Amplitude Of Relative Displacement Research Articles

An Investigation of the Effects of a Dynamic Vibration Absorber (DVA) to the Comfort of a Bus's Driver Seat

The frequency weighted acceleration, relative displacement, and Seat Effective Amplitude Transmissibility (SEAT) of a bus driver's seat are investigated by a 4 degrees of freedom (4DOF) vertical dynamic model, including a dynamic vibration absorber (DVA). The Root Mean Squared (RMS) values of the gain responses in the frequency domain are analyzed in the DVA damping ratio domain to help determine the optimal value of the DVA' s suspension. The obtained results show that the comfort evaluation index, in the case of a bus driver's seat with DVA, can be improved by more than 15% and nearly 10%, respectively, with the seat suspension natural frequency of 1~Hz and 4~Hz respectively. The comfort is better with the lower seat suspension natural frequency and vice versa. Especially in the case of both the seat and the DVA suspensions with low natural frequencies, all the three mean of evaluation indexes in the whole damping ratio domain of the DVA, have improved by more than 12%. This is the case with all three evaluation indexes which are the best when the damping ratio of the DVA is greater than 0.6.

A semi-analytical approach for site-city interaction under oblique incident SH waves

In this paper, a semi-analytical approach was proposed for investigating the site-city interactions (SCI). The site was modelled as a horizontal layered half-space, while the building was represented as a collection of shear wall structures fixed on the surface of half-space. The total wave field was considered as a combination of free field and scattering wave field generated by buildings, simulated by direct stiffness method and Green's function, respectively. The coupling between the site and the city is achieved through the displacement continuity conditions at the bottom of the building. Finally, the impact and some influencing factors of SCI effect on site and buildings were studied. It is found that the SCI effect has a significant impact on surface displacement and building response. The SCI effect typically reduces surface displacement near cities and the amplitude of relative displacement of buildings, while increases the seismic duration of buildings. However, this influence will be affected by the incident angle, building layout, building height, and building spacing, so these factors should be comprehensively considered when analyzing the SCI effect. Through the case studies, it is demonstrated that this method can quickly calculate SCI models with complex factors without being limited by the number and thickness of soil layers, incidence angles, and different sizes and spacing of buildings.

Seeking the Oxidation Mechanism of Debris in the Fretting Wear of Titanium Functionalized by Surface Laser Treatments

Surface laser treatment (SLT) using nanosecond IR lasers has been shown to improve the tribological behaviour of titanium. Here, we studied the fretting wear of SLT-functionalized pure titanium in a mixture of reactive gases O2 (20 vol.%) + N2 (80 vol.%). The contact geometry was a ball on a plane and the ball was made of bearing steel. The very small amplitude of relative displacement between reciprocating parts in fretting wear makes the evacuation of wear particles difficult. Moreover, the oxidation mechanism of the debris depends on the accessibility of the surrounding atmosphere to the tribological contact. This work focused in the analysis of debris generation and oxidation mechanisms, and sought to differentiate the role of oxygen forming part of the ambient O2 + N2 gas mixture from oxygen present in the surface layer of the SL-treated titanium. Before the fretting test, the surface of the commercially pure titanium plates was treated with a laser under a mixture of O2 + N2 gases with oxygen enriched in the 18O isotope. Then, the fretting tests were performed in regular air containing natural oxygen. Micro-Raman spectroscopy and ion beam analysis (IBA) techniques were used to analyse the TiO2 surface layers and fretting scars. Iron oxide particles were identified by Raman spectroscopy and IBA as the third body in the tribological contact. The spatial distribution of 18O, Ti, 16O and Fe in the fretting scars was studied by IBA. The analysis showed that the areas containing high concentrations of Fe displayed also high concentrations of 16O, but smaller concentrations of 18O and Ti. Therefore, it was concluded that tribological contact allows the oxidation of iron debris by its reaction with ambient air.

Fatigue behaviour analysis of aluminium alloy riveted single-shear lap joints

Analysing the dynamic response, the fatigue failure process of aluminium alloy riveted single-shear lap joints is quantitatively described. Firstly, numerical analysis of hysteretic loops based on MATLAB is proposed, and cyclic relative displacement amplitude, stiffness and dissipated energy are calculated. Secondly, the service behaviour corresponding to the evolution of relative displacement amplitude and dissipated energy is analysed and verified by finite element simulation. Finally, based on the evolution of cyclic compression stiffness, the cycles corresponding to crack initiation, as well as slow and rapid propagation, are calculated and verified by observing crack growth propagation through interruption tests.

Effect of Stiffening the Printed Circuit Board in the Fatigue Life of the Solder Joint.

Predictive analysis of the life of an electronic package requires a sequence of processes involving: (i) development of a finite element (FE) model, (ii) correlation of the FE model using experimental data, and (iii) development of a local model using the correlated FE model. The life of the critical components is obtained from the local model and is usually compared to the experimental results. Although the specifics of such analyses are available in the literature, a comparison among them and against the same electronic package with different user printed circuit board (PCB) thicknesses does not exist. This study addresses the issues raised during the design phase/life analysis, by considering a particular package with a variable geometric thickness of the user PCB. In this paper, the effect of stiffening the user PCB on the fatigue life of a ball grid array (BGA), SAC305 solder joint is studied. The board stiffness was varied by changing the thickness of the PCB, while the size of the substrate, chips, and solder balls were kept constant. The test vehicle consisted of BGA chips soldered to a user PCB. The thickness of the user PCB was varied, but the surface area of the BGA chip remained identical. The test vehicle was then modeled using a finite element analysis tool (ANSYS). Using a global/local modeling approach, the modal parameters in the simulations were correlated with experimental data. The first resonance frequency dwell test was carried out in ANSYS, and the high-cycle fatigue life was estimated using the stress-life approach. Following the simulation, the test vehicle was subjected to resonance fatigue testing by exciting at the first mode resonance frequency, the mode with the most severe solder joint failure. The resistance of the solder joint during the experiment was monitored using a daisy-chain circuit, and the point of failure was further confirmed using the destructive evaluation technique. Both the experimental and simulation results showed that stiffening the board will significantly increase the fatigue life of the solder joint. Although the amplitude of the acceleration response of the test vehicle will be higher due to board stiffening, the increase in natural frequencies will significantly reduce the amplitude of relative displacement between the PCB and the substrate.

Effect of uncertainty on dynamic damping and stiffness of spherical hollow rubber isolators based on harmonic experiment

This study aims to identify the effect of uncertainty on the dynamic characteristics of a thin-walled hollow spherical rubber isolator. Firstly, the nonlinearity and uncertainties of the spherical rubber isolator were obtained by swept-sine experiments. The relationship between dynamic stiffness and damping against relative displacement amplitude was established. Then, a high-order polynomial function with uncertain parameters introduced was used for simulation. The uncertain parameters were quantified using the singular value decomposition and Monte Carlo simulations. Furthermore, the dynamic stiffness and damping of the experimental data were optimized using the Covariance Matrix Adaptation and Evolution Strategy. Finally, the high consistency between the simulation results and experimental results were demonstrated. Overall, the nonlinear model established according to the uncertain parameter quantization is feasible. This method can predict the nonlinear characteristics of the rubber isolator well and also may be applied to other nonlinear models.

Ultra-low wide bandwidth vibrational energy harvesting using a statically balanced compliant mechanism

Structure design of ultra-low wide bandwidth vibrational energy harvesters remains an open issue. In this research, a statically balanced compliant mechanism (SBCM) is proposed, dynamically modelled, and experimentally demonstrated to address this need. This SBCM is designed based on the concept of stiffness compensation between a linear component with positive-stiffness (two double parallelograms in parallel) and a nonlinear component with negative-stiffness (two sets of post-buckled fixed-guided compliant beams in parallel). A design guideline of the SBCM starting from using rapid-design stiffness compensation equation is provided for reasonably approximate and accurate results. Subsequently, a dynamic analytical model of the displacement response of the SBCM to harmonic base excitation has been derived based on the averaging method. The nonlinear force-displacement relationship of the system was obtained through nonlinear finite element analysis (FEA) simulations in this regard and a 5th order polynomial fit was chosen taking only odd terms into account. The accuracy of this analytical model is confirmed by numerical analysis. Next, a prototype of the SBCM was fabricated and its applicability to piezoelectric vibrational energy harvesters (PVEHs) was demonstrated by integrating piezoelectric capacitors made of PVDF films with compliant beams of the SBCM to generate electric outputs in response to the bending of the beams. Static balancing is achieved over a continuous displacement range of 2 mm around the origin. Bi-stability and mono-stability were observed with the same prototype by adjusting the length of the positive-stiffness beams. Under static-balancing condition, the SBCM is able to respond to a wide range of ultra-low frequencies with low accelerations, which has been established experimentally, analytically and numerically. In dynamic experiments, the steady-state relative displacement amplitude H is 2.9 mm under an excitation condition of 6 Hz and 0.1g (1g=9.8 m/s2), and it reaches a maximum of 9.4 mm under 12.75 Hz and 0.25 g. A 30%-Hmax frequency bandwidth is introduced to assess the nonlinear dynamic performance of the SBCM from a mechanical perspective. The maximum experimental 30%-Hmax bandwidth of the structure is 6.75 Hz (from 6 Hz to 12.75 Hz) at 0.25 g and the corresponding theoretical value is 8.73 Hz (from 3.34 Hz to 12.07 Hz). Under the same excitation condition, it is shown that the maximum relative displacement amplitude deceases as the jump-down frequency increases. In addition, super-harmonic and sub-harmonic oscillations are observed in the dynamic experiments. The SBCM can provide a practical structural solution for harvesting energy from a range of vibrational scenarios (e.g. ocean waves, human motions and bridge vibrations) with ultra-low wide bandwidth frequencies and weak accelerations. The concept of SBCM is suitable to be combined with various energy conversion principles and is not limited to piezoelectric sources alone. When miniaturized, the SBCM concept can be of particular interest to researchers active in energy harvesting for microelectromechanical systems (MEMS) technology.

A unified description of surface waves and guided waves with relative amplitude dispersion maps

SUMMARYCompared with surface waves, guided waves are rarely applied in near-surface investigation. The main reason may lie in the complexity of their dispersion curves. Besides, the study and understanding of guided wave dispersion characteristics are now also inadequate and not deep enough. In this paper, we derived the complete theoretical dispersion curves of P–SV-wave and pure P-wave systems in layered media based on the transmission matrix method and obtained the relative displacement amplitude coefficients at the free surface as a function of frequency and phase velocity for both surface and guided waves. By assigning the value of relative displacement amplitude coefficient to the corresponding point (f,v) on dispersion curve, we got a multi-information diagram called relative amplitude dispersion map (RADM). As a unified description of surface and guided waves, RADM not only shows the velocity–frequency relationship but also represents the polarized energy ratio at the free surface by display colours. The accuracy of RADM was proved by synthetic seismic records, in which RADMs fit well with the corresponding dispersion energy of surface and guided waves. In addition, we designed six models with different Poisson's ratio (PR) and different layer numbers for comparison. It shows that the dispersive vertical-to-horizontal amplitude ratio of guided waves is complex and discontinuous in RADM, which brings great difficulty for mode identification and even affects the subsequent inversion. Tests also show that for high PR layers, the trends of guided P–SV-wave dispersion curves are basically consistent with those of pure P wave. With the decrease of PR, dispersion curves of guided P–SV wave gradually deviate from those of pure P wave. However, RADMs can be greatly consistent with the dispersion energy in either case. This is of great significance for the inversion of near-surface P and S velocities by using dispersion relationships of multimode surface and guided waves.

Study of the Lifetime Testing of Spherical Rubber Isolators

This study aims to identify the fatigue lifetime of a thin-walled hollow spherical rubber isolator subjected to harmonic and random vibrations. Firstly, the nonlinear characteristics of the rubber materials are tested and analyzed through vibration experiments. The relationship among the nonlinear stiffness, nonlinear damping, and relative displacement amplitude is established. Secondly, an accelerated lifetime experiment under random excitation is carried out. The correlation between the root-mean-squared acceleration response of the random vibration system and the stiffness attenuation of the rubber isolator is established and modeled. A lifetime prediction method for rubber isolators is proposed based on the model. Finally, the influence of different loads on the lifetime of the rubber isolator is investigated. These methods provide an additional rationale for the further theoretical research and practical engineering application of rubber damping systems.

