Stiffness Asymmetry Research Articles

Nonlinear Dynamics of Whirling Rotor with Asymmetrically Supported Snubber Ring

Rotor–stator whirling is a critical malfunction frequently encountered in rotating machinery, often resulting in severe damages. This study investigates the nonlinear dynamics of a whirling rotor interacting with a snubber ring through numerical simulations that account for the stiffness asymmetries of the snubber ring. A two-degrees-of-freedom (DOF) model is employed to analyse the contact interactions that occurred between the rotor and the snubber ring, assuming a linear elastic contact model. The analysis also incorporates the static offset between the centers of the rotor and the snubber ring. The dynamic behaviour of the whirling system is characterised by pronounced nonlinearity due to transitions between contact and non-contact states. The model is first validated against our prior theoretical and experimental studies. The nonlinear responses of the rotor are analysed to evaluate the effects of stator asymmetry through various techniques, including time-domain waveforms, frequency spectra, rotor orbits, and bifurcation diagrams. Furthermore, the influence of varying system parameters, such as rotational speed and the damping ratio, both with and without stator asymmetry, are systematically analysed. The results demonstrate that the rubbing response is highly sensitive to small variations in system parameters, with stator asymmetry significantly affecting system behaviour, even at low asymmetry levels. Direct stiffness asymmetry is shown to have a more pronounced effect than cross-coupling stiffness. The system exhibits a range of dynamics, including periodic, quasi-periodic, and chaotic responses, with regions of periodic orbits coexisting with chaotic ones. Complex phenomena such as period doubling, period halving, and jump bifurcations are identified, alongside quasi-periodic and period doubling routes to chaos. These findings contribute to a deeper understanding of the nonlinear phenomena associated with rotor–stator whirling and provide valuable insights into the unique characteristics of rubbing faults, which could facilitate fault diagnosis.

Experimental and numerical investigation on failure behaviour of aluminum-polymer friction stir composite joints

Friction stir composite joints between an aluminum alloy (AA6082-T6) and reinforced polymer (NorylTM GFN2) were studied regarding their failure characteristics. A comprehensive analysis on the mechanical behaviour of the joints was carried out, assessing the resulting deformed shape, the associated strain field and the observed failure modes using a digital image correlation (DIC) system and comparing with a finite elements method (FEM) model. The numerical model evidenced a good fitness to the experimental results since both the displacements and strain fields were found to be very similar. Both numerical and experimental strain fields in the longitudinal direction exhibited a localized spot of highly strained material, clearly indicating the nucleation site. Since secondary bending occurs in structural elements under tension due to geometrical and stiffness asymmetries, as is the case of overlap composite joints, a bending stress is induced, increasing the local stress compared to the nominal tension stress values. The ultimate tensile stress of the joints was found to range between 60.2 and 70.4 MPa, leading to an average joint efficiency of 82.6 %. The bending factor (kb) at the failure region was found to be 2.0, which means that the bending stress accounts for 2/3 of the total stress, acting as main failure catalyst.

Stress distribution in multilayer structural element subjected to skew bending

Results of researches on strength and stiffness of diagonally bending sandwich girders having geometric and/or stiffness asymmetry have been given. A mathematical module for calculation of normal strain (strength) and stiffness on bending at any cross-section point of sandwich girder has been proposed. The kinetics of stiffness on bending and strength variation dependences when geometric parameters of a cross-section and tension modulus ratios of girder layers are changing have been examined. It has been established that the strength of a diagonally bending sandwich girder on the whole depends on the position of the centre of stiffness and the position of the neutral plane.

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior, the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression, and has attracted a lot of attention. In this paper, an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks (NESs) for the first time. The proposed asymmetric tristable NES (ATNES) is composed of a pair of oblique springs and a vertical spring. Then, the three stable states, symmetric and asymmetric, can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs. The governing equations of a linear oscillator (LO) coupled with the ATNES are derived. The approximate analytical solution to the coupled system is obtained by the harmonic balance method (HBM) and verified numerically. The vibration suppression efficiency of three types of ATNES is compared. The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states. In addition, compared with the symmetrical tristable NES (TNES), the ATNES can effectively control smaller structural vibrations. In other words, the ATNES can effectively solve the threshold problem of TNES failure to weak excitation. Therefore, this paper reveals the vibration reduction mechanism of the ATNES, and provides a pathway to expand the effective excitation amplitude range of the NES.

How Fault‐Normal and Shear‐Parallel Stiffness Influence Frictional Sliding Behavior

AbstractThe potential of faults to show earthquake‐generating slip instabilities depends not only on the intrinsic frictional properties of the fault zone, but also on the elasticity of the surrounding material. A velocity‐weakening fault is expected to show increasingly unstable frictional behavior with decreasing local elastic stiffness around the fault zone. Fault zone roughness can cause slip in the shear direction to be accompanied by fault‐normal movement, modulated by fault‐normal elastic properties, however these effects are poorly understood. Here, we systematically vary the stiffness surrounding the fault in both the shear‐parallel and fault‐normal directions, to investigate the origin of slip instabilities and changes in friction constitutive properties. We confirm the transition from stable sliding through slow slip to stick‐slip due to reduced fault‐parallel stiffness, and that the occurrence of different types of slip events can be explained by the ratio between shear and critical stiffness. In contrast, reducing the fault‐normal stiffness produces stick‐slip instabilities under conditions where the conventional critical stiffness criterion predicts stable sliding, and does not produce transitional slow slip events. Our data suggest that: (a) the stability criterion for frictional slip should be modified to incorporate fault‐normal stiffness, and (b) the unexpected slip instabilities may represent wrinkle‐like slip pulses, possibly due to a stiffness asymmetry introduced by lowering the fault normal stiffness on one side of the fault. This implies that earthquakes may occur when the fault‐normal stiffness, or bulk modulus for natural faults, is decreased and/or asymmetric across the fault zone, both of which may be common in nature.

Enhancement of in-plane shear performance in masonry walls strengthened with high-performance fiber-reinforced cementitious composites

This study aims to design a high-performance fiber-reinforced cementitious composite (HPFRCC) material for reinforcing masonry walls and assess its impact on in-plane shear performance. Different specimens were compared, including an unreinforced one, a conventional mortar-reinforced one, and HPFRCC-reinforced specimens of varying thicknesses ranging from 10 mm to 20 mm. Aspects such as failure modes, shear stress–strain curves, pseudo-ductility, and energy dissipation were evaluated. Test results indicated that the unreinforced and mortar-reinforced masonry walls demonstrated brittle failure with wide cracks on both sides, whereas HPFRCC-reinforced walls exhibited ductile failure with controlled crack propagation owing to the excellent mechanical properties of HPFRCC, such as an average tensile strength of 7.32 MPa and a tensile strain capacity of 4.60 %. The HPFRCC significantly enhanced the shear strength and modulus of the masonry walls. The wall reinforced with 20 mm-thick HPFRCC showed a remarkable 26-fold increase in the energy dissipation capacity compared to the unreinforced one, and the 10-mm-thick and 15 mm-thick strengthening demonstrated 4.0- and 5.7-times improvement, respectively. The ideal HPFRCC overlay thickness was found to be between 15 mm and 20 mm. Beyond this thickness, gravitational flow and stiffness asymmetry negatively impacted shear performance.

Ankle stiffness asymmetry is associated with balance function in individuals with chronic stroke

Ankle joint is one of important contributors on balance in stroke survivors. This study aimed to investigate the relationships of ankle stiffness symmetry ratios along the talocrural and subtalar axes with clinical balance measures and weight distribution during quiet standing in ambulatory chronic post-stroke survivors. The clinical trials involved 15 ambulatory elderly with chronic post-stroke hemiparesis and 15 healthy controls. Ankle stiffness was evaluated during non-weight-bearing isokinetic passive biaxial ankle movements, and ankle stiffness symmetry ratios between paretic and non-paretic ankle stiffness (SR: Inversion/Eversion SRIE & Dorsi-/Plantarflexion SRDP) were measured. A certified physiotherapist evaluated the Berg Balance Scale (BBS) and weight-distribution ratio (WDR) on bilateral force plates during quiet standing. Correlation coefficients, the factor analysis, and Pearson linear multiple regression were assessed with measured parameters. Correlation coefficients showed significances in-betweens; BBS and SRDP (r = −0.543, p = 0.022), WDR and SRIE (r = −0.667, p = 0.004), SRIE and SRDP (r = −0.604, p = 0.011). The exploratory factor analysis suggested four extracted factors; (1) Balance & Gait, (2) Stroke, (3) Symmetry and (4) Dimension. The first and second factors include general and pathological characteristics in stoke participants respectively. The third factor is associated with symmetrical characteristics explaining up to 99.9% of the variance. Multiple regression analysis showed ankle stiffness ratios predict BBS up to 60% of variance. The biaxial ankle stiffness ratio is a useful clinical variable that assesses balance function, in ambulatory chronic stroke survivors.

Gear mesh stiffness and dynamics: Influence of tooth pair structural stiffness asymmetry

There are certainly a lot of different gear mesh stiffness models in the literature, nonetheless, it is not possible to find comprehensive and in-depth gear parametric studies that sweep the gear geometrical domain. To do so, it is required to have a fast and accurate gear mesh stiffness model, which is precisely one of the main developments of this work. By taking advantage of this new model, a parametric study on the influence of tooth pair structural stiffness asymmetry is conducted. This investigation evaluates how the referred stiffness asymmetry affects the gear mesh stiffness, dynamic displacements and load distribution by performing an extensive number of simulations that cover the entire selected gear geometry spectrum — two randomly generated populations of gears, one for spur and another for helical, are tested with and without the tooth pair structural stiffness asymmetry. It is concluded that tooth pair structural stiffness asymmetry cannot be neglected since it can lead to significant modifications on the frequency content of the gear mesh stiffness signal as well as the dynamic behavior of the geared system.

Dynamic characteristics analysis and the identification signal of the horizontal tail drive shaft system with the ballistic impact damage of a helicopter

The ballistic impact damage (BID) will change the dynamic characteristics of the horizontal tail drive shaft system (HTDSS) and will directly affect the flight safety of the helicopter. Aiming at the problem of how the BID affects the dynamic characteristics of the HTDSS and how to identify the BID in time, the dynamic characteristics of the HTDSS with the BID are studied in this paper. The BID is simplified as the ideal geometric damage, and the calculation method of the BID is given. The finite element dynamic equation of the HTDSS with the BID is established, and the effect mechanism of the ballistic impact parameters on the dynamic characteristics is revealed. The result shows: the BID causes the mass loss and the stiffness asymmetric of the ballistic impact position of the TDS; the eccentric excitation introduced by the BID leads to the obvious increase of the system response, and the stiffness asymmetry leads to the super-harmonic resonance of the system. The obvious increase of system response and the appearance of 2Ω frequency component can be used as the identification signal of the BID. Finally, the experiment was carried out, which verified the correctness of the established dynamic model, and explained the reliability of the proposed identification signal of the BID.

In Achilles Tendinopathy the Symptomatic Tendon Differs from the Asymptomatic Tendon While Exercise Therapy Has Little Effect on Asymmetries-An Ancillary Analysis of Data from a Controlled Clinical Trial.

As inter-limb asymmetries can be associated with higher injury risk, we aimed to investigate their role in Achilles tendinopathy patients. In Achilles tendinopathy patients (n = 41), we assessed inter-limb asymmetries of mechanical, material, and morphological musculoskeletal properties and function and how those were affected by 12 weeks of exercise intervention (high-load protocol, n = 13; Alfredson protocol, n = 11). Moreover, we assessed whether asymmetry reductions correlated with improved Patient-Reported Outcomes (VISA-A score). At baseline, tendinopathic tendons demonstrated lower tendon force (p = 0.017), lower tendon stress (p < 0.0001), larger tendon cross-sectional area (CSA) (p < 0.001), and increased intratendinous (p = 0.042) and tendon overall (p = 0.021) vascularization. For the high-load group, PRE-to-POST asymmetry comparisons revealed an asymmetry increase for the counter-movement jump (CMJ) (p = 0.034) and PRE-to-POST VISA-A score improvements correlated with CSA asymmetry reductions (p = 0.024). Within the Alfredson group, PRE-to-POST VISA-A score improvements correlated with CMJ asymmetry reductions (p = 0.044) and tendon stiffness asymmetry increases (p = 0.037). POST-to-POST in-between group comparisons revealed lower asymmetry in the high-load group for tendon elongation (p = 0.021) and tendon strain (p = 0.026). The tendinopathic limb differs from the asymptomatic limb while therapeutic exercise interventions have little effect on asymmetries. Asymmetry reductions are not necessarily associated with tendon health improvements.

Nonlinear dynamics of asymmetrically supported supercritical rotor equipped with a dry friction damper

To suppress the excessive transcritical vibration of a supercritical rotor, dry friction damper is a popular choice especially in rotorcraft and aero-engine design. In the current work, we focus on the nonlinear dynamics of asymmetrically supported supercritical rotor equipped with a dry friction damper and the influence of support asymmetry on damper’s performance. Governing equations of the rotor/damper system, which fully consider the nonlinear rub-impact and side dry friction effects, are derived. Typical results of symmetrically supported rotor/damper systems are firstly demonstrated and quantitatively compared with experimental counterparts to confirm the predicting capability of the nonlinear dry friction damper model. Afterward, influences of asymmetric direct stiffness and skew-symmetric cross-coupling stiffness are discussed. It is found that direct stiffness asymmetry deteriorates the transcritical vibration attenuation capability of the damper but reduces the width of transcritical region. For system with a severer direct stiffness asymmetry, a larger pre-tightening force is suggested to be imposed. Besides, unstable self-excited vibration induced by skew-symmetric cross-coupling stiffness is found to be well-limited by the dry friction damper within entire interested rotational speed range. Moreover, during critical speed transition, the self-excited frequency component is completely suppressed.

Approximation of the Statistical Characteristics of Piecewise Linear Systems with Asymmetric Damping and Stiffness under Stationary Random Excitation

In this paper, the dynamic response of piecewise linear systems with asymmetric damping and stiffness for random excitation is studied. In order to approximate the statistical characteristics for each significant output of piecewise linear system, a method based on transmissibility factors is applied. A stochastic linear system with the same transmissibility factor is attached, and the statistical parameters of the studied output corresponding to random excitation having rational spectral densities are determined by solving the associated Lyapunov equation. Using the attached linear systems for root mean square and for standard deviation of displacement, the shift of the sprung mass average position in a dynamic regime, due to damping or stiffness asymmetry, can be predicted with a good accuracy for stationary random input. The obtained results are compared with those determined by the Gaussian equivