head in upstream of the valve as a function of time was obtained. Two comparative schemes were proposed to simulate the process of self-excited vibration by changing the length, the material of the pipeline and the leakage of valves in the above pump system. It is shown that the length and material of the pipe significantly affect the amplitude and cycle of self-excited vibration as well as the increasing rate of the vibration amplitude. In addition, the leakage of the valve has little influence on the amplitude and cycle of self-excited vibration, but has a significant effect on the increasing rate of vibration amplitude. A pipe explosion accident may occur without the inhibiting of self-excited vibration.

Dynamic characteristics of saturated loess under different confining pressures: a microscopic analysis

To explore the influence of confining pressure on the dynamic characteristics of saturated loess and variation of the characteristics in micro-mechanisms therein, dynamic triaxial testing of loess from Xianyang was carried out. The dynamic elastic modulus of saturated loess after different numbers of cycles was available through the test and the relationship between the dynamic elastic modulus and confining pressure can be analysed. A scanning electron microscope (SEM) examination was conducted to assess the microstructural characteristics of the specimens. From both qualitative and quantitative aspects, the variations in microstructure were analysed. The microstructural parameters which had greater correlation with macroscopic strength were found based on grey relationship theory, then the relationship between them was found by curve-fitting. The results show that, the dynamic elastic modulus of saturated loess was increased as the confining pressure increases, but decreased with increasing vibration cycle and tended to be stable over time. The approximate microstructural parameters selected were correlated to the dynamic elastic modulus in addition to the average pore shape factor; because of the high correlation with the dynamic elastic modulus, the average diameter of the pores, the average shape factor and fractal dimension of the morphology of structural units were selected to fit the dynamic elastic modulus.

Effect of Vibration Cycles Batches on Shear Modulus and Damping of Dry Sand

AbstractResonant column tests were conducted to examine the variation in shear modulus (G) and damping ratio (D) of dry sand subjected to 10 batches of vibration cycles. Each batch increment compri...

Dynamics of the Driving Force During the Normal Vocal Fold Vibration Cycle

Intraglottal pressure is the driving force of vocal fold vibration. Theoretically, simultaneous quantification of glottal area and transglottal airflow allows the calculation of the intraglottal pressure waveform during a single vibration cycle. In this study, we show that, by combining photoglottography (transglottal light transmission) and airflow (Rothenberg mask) measurements during sustained vocal emissions in vivo, the intraglottal pressure wave can be approximated in a way similar to what has been done in models. The results confirm in vivo that the intraglottal pressure is systematically larger during the opening phase than during the closing phase, so that over one whole cycle, the driving force performs net positive work, accounting for sustained vocal fold motion. A component of this driving force asymmetry is related to vocal tract inertance, which also accounts for the skewing of the airflow waveform compared with the area waveform. Furthermore, the intraglottal pressure ratio (opening:closing) increases with voicing intensity, reaches a maximum around 76 dB, and significantly decreases at higher intensities. This rise and fall suggests that there is a range of intensity values in which, mechanically, a maximum of the driving force is imparted to the vocal fold mass. This finding could have implications for voice economy in professional speakers.

Investigation on two-phase distribution in a vibrating annulus

Seismic vibration can induce additional interphase forces acting on bubbles and change flow characteristics in two-phase flow system. Local measurements of air-water two-phase flow parameters, namely void fraction, interfacial area concentration and Sauter mean diameter, were conducted in a vibrating annulus. The vibration acceleration ranged from 0.05g to 0.24g. Nine inlet flow conditions were selected, which covered bubbly and slug flows. No significant difference was observed in the time-averaged flow parameters between reference and vibration experiments. During vibration cycle, the radial two-phase flow distribution varied continuously with vibration phase. The change in non-dimensional line-averaged void fraction decreased with the increase of void fraction. As the vibration amplitude increased from 3.04mm to 10.08mm, the vibration effects on variations of local flow parameters were greatly enhanced with the mean relative variation (MRV) of void faction reached up to 55%. The study on MRV of local parameters showed that the vibration effects were strongly related to specific flow conditions. With the increase of superficial gas velocity and void fraction, the vibration effects were reduced and the MRV of void fraction decreased from 55% to 18%.

Vibrations of mechanical systems with energy dissipation hysteresis

A phenomenological approach which we refer to as kinematic is proposed to describe hysteresis; according to this approach, the force and kinematic parameters of a mechanical system are related by a first-order ordinary differential equation. The right-hand side is chosen in the class of functions ensuring the asymptotic approach of the solution to the curves of the enveloping (limit) hysteresis cycle of steady-state vibrations. The coefficients of the equation are identified by experimental data for the enveloping cycle. The proposed approach permits describing the hysteresis trajectory under the conditions of unsteady vibrations with an arbitrary starting point inside the region of the enveloping cycle. As an example, we consider the problem on forced vibrations of a pendulum-type damper of low-frequency vibrations.

A comparison methodology for measured and predicted displacement fields in modal analysis

Recent advances in experimental mechanics have enabled full-field measurements of deformation fields and - particularly in the field of solid mechanics - methodologies have been proposed for utilizing these fields in the validation of computational models. However, the comparison of modal shapes and the path from the undeformed shape to the deformed shape at the extreme of a vibration cycle is not straightforward. Therefore a new method to compare vibration data from experiment to simulations is presented which uses full-field experimental data from the entire cycle of vibration. Here, the first three modes of vibration of an aerospace panel were compared, covering a frequency range of 14–59Hz and maximum out-of-plane displacements of 2mm. Two different comparison methodologies are considered; the first is the use of confidence bands, previously explored for quasi-static loading, the second is the use of a concordance correlation coefficient, which provides quantifiable information about the validity of the simulation. In addition, three different simulation conditions were considered, representing a systematic refinement of the model. It was found that meaningful conclusions can be drawn about the simulation by comparing individual components of deformation from the image decomposition process, such as the relative phase and magnitude. It was ultimately found that the best performing model did not entirely fall within the confidence bounds for all conditions, but returned a concordance correlation coefficient of nearly 70% for all three modes.

A reflected wave superposition method for vibration and energy of a travelling string

This paper considers the analytical free time domain response and energy in an axially translating and laterally vibrating string. The domain of the string is either a constant or variable length, dependent upon the general initial conditions. The translating tensioned strings possess either fixed-fixed or fixed-free boundaries. An alternative analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycles of vibration for both constant and variable length strings are provided, which for the latter are dependent upon the variable string length. Each cycle is divided into three time intervals according to the magnitude and the direction of the translating string velocity. Applying d’Alembert's method combined with the reflection properties, expressions for the reflected waves at the two boundaries are obtained. Subsequently, superposition of all of the incident and reflected waves provides results for the free vibration of the string over the three time intervals. The variation in the total mechanical energy of the string system is also shown. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-Beta method solution and an existing state space function representation of the string dynamics.

Finite element method-based study for effect of adult degenerative scoliosis on the spinal vibration characteristics

Finite element analysis was used to investigate the responses of five healthy subjects and five adult degenerative scoliosis (ADS) subjects to cyclic vibration. The dynamic responses of the healthy and scoliotic spines to the sinusoidal cyclic vibrations have been investigated in previous studies by simulation or experimental approaches. However, no simulation or experimental results were available for the ADS subjects. The effect of the ADS on the vibrational characteristics of spines remained unknown. The objective of this study was to compare differences of the dynamic responses to the cyclic vibration input between the healthy subjects and subjects with ADS. Based on the simulations results in this study, the scoliotic spines are more sensitive to the cyclic vibrations than the healthy spines. More resonant frequencies were predicted in the scoliotic spines than the healthy spines. The scoliotic deformity in the spine was to make the vibrational response of the spine significantly more complex at the apical scoliotic region. This study suggested that ADS could severely increase spinal response to the cyclic vibrations, which could potentially lead to further scoliotic deformity in the spine.

Aerodynamic force and moment measurement of 10° half-angle cone in JF12 shock tunnel

An aerodynamic force and moment measurement was conducted in JF12 long-test-duration detonation-driven shock tunnel of Institute of Mechanics, Chinese Academy of Sciences. The test duration of JF12 is 100–130ms. The nominal Mach number is 7.0 and the exit diameter of the contoured nozzle is 2.5m. The total enthalpy is 2.5MJ/kg which duplicates the hypersonic flight conditions of Mach number 7.0 at 35km altitude. The test model is the standard aerodynamic force model of 10° half-angle sharp cone. The length of the test model is 1500mm and the weight is 57kg. The aerodynamic forces were measured with a six-component strain balance. The angles of attack were set to be −5°, 0°, 5°, 10° and 14°, respectively. The experimental results show that in the 100–130ms test duration, the signals of strain balance have 3–4 complete vibration cycles. So, the aerodynamic forces and moments can be obtained directly by averaging the signals of balance without acceleration compensation. The force measurement error of repeatability of JF12 is less than 2%. The aerodynamic force coefficients of JF12 are in good agreement with those of conventional hypersonic wind tunnels. For this test model at Mach number 7.0 and total enthalpy of 2.5MJ/kg, the real-gas effects on aerodynamic force characteristics are not very evident.

Adaptive synchronized switch damping on an inductor: a self-tuning switching law

Synchronized switch damping (SSD) techniques exploit low-power switching between passive circuits connected to piezoelectric material to reduce structural vibration. In the classical implementation of SSD, the piezoelectric material remains in an open circuit for the majority of the vibration cycle and switches briefly to a shunt circuit at every displacement extremum. Recent research indicates that this switch timing is only optimal for excitation exactly at resonance and points to more general optimal switch criteria based on the phase of the displacement and the system parameters. This work proposes a self-tuning approach that implements the more general optimal switch timing for synchronized switch damping on an inductor (SSDI) without needing any knowledge of the system parameters. The law involves a gradient-based search optimization that is robust to noise and uncertainties in the system. Testing of a physical implementation confirms this law successfully adapts to the frequency and parameters of the system. Overall, the adaptive SSDI controller provides better off-resonance steady-state vibration reduction than classical SSDI while matching performance at resonance.

Influence of principal stress rotation of unequal tensile and compressive stress amplitudes on characteristics of soft clay

Soil behavior can reflect the characteristics of principal stress rotation under dynamic wave and traffic loads. Unequal amplitudes of tensile and compressive stresses applied to soils have complex effects on foundation soils in comparison with the pure principal stress rotation path. A series of undrained cyclic hollow torsional shear tests were performed on typical remolded soft clay from the Ilexi area of Nanjing, China. The main control parameters were the tensile and compressive stress amplitude ratio (α) and the cyclic dynamic stress ratio (η). It was found that the critical η tended to remain constant at 0.13, when the value of the compressive stress amplitude was higher than the tensile stress amplitude. However, the influence of the tensile stress was limited by the dynamic stress level when α= 1. For obvious structural change in the soil, the corresponding numbers of cyclic vibration cycles were found to be independent of α at low stress levels and were only related to η. Finally, a new method for evaluating the failure of remolded soft clay was presented. It considers the influence of the tensile and compressive stresses which caused by complex paths of the principal stress rotation. This criterion can distinguish stable, critical, and destructive states based on the pore-water-pressure-strain coupling curve while also providing a range of failure strain and vibration cycles. These results provide the theoretical support for systematic studies of principal stress rotation using constitu tive models.