Vibration Analysis of a Bus’s Air Spring Suspension Subjected to Random Road Profile

Vehicle dynamics model in type of 1/4 is used for vibration analysis under the effect of random road profile with different grades. The mathematical model to describe the used random road profile is able to change the type of investigated road grades by selecting the corresponding power spectral density parameter of the road grade according to the ISO 8608 standard. Random road profile is ivestigated in the range of frequency domain from 0 to 50 (Hz). The air spring stiffness and the damping coefficience are determined on the basis of reference to the practical vehicle. The variation of relative displacement amplitude of the suspension in the range of investigation domain is small, the air spring stiffness used in the calculation is constant. The obtained results corresponding to different grades of road surface roughness including displacement and acceleration parameters. Relative displacement is a parameter that aims to verify the ability to ensure safe working of the suspension, namely rattle spacing. Acceleration is used to evaluate the vehicle's comfort. Calculation results are analyzed as the basis for evaluating the influence of the air spring stiffness and road surface conditions on the comfort of the vehicle, as the basis for changing the air spring stiffness in accordance with adjusting the pressure of it according to the type of road profile quality.

Evolutionary mechanism of safety performance for spur gear pair based on meshing safety domain

Drive-side teeth engaging, tooth disengagement and back-side teeth contacting are three meshing states of the spur gear pair. The influence of different meshing states on system safety is different. The safety performances of the system are classified into three safety levels, i.e., safe, quasi-safe and unsafe according to the influence of the meshing state. Three safety domains corresponding to three safety levels are established, respectively. The evolutionary mechanism of the system meshing safety performance is researched in the established safety domain. Multi-initial values bifurcation diagrams and the corresponding top Lyapunov exponents (TLE) of the spur gear pair considered the multiple meshing states are numerically calculated by the 4-order Runge–Kutta method in the C program. The bifurcation & safety dendrograms are constructed to analyze the transition process of the safety performance and the transition mechanism from safe to unsafe. The global integrity measure and integrity factor of the co-existing attraction domains in the safety basins are calculated to identify properly the erosion due to the meshing frequency and damping. It is determined that the safety performance of the system is changed by two patterns. One is the combined action of the bifurcation and varying with the relative displacement amplitude caused by the motion sensitive parameters. The other is one-to-two bifurcation caused by the sensitive parameters of the meshing state. The results provide a theoretical basis for the prediction and control of the meshing state and unsafe performance of the gear pair.

Coupling effects of particle shape and cyclic shear history on shear properties of coarse-grained soil–geogrid interface

Accurate measurement of particle shape is necessary to properly investigate the cyclic shear behavior of a soil–geogrid interface. In this study, the particle shapes of crushed limestone, quartz sand, round gravel and spherical granular media were described and quantified in terms of particle regularity. Cyclic direct shear tests were then performed with particles of various shapes for different relative densities and shear displacement amplitudes. Monotonic direct shear tests and post cyclic direct shear tests were performed to compare the relationship between particle regularity and interface friction angle. The test results showed that the interface underwent cyclic shear hardening for relative densities between 0.453 and 0.672. The area of the hysteresis loop, cyclic peak shear strength and maximum vertical displacement increased with increasing shear displacement amplitude, and decreased with increasing particle regularity. In monotonic and post cyclic direct tests, the friction angle decreased linearly as particle regularity increased. Comparing to the monotonic direct shear tests, the slope and intercept of the regression lines increased in the post cyclic direct shear tests after undergoing cyclic shearing. This study shows that it is important to analyze the interface shear behavior in the monotonic, cyclic and post cyclic direct shear tests using parameterized particle shapes.

Research on Squeak Noise from Polypropylene in Frictional Contact with Leather for Automotive Interior Assembly

To explore the mechanisms of squeak generation in automotive interiors, stick–slip experiments on polypropylene versus leather were conducted under various conditions. The friction properties were researched with changes in normal force, velocity, and temperature and static friction coefficients were generally lower at low temperature, higher at room temperature, and intermediate at high temperature and generally increased with an increase in velocity from 1 to 4 mm/s except in some individual cases. The dynamic friction coefficients as a whole presented a significant decrease but displayed similar trends in comparison with the static values. A simplified spring–mass model was built to illustrate the stick–slip physics of movement of polypropylene versus leather. The concomitant squeak characteristics are discussed. Risk priority indexes were acquired to evaluate the level of squeak noise. The inverse of the impulse rate obtained from stick–slip tests was perceived as the crucial threshold for squeak evaluation. A finite element simulation was developed to study the squeak problems of a trimmed vehicle door, and some risk locations were identified by comparing the maximal peak-to-peak amplitude of relative displacement in the main direction with the inverse of the tested impulse rate. The weak area where the squeak originated can be located from the modal contribution analysis for enhancement in the design phase.

Dual-Connected Synchronized Switch Damping for Vibration Control of Bladed Disks in Aero-Engines

An enhanced SSDI (synchronized switch damping on inductor) approach is proposed to suppress the vibration of bladed disks in aero-engines. Different from the authors’ former work (MSSP, 2017; JIMSS, 2018) where a local SSDI circuit is shunted to the piezoelectric materials at each blade sector, in this work two blade sectors are interconnected by a shared SSDI circuit. In this way, the switching action of SSDI is triggered by the relative displacement between two blade sectors. The feasibility of the dual-connected SSDI is numerically examined by a 2-DOF (degree-of-freedom) mechanical system, and further experimentally validated on a single-beam and a double-beam system. Results show that the damping performance increases with the amplitude of relative displacement. This feature is especially favorable for the application of blisks where the blade normally vibrates in different amplitudes and phases. Eventually, we conduct numerical simulation on the forced response of mistuned bladed disk undergoing travelling wave excitation. Results show that the dual-connected configuration can reduce at least half the number of switching shunts while maintain nearly the same performance as the conventional (local) SSDI.

Study on tribo-chemical and fatigue behavior of 316L austenitic stainless steel in torsional fretting fatigue

Fretting fatigue is a complex tribological phenomenon that can cause premature failure of connected components. Combining with the effects of tribological and fatigue, the components have premature fracture, which ultimately leads to disastrous consequences. In this work, the fretting fatigue tests of 316L austenitic stainless steel have been carried out with same normal load and varied torsional torques. The results indicate that the fretting fatigue life significantly depends on the torque amplitude, wear degree of the fretting damage zone, hysteresis loops and energy dissipation. A physical model for fretting crack initiation and propagation is created to explain the failure process of torsional fretting fatigue. The results from X-ray photoelectron spectroscopy analysis show that the extent of oxidation in the fretting damage zone is affected by the amplitude of relative displacement. The tribo-chemical reaction in the slip regime is more activated than that in partial slip regime. It can lead to more severe wear in the slip regime. The wear debris of the fretting damage zone is composed of metallic Fe, Fe2+ and Fe3+.

Vibration fatigue study of the helical spring in the base-excited inerter-based isolation system

The aim of this study is to analytically and numerically model the vibration-induced helical spring fatigue in a generalized vibration isolation system. The system consists of a receiving body and a dynamically active base coupled through a passive isolator. The isolator consists of a coupling helical spring and an inerter. System inherent damping is considered through modal damping. Vibration isolation system is analysed parametrically by varying its corresponding dimensionless coefficients. The coupling helical spring fatigue life extension is used as the isolation quality criterion. Since isolator spring stress and related fatigue life directly correspond to relative displacement between spring terminals, the effect of inerter on relative displacement amplitudes is determined. Novel helical spring stress and deflection correction factors are proposed based on the theory of elasticity and finite element analysis results. The proposed helical spring correction factors are more accurate compared to correction factors available in the current literature, especially when considering very large pitch angles. Fatigue life improvement of considered helical spring is achieved due to introduction of inerter in the isolator system, which is especially evident in the resonant working conditions.

Micro-scale frictional behavior of a bearing steel (JIS SUJ2) in cyclic sliding motion

Application of fracture mechanics has recently been emphasized to establish the mechanics-based evaluation of the rolling contact fatigue strength for designing mechanical elements such as bearing, rail/wheel, gear, etc. Flaking that is a typical rolling contact failure mode is intimately related to the shear-mode (modes II and III) fatigue crack growth, which is significantly affected by the interaction of opposing crack faces. Understanding the tribological properties on the crack faces being in the reciprocating sliding contact is therefore essential for the material design as well as the mechanical design of many components associated with rolling contact fatigue. The present study carried out a ring-on-ring test by making use of a combined axial-torsional fatigue testing machine to investigate the micro-scale frictional phenomena under the non-lubricated condition. The material investigated was a heat-treated high-carbon-chromium bearing steel (JIS SUJ2) with a Vickers hardness of 753. The tests were conducted up to 104 cycles under the various conditions of mean contact pressures of 10-100 MPa, relative displacement amplitudes of about 10-100 μm, sinusoidal frequencies of 0.1-10Hz, and initial surface roughness values, Ra, of 0.2-1.7. The time variations of the tangential force, contact load and the relative displacement between contact surfaces were periodically monitored at a predetermined number of cycles during testing.

The effect of a weak nonlinearity on the lowest cut-off frequencies of a cylindrical shell

The plane strain problem for a thin circular cylindrical shell is considered within the framework of the Sanders–Koiter theory. The relative shell thickness and displacement amplitude are chosen to be of the same asymptotic order. The leading nonlinear correction to the lowest cut-off frequencies is derived using the method of multiple scales. In contrast to the traditional two-mode Galerkin expansions assuming inextensibility of the shell transverse cross section, the developed fourth-order asymptotic scheme operates with five angular modes. The obtained results reveal asymptotic inconsistency of previous approximate solutions to the problem.

Characterization of damage and triboparticles resulting from fretting of Incoloy 800 steam generator tubes against different materials

Fretting experiments of Incoloy 800 steam generator tubes against AISI 304, AISI 1060 and Cu (99.9%) cylindrical pads were carried out to evaluate the influence of pad composition on wear damage and on the nature of the triboparticles originated in the process. Tests were performed up to 106 cycles in air under an imposed relative displacement amplitude of 75 ± 5µm and a normal contact load of 40 ± 5N. Surface damage was characterized using light microscopy, scanning electron microscopy and optical profilometry. The triboparticles detached during the tests were analyzed by transmission electron microscopy and energy dispersive X-ray spectroscopy. Debris particles were agglomerates of nano-crystalline oxide grains sized between 5nm and 20nm of the following phases: NiO, (Fe,Cr)2O3 and (Ni,Fe)(Fe,Cr)2O4 in the case of the AISI 304 pad, (Cu,Ni)(Fe, Cr)2O for the Cu pad and (Fe,Cr)2O3 in the case of the AISI 1060 pad. A preponderance of adhesive wear was found for the Cu and AISI 1060 pads while abrasive wear was predominant in the case of the AISI 304 pad. Tube-pad differential hardness was found to have a minor influence on wear rate compared to the acting main wear mechanism.

A Comprehensive Empirical Correlation for Finned Heat Exchangers with Parallel Plates Working in Oscillating Flow

The oscillating-flow heat transfer performance in finned heat exchangers is one of the main factors affecting the working efficiency of regenerative heat engines and refrigerators. In addition to the working parameters, the geometrical parameters of finned heat exchangers are also major influencing factors. In the present study, the ratio of the heat exchanger length and hydraulic diameter is applied as an independent similarity criterion. An experimental study has been carried out with six different geometrical dimensions of finned heat exchangers with parallel plates, in order to analyze the impacts of fin length, plate spacing, and corresponding relative fluid displacement amplitude, under various working conditions. Based on 298 tested points, a comprehensive empirical correlation for the finned heat exchangers with parallel plates working in oscillating flow has been proposed, providing a relatively accurate prediction, with 98.6% of data in the ±20% deviation and 83.9% of data in the ±10% deviation, within the range discussed.