Harmonic Finite Element Analysis Research Articles

Finite element modelling of sound transmission in the Weberian apparatus of zebrafish (Danio rerio).

Zebrafish, an essential vertebrate model, has greatly expanded our understanding of hearing. However, one area that remains unexplored is the biomechanics of the Weberian apparatus, crucial for sound conduction and perception. Using micro-computed tomography (μCT) bioimaging, we created three-dimensional finite element models of the zebrafish Weberian ossicles. These models ranged from the exact size to scaled isometric versions with constrained geometry (1 to 10 mm in ossicular chain length). Harmonic finite element analysis of all 11 models revealed that the resonance frequency of the zebrafish's Weberian ossicular chain is approximately 900 Hz, matching their optimal hearing range. Interestingly, resonance frequency negatively correlated with size, while the ratio of peak displacement and difference of resonance frequency between tripus and scaphium remained constant. This suggests the transmission efficiency of the ossicular chain and the homogeneity of resonance frequency at both ends of the chain are not size-dependent. We conclude that the Weberian apparatus's resonance frequency can explain zebrafish's best hearing frequency, and their biomechanical characteristics are not influenced by isometric ontogeny. As the first biomechanical modelling of atympanic ear and among the few non-human ear modelling, this study provides a methodological framework for further investigations into hearing mechanisms and the hearing evolution of vertebrates.

Piezo-actuated device for a bio-structural monitoring application through vibration-based condition and electromechanical impedance measurements

This study presents a numerical and experimental development of a piezo-actuated device used for monitoring the stiffness variations of its support through electromechanical impedance measurements. The piezo-device and its components define a clamped beam system activated dynamically by two piezo-transducers that transmit vibrations to the support (monitoring substrate). An harmonic finite element analysis was carried out to understand the effects of the substrate properties on the dynamics of the piezo-device. Experimental tests corroborated the simulations with the correspondence of modal shapes and frequency response functions (FRFs) when the substrate varies its stiffness. A biomedical application was conducted in a bone specimen with three embedded teeth to monitor the stiffness variations induced by drillings in the bone. Results showed that the bone stiffness monitoring could be possible through the teeth due to that the drillings effect were quantified by electrical impedance signals.

Finite element analysis of acoustic streaming in a Kundt tube with bended wall

Acoustic streaming near artificially prescribed ridges is simulated and discussed to understand the mechanism of Kundt tube powder-ridge generation. A viscoacoustic harmonic finite element analysis (FEA) and a static-fluid FEA are coupled using an acoustic streaming driving force to derive acoustic streaming. The half-wavelength mode is excited in an acoustic tube where the calculation mesh is distorted to form a sinusoidal bottom stick wall. Consequently, intense Schlichting streaming is obtained when the height and interval of the ridge agree with those in the literature. The mechanism underlying the regular ridge interval is related to the conversion of mainstream particle velocity into ridge-localized velocity, which produces an inlet or outlet vertical streaming in ridge valleys.

Toward identifying crack-length-related resonances in acoustic emission waveforms for structural health monitoring applications

In this study, we focus on analyzing the acoustic emission waveforms of the fatigue crack growth despite the conventional statistics-based analysis of acoustic emission. The acoustic emission monitoring technique is a well-known approach in the non-destructive evaluation/structural health monitoring research field. The growth of the fatigue crack causes the acoustic emission in the material that propagates in the structure. The acoustic emission happens not only from the crack growth but also from the interaction of the crack tips during the fatigue loading in the structure. The acoustic emission waveforms are generated from the acoustic emission events; they propagate and create local vibration modes along the crack faces (crack resonance). In-situ fatigue and acoustic emission experiments were conducted to monitor the acoustic emission waveforms from the fatigue cracks. Several test specimens were used in the fatigue experiments, and corresponding acoustic emission waveforms were captured. The acoustic emission waveforms were analyzed and distinguished into three types based on the similar nature in both time and frequency domains. Three-dimensional harmonic finite element analyses were performed to identify the local vibration modes. The local crack resonance phenomenon has been observed from the finite element simulation that could potentially give the geometric information of the crack. The laser Doppler vibrometry experiment was performed to identify the crack resonance phenomenon, and the experimental results were used to verify the simulated results.

Magnetic resonance elastography of the brain: An in silico study to determine the influence of cranial anatomy

Magnetic resonance elastography (MRE) of the brain has demonstrated potential as a biomarker of neurodegenerative disease such as dementia but requires further evaluation. Cranial anatomical features such as the falx cerebri and tentorium cerebelli membranes may influence MRE measurements through wave reflection and interference and tissue heterogeneity at their boundaries. We sought to determine the influence of these effects via simulation. MRE-associated mechanical stimulation of the brain was simulated using steady state harmonic finite element analysis. Simulations of geometrical models and anthropomorphic brain models derived from anatomical MRI data of healthy individuals were compared. Constitutive parameters were taken from MRE measurements for healthy brain. Viscoelastic moduli were reconstructed from the simulated displacement fields and compared with ground truth. Interference patterns from reflections and heterogeneity resulted in artifacts in the reconstructions of viscoelastic moduli. Artifacts typically occurred in the vicinity of boundaries between different tissues within the cranium, with a magnitude of 10%-20%. Given that MRE studies for neurodegenerative disease have reported only marginal variations in brain elasticity between controls and patients (e.g., 7% for Alzheimer's disease), the predicted errors are a potential confound to the development of MRE as a biomarker of dementia and other neurodegenerative diseases. Magn Reson Med 76:645-662, 2016. © 2015 Wiley Periodicals, Inc.

Effects of flexural and extensional excitation modes on the transmission spectrum of phononic crystals operating at gigahertz frequencies

Phononic crystals (PnCs) are a class of materials that are capable of manipulating elastodynamic waves. Much of the research on PnCs, both theoretical and experimental, focus on studying the transmission spectrum of PnCs in an effort to characterize and engineer their phononic band gaps. Although most studies have shown acceptable agreement between the theoretical and experimental bandgaps, perfect matches are elusive. A framework is presented wherein two and three dimensional harmonic finite element analyses are utilized to study their mechanical behavior for the purpose of more accurately predicting the spectral properties of PnCs. Discussions on a Harmonic Finite Elements Analysis formulation of a perfectly matched layer absorbing boundary and how reflections from absorbing boundaries can be inferred via standing wave ratios are provided. Comparisons between 2D and 3D analyses are presented that show the less computationally intensive 2D models are equally accurate under certain conditions. Finally, it is shown that a surface excitation boundary condition in a 3D model can significantly improve understanding of the experimental results for PnCs excited by surface mounted excitation sources.

Finite Element Analysis of Mode Stirrer Impact on Electric Field Uniformity in a Microwave Applicator

Nonuniformity of the electromagnetic field in microwave ovens is assumed to be one of the reasons for nonuniform drying of materials. There are several approaches that are partly able to eliminate such a negative phenomenon. One of them is a placement of mode stirrers in the microwave (MW) applicator. Therefore, the goal of this study was to numerically investigate the influence of a proposed fan-like mode stirrer on the uniformity of the electric field (EF) in an experimental MW device. This was done with the help of 3D harmonic high-frequency finite element (FE) simulation of the EF distribution in the MW applicator. Within the work, two FE models of the MW device were built, analyzed, and compared to each other. The first FE model does not incorporate the mode stirrers. The other one has two mode stirrers, each placed in front of two waveguide ports. In both models, the EF uniformity is studied in 10 height levels and in two mutually perpendicular directions. Change of the EF uniformity was analyzed in terms of coefficients of variation (CoVs) of the electric vector sum across the applicator. Results of simulations show that the mode stirrers decrease CoVs (EF uniformity) in 8 of 10 studied height levels ranging from 2 to 20% and increase them in two topmost levels ranging from 3 to 7.3%. With respect to the fact that the simulations did not consider the mode stirrers’ rotation, the calculated effect might be lower than the actual effect. However, harmonic FE analysis was shown to be an efficient way for investigating, to a degree, the mode stirrer influence on the EF uniformity in a microwave applicator.

Absorbing boundary conditions for solid waveguides

Abstract We present two simple and effective schemes to formulate absorbing boundary conditions for time harmonic finite element analyses of waveguide structures. An impedance matching condition, applicable to single mode waveguides, is derived as well as an enhanced method for multi-modal wave propagation, making use of guided wave mode orthogonality. Both types are implemented in models generated with standard finite element software. Two examples of ultrasonic transducers attached to cylindrical waveguides are presented.

Analysis of Piezoelectric Energy Harvesting Systems with Non-linear Circuits Using the Harmonic Balance Method

There is substantial promise in the use of piezoelectric energy harvesting systems to power electronics and devices through the conversion of ambient vibrations into electrical energy. Accurately predicting the energy harvesting capability in these systems is of paramount importance as the harvesting structure and the associated circuit must be ‘tuned’ in concert to the signature of the ambient vibrations. Here, we develop a numerical simulation methodology for piezoelectric harvesting systems that allows for high-fidelity finite element models of the harvester electromechanics as well as realistic non-linear circuits models. Our approach synthesizes conventional harmonic finite element analysis and a harmonic balance approach that accounts efficiently for the non-linear circuit behavior, bypassing the need for computationally expensive time marching schemes. The proposed methodology solves, via an iterative residual reduction scheme, for the coupled electrical output and structural dynamics of the piezoelectric harvesting structure. The proposed method is well suited for integration into model-predictive design methods. By numerical examples we illustrate the capability of the proposed approach to predict previously unreported coupling phenomena between the non-linear circuit response and piezoelectric structural behavior. The increased accuracy in the circuit model and flexibility of this method over current models outweighs the increased numerical costs.

Finite Element Analysis for Stress and Magnetic Field of a 40 kA Protection Inductor

The protection inductor serves for limiting the peak current in order to protect the thyristor switch of the pulsed magnetic field facility in case of a short circuit. Because of the high current and strong magnetic field, the Lorentz force in the protection inductor is large. This paper describes the calculation of the inductance and the optimization of the stresses in the protection inductor. A finite element analysis with the ANSYS software is used to calculate the magnetic field and stresses in the protection inductor. A three-dimensional static finite element analysis model of the inductor has been built for calculating the stresses in the copper coils and stainless steel rings as well as the static inductance. Furthermore, a harmonic finite element analysis model has been built to analyse effects such as the influence of eddy currents in the copper wires and induced current in the stainless steel rings on stress and inductance. Eddy currents cause an uneven distribution of stresses; induced current can decrease the stresses in the copper coils but increase those in the stainless steel rings. Both effects reduce the inductance. The typical maximum stresses in our design are 70 MPa in the copper coils and 210 MPa in the stainless steel rings; these are both below the yield strength of these materials. The inductance is 1.05 mH at the frequency of 50 Hz. The protection inductor has been manufactured according to the design and the performance testing has been successfully completed.

Vibration reliability test and finite element analysis for flip chip solder joints

Vibration fatigue test and analysis methodology for flip chip solder joint fatigue life assessment have been developed by performing vibration tests with constant G-level and varying G-level input excitation. The linear cumulative damage analysis method (Miner’s rule) predicts non-conservative result for vibration fatigue life of flip chip solder joint. Finite element analysis (FEA) using a global-local-beam modeling method was used to calculate the natural frequency and were compared to experimental data. A quasi-static finite element analysis method was developed to investigate solder joint stress strain behavior for solder joint vibration fatigue life prediction. Harmonic finite element analysis was also carried out to predict solder joint fatigue life. Results from quasi-static analysis and harmonic analysis were compared. Based on Miner’s rule and stress amplitude results from FEA results, different assumed cumulative damage index (CDI) factors were investigated in fatigue life prediction.

Development of a suitable PML for an harmonic study of a finite 1D phononic crystal

This paper deals with the interaction of ultrasonic Lamb waves with a 1D phononic crystal. The studied structure is a finite plate with a periodic corrugated surface. Two types of forbidden bands arise in the Lamb wave dispersion curves. The first one is located at the limit of the first Brillouin zone, the second one exists at the crossing of dispersion curves of two different Lamb modes. These forbidden bands lead to conversion phenomena. In order to study accuratly the conversion phenomena in the band gaps, harmonic finite element analysis are performed. Perfect matching layers (PML) on both sides of the plate are then necessary to avoid stationnary waves. PML, adapted for Lamb modes involved at a given frequency, must be designed. By using these PML, the attenuation of Lamb waves propagating in the phononic crystal is clearly shown and is related to the existence of the forbidden band.