Vibration Cycle Research Articles

Sound scattering in dense granular media

The sound propagation in a dense granular medium is basically characterized by the ratio of wavelength to the grain size. Two types of wave transport are distinguished: one corresponds to coherent waves in the long wavelength limit, the other to short-wavelength scattered waves by the inhomogeneous contact force networks. These multiply scattered elastic waves are shown to exhibit a diffusive characteristics of transport over long distances of propagation. Determination of the transport mean free path l* and the inelastic absorption (Q −1) allows the inference of the structural properties of the material such as the heterogeneity and internal dissipation. The relevance of our experiments for seismological applications is discussed. Moreover, we apply the correlation technique of the configuration-specific sound scattering to monitoring the dynamic behaviour of the granular medium (irreversible rearrangements) under strong vibration, shearing and thermal cycling, respectively.

Environmentally Robust MEMS Vibratory Gyroscopes for Automotive Applications

Automotive applications are known to impose quite harsh environmental conditions such as vibration, shock, temperature, and thermal cycling on inertial sensors. Micromachined gyroscopes are known to be especially challenging to develop and commercialize due to high sensitivity of their dynamic response to fabrication and environmental variations. Meeting performance specifications in the demanding automotive environment with low-cost and high-yield devices requires a very robust microelectromechanical systems (MEMS) sensing element. This paper reviews the design trend in structural implementations that provides inherent robustness against structural and environmental parameter variations at the sensing element level. The fundamental approach is based on obtaining a gain and phase stable region in the frequency response of the sense-mode dynamical system in order to achieve overall system robustness. Operating in the stable sense frequency region provides improved bias stability, temperature stability, and immunity to environmental and fabrication variations.

A MEMS-based silicon micropump with intersecting channels and integrated hotwires

This paper presents the development of a gas-jet micropump with different cross-junctions and integrated hotwire. The device is actuated by a piezoelectric lead zirconate titanate (PZT) diaphragm at its resonant frequency. The design focuses on a cross-junction formed by the intersection of the channels and neck of the pump chamber, which allows differences in fluidic resistance and fluidic momentum during each PZT diaphragm vibration cycle and thus enables rectification of the gas without valves. Three different designs were investigated by utilizing the ANSYS-FLUENT software. Simulations and experimental data revealed that the step nozzle structure with anti-choking space has much more advantages than the others. The device has been fabricated by the standard MEMS process, and the tiny hotwire has been realized together with the fluidic network. Experiments have been carried out. At a driven frequency of 7.9 kHz, a flow rate of 5.2 ml min−1 was obtained with an applied sinusoidal voltage of 50 Vp-p. The output voltage on the hotwire was measured to be 130 mV at a constant current of I = 0.1 mA.

Reflow profile optimization of μBGA solder joints considering reflow temperature and time coupling

PurposeThe purpose of this paper is to present a novel reflow profile optimization method using mechanical reliability estimation of micro‐ball grid array (μBGA) solder joints, based on the heating factor, Qη is introduced, where the coupling effect of reflow temperature and time on the mechanical reliability of μBGA joints is considered.Design/methodology/approachThe method presented is actualized through vibration fatigue tests. First, a two‐parameter Weibull distribution is used to model the collected data of vibration fatigue lifetime for different Qη. After that, two explicit functions are deduced in a unified mathematic expression form, which give an intuitionistic description of the mean time to failure and reliability of solder joints against induced variable Qη, thus revealing definitely the effect of Qη on the mechanical fatigue lifetime of solder joints suffering from cyclic vibration loading. Finally, for a specified reliability goal, how to choose proper Qη values, based an improved Golden Section Search arithmetic, is discussed.FindingsNumerical analysis and calculation are performed. The results show that the solder joints made at Qη near 510 have higher mechanical reliability, and those reflowed farther away this optimal value have less reliability.Originality/valueThis paper presents a useful and applicable solution to achieve reflow profile optimization and process control for a quantitative mechanical reliability estimation of μBGA solder joints.

Estimating Damping Parameters in Multi-Degree-of-Freedom Vibration Systems by Balancing Energy

A method of estimating damping parameters for multi-degree-of-freedom vibration systems is outlined, involving a balance of dissipated and supplied energies over a cycle of periodic vibration. The power is formulated as the inner product between the velocity and force terms and integrated over a cycle. Conservative terms (mass and stiffness) drop out of the formulation. The displacement response and the input are measured, and the damping coefficients are estimated without knowledge of the mass and stiffness, which can be nonlinear, as illustrated in one example. The identification equations are also obtained with a modal reduction based on proper orthogonal decomposition. The method can be applied with a harmonic motion assumption or by simple numerical integration. The method is illustrated with linear and quadratic damping, in simulations of a four degree-of-freedom system, and in a string with and without noise.

A Rapid Life-Prediction Approach for PBGA Solder Joints Under Combined Thermal Cycling and Vibration Loading Conditions

While some electronic products are routinely subjected to concurrent vibration and temperature cycle loading, the ability to accurately model and estimate life expectancy of hardware under such conditions still presents a unique challenge. For combined vibration and temperature cycling, one of the most likely causes of failure is the fatigue of solder interconnects. This paper presents an approach to predict solder joint life under combined thermal cycling and vibration loading conditions, by taking into account temperature effects and loading interactions. Combined loading experiment on a test vehicle populated with PBGA packages was used to demonstrate this approach.

A cross-junction channel valveless-micropump with PZT actuation

A gas-jet micro pump with novel cross-junction channel has been designed and fabricated using a Si micromachining process. The valveless micro pump is composed of a piezoelectric lead zirconate titanate (PZT) diaphragm actuator and fluidic network. The design of the valveless pump focuses on a cross-junction formed by the neck of the pump chamber and one outlet and two opposite inlet channels. The structure of cross-junction allows differences in fluidic resistance and fluidic momentum inside the channels during each PZT diaphragm vibration cycle, which leads to the gas flow being rectified without valves. The flow channels were easily fabricated by using silicon etching process. To investigate the effects of the structure of the cross-junction on the gas flow rate, two types of pump with different cross-junction were studied. The design and simulation were done using ANSYS-Fluent software. The simulations and experimental data revealed that the step-nozzle structure is much more advantageous than the planar structure. A flow rate of 5.2 ml/min was obtained for the pump with step structure when the pump was driven at its resonant frequency of 7.9 kHz by a sinusoidal voltage of 50 Vp–p.

Three-dimensional simulations of a vertically vibrated granular bed including interstitial air

We present a numerical study of the effect of interstitial air on a vertically vibrated granular bed within one period of oscillation. We use a three-dimensional molecular-dynamics simulation including air phenomenologically. The simulations are validated with experiments made with spherical glass beads in a rectangular container. After validation, results are reported for a granular column of 9000 grains and approximately 50 layers deep (at rest), agitated with a sinusoidal excitation with maximal acceleration 4.7g at 11.7 Hz. We report the evolution of density, granular temperature, and coordination number within a vibration cycle, and the effect of interstitial air on those parameters. In three-dimensional computer simulations we found that the presence of interstitial air can promote the collective motion of the granular material as a whole.

A study on tooth mobility following periodontal surgery

The purpose of this study was to evaluate the quantitative changes in tooth mobility before and after periodontal surgery using a tooth mobility tester. The tester was so designed as to be able to measure the cycle of sympathetic vibrations produced when a tooth was tapped with a impact hammer. Initially the degrees of tooth mobility, which were clinically classified from 0 to 3, were observed and the mode of mobility was assessed by the tester. Then, we examined the changes of tooth mobility after flap surgery. The following is a summary of findings.

Development of a noncontact and long‐term respiration monitoring system using microwave radar for hibernating black bear

The aim of this study is to develop a prototype system for noncontact, noninvasive and unconstrained vital sign monitoring using microwave radar and to use the system to measure the respiratory rate of a Japanese black bear (Ursus thibetanus japonicus) during hibernation for ensuring the bear's safety. Ueno Zoological Gardens in Tokyo planned to help the Japanese black bear (female, approximately 2 years of age) going into hibernation. The prototype system has a microwave Doppler radar antenna (10-GHz frequency, approximately 7 mW output power) for measuring motion of the body surface caused by respiratory activity without making contact with the body. Monitoring using this system was conducted from December 2006 to April 2007. As a result, from December 18, 2006, to March 17, 2007, similar behaviors reported by earlier studies were observed, such as sleeping with curled up posture and not eating, urinating or defecating. During this hibernation period and also around the time of hibernation, the prototype system continuously measured cyclic oscillations. The presence of cyclic vibrations at 8-sec intervals (about 7 bpm) was confirmed by the system before she entered hibernation on December 3, 2006. The respiratory rate gradually decreased, and during the hibernation period the respiratory rate was extremely low at approximately 2 bpm with almost no change. The results show that motion on the body surface caused by respiratory activity can be measured without touching the animal's body. Thus, the microwave radar employed here can be utilized as an aid in observing vital signs of animals.

A thermal-energy method for calculating thermoelastic damping in micromechanical resonators

In this paper, a thermal-energy method is presented for calculating thermoelastic damping in micromechanical resonators. In this method, thermoelastic damping is interpreted as the generation of thermal energy per cycle of vibration and consequently is expressed in terms of entropy—a thermodynamic parameter measuring the irreversibility in heat conduction. As compared with a commonly used complex-frequency method, this thermal-energy method does not involve complex values and thus can be implemented in ANSYS/Multiphysics, a finite element modeling software, with fast speed. Based on the governing equations of linear thermoelasticity, the mathematical expressions are first derived for thermoelastic damping in micromechanical resonators made from isotropic and anisotropic materials, respectively. Through two sequential numerical simulations: uncoupled elastic modal simulation and transient heat conduction, the numerical values for these expressions are then calculated in ANSYS/Multiphysics for micromechanical resonators taking different structural geometries. This method is verified using the well-known theoretical solution to thermoelastic damping in a beam resonator and experimental data. As a result, the developed thermal-energy method can calculate thermoelastic damping in micromechanical resonators with any complex structural geometry and made from isotropic and/or anisotropic materials.

Design of Experiments for Board-Level Solder Joint Reliability of PBGA Package Under Various Manufacturing and Multiple Environmental Loading Conditions

A design of experiments was conducted to determine the reliability of plastic ball grid array packages under various manufacturing and multiple environmental loading conditions. Parameters included conformal coating methods, underfill, solder mask defined, and non-solder mask defined pads. Board-level temperature cycling, vibration, and combined temperature cycling and vibration testing were performed to quantify the reliability and identify preferred design parameters. Through the main effects and interaction analysis, test results show underfill is the key parameter related to the solder joint reliability improvement. Conformal coat method and printed circuit board pad design are not main effects on solder joint reliability. No interactive relationship exists among these three factors under temperature cycling loading, but some interactive relationship between printed circuit board pad type and the conformal coating method exists under vibration and combined loading conditions.

Glottal inverse filtering with the closed-phase covariance analysis utilizing mathematical constraints in modelling of the vocal tract

Closed-phase (CP) covariance analysis is a glottal inverse filtering method based on the estimation of the vocal tract with linear prediction (LP) during the closed phase of the vocal fold vibration cycle. Since the closed phase is typically short, the analysis is vulnerable with respect to the extraction of the covariance frame position. The present study proposes a modified CP algorithm based on imposing certain predefined values on the gains of the vocal tract inverse filter at angular frequencies of 0 and π in optimizing filter coefficients. With these constraints, vocal tract models are less prone to show false low-frequency roots. Experiments show that the algorithm improves the robustness of the CP analysis on the covariance frame position.

MR elastography of the human heart: Noninvasive assessment of myocardial elasticity changes by shear wave amplitude variations

Many cardiovascular diseases and disorders are associated with hemodynamic dysfunction. The heart's ability to contract and pump blood through the vascular system primarily depends on the elasticity of the myocardium. This article introduces a magnetic resonance elastography (MRE) technique that allows noninvasive and time-resolved measurement of changes in myocardial elasticity over the cardiac cycle. To this end, low-frequency shear vibrations of 24.3 Hz were induced in the human heart via the anterior chest wall. An electrocardiograph (ECG)-triggered, steady-state MRE sequence was used to capture shear oscillations with a frame rate of eight images per vibration cycle. The time evolution of 2D-shear wave fields was observed in two imaging planes through the short axis of the heart in six healthy volunteers. Correlation analysis revealed that wave amplitudes were modulated in synchrony to the heartbeat with up to 2.45 +/- 0.18 higher amplitudes during diastole than during systole (interindividual mean +/- SD). The reduction of wave amplitudes started at 75 +/- 9 ms prior to changes in left ventricular diameter occurring at the beginning of systole. Analysis of this wave amplitude alteration using a linear elastic constitutive model revealed a maximum change in the myocardial wall stiffness of a factor of 37.7 +/- 10.6 during the cardiac cycle.

Damping associated with porosity in alumina

Materials subjected to alternating stresses exhibit temperature fluctuations indicative of damping. Temperature effects give rise to entropy production. An analysis is made to obtain the entropy produced for a vibration cycle. This corresponds to the reciprocity of temperature rise and strain yielded that alter the material damping factor as a function of shape and magnitude of material porosity. Prototype bars of pure aluminum oxide with different porosity are considered. They consist of uniformly distributed cavities and are subjected to alternating axial stress. Dynamic characteristics of the porous medium are determined to evaluate the damping factor of the tested bars. The experimental data correlate well with the analytical results. The damping factor measured and calculated in this work, can be used as an indicator of structural integrity.

Effect of dynamic response and displacement/stress amplitude on ultrasonic vibration cutting

In this report, the behavior of the cutting force measured through the dynamic response of tool–work piece system in ultrasonic vibration cutting was discussed first. Measured cutting force mainly depends on the ratio of net cutting time to a vibration cycle in vibration cutting ( t c / T) because the tool–work piece system has much lower natural frequency comparing with the ultrasonic vibration cycle. It was confirmed by the newly proposed cutting experiment using resonated-horn-type work piece, displacement amplitude and stress amplitude at the cutting point vary continuously in this device. It was shown that the measured cutting force varies corresponding to the displacement amplitude. It was also indicated that the measured cutting force does not decrease when the cutting point is on the node of the resonated-horn-type work piece, where the stress amplitude is the maximum but there is no displacement amplitude. It means that there should be the relative intermittent displacement between the tool and the chip in order to decrease the measured cutting force. In addition, the deformation resistance of the work piece material itself does not decrease with ultrasonic vibration of the stress field. Secondly, the significance of the elastic deformation of the tool–work piece system of several microns in ultrasonic intermittent cutting was also indicated from an analytical and experimental point of view. The effect of the elastic behavior on the cutting force becomes relatively large as t c / T becomes small. The above-mentioned characteristics will be helpful to utilize the ultrasonic vibration cutting system more efficiently.

Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades

The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig–Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical degrees of freedom. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multiharmonic hybrid frequency∕time-domain technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack, shifts in resonant frequencies, and the existence of multiple solutions. For the cases considered, it is found that the nonlinear vibration response exhibits the jump phenomenon only when rotation is included in the model.

Fabrication and Basic Characterization of a Piezoelectric Valveless Micro Jet Pump

A piezoelectric-driven valveless micro jet pump with a novel channel structure has been designed and fabricated. The simple structure micro jet pump consists of a lead zirconate titanate (PZT) diaphragm and flow channels. The design of the flow channels focuses on a cross junction formed by the neck of the pump chamber and one outlet and two opposite inlet channels. This structure allows differences in fluidic resistance and fluidic momentum inside the channels during each pump vibration cycle. To confirm the pump operation, a prototype was fabricated using polymethyl methacrylate as a base plate and a conventional machining technique. Two types of pump with nozzle depths of 0.5 and 0.2 mm were prepared, and the depth effect on the flow rate was investigated. The pump chamber has an 11.8 mm diameter, a 0.5 mm depth, and a volume of 0.055 cm3. The maximum flow rate of 17 ml/min at 400 Pa was obtained when the pump was driven at a resonant frequency of approximately 6 kHz by a sinusoidal voltage of 30 Vp–p.

Modeling of Combined Temperature Cycling and Vibration Loading on PBGA Solder Joints Using an Incremental Damage Superposition Approach

Concurrent vibration and temperature cycle environments are commonly encountered in the service life of many electronic products, particularly those used in automotive, avionic, and military applications. However, the ability to predict life expectancy under these types of environments remains a technical challenge. In this paper, a traditional linear damage superposition modeling approach and a damage superposition approach that considers the temperature imposed load state on vibration damage are compared with experimental test results for plastic ball grid array (PBGA) assemblies subjected to temperature cycling, vibration loading, and combined temperature cycling and vibration loading conditions. The results showed much earlier PBGA solder-joint failure under combined loading than with either separate temperature cycling or room temperature vibration loading. Traditional linear superposition was found to over-predict the solder-joint fatigue life, since it neglects the interaction effects of two different loadings. The damage superposition approach that considers the temperature imposed load state on vibration damage is found to be more representative of test data.

FE MODELLING OF A UNILATERAL FIXATOR FOR BONE RECONSTRUCTION: IMPORTANCE OF CONTACT SETTINGS

Ultrasonically assisted turning is a promising machining technology, where high frequency vibration (f≈20 kHz) with an amplitude a≈10 μm is superimposed on the movement of the cutting tool. Ultrasonic turning yields a noticeable decrease in cutting forces, heat and noise radiation, as well as a superior surface finish, comparing to the conventional machining technology. The present study utilizes both experimental techniques and numerical (finite element) simulations to analyze the microstructural processes at the cutting tool–chip interface. High-speed filming of the chip–tool interaction zone during cutting and microstructural and nanoindentation analyses of the machined surfaces are used to compare process zones and deformation processes for both conventional and ultrasonically assisted technologies. The suggested finite-element (FE) model, which utilizes MSC Marc/Mentat general FE code, provides a transient analysis for an elasto-plastic material, accounting for the frictionless contact interaction between a cutter and workpiece as well as material separation in front of the cutting edge. A detailed analysis of cutting for a single cycle of ultrasonic vibration is carried out for isothermal conditions. Differences between conventional and ultrasonic turning in stress distribution in the process zone and contact conditions at the tool/chip interface are investigated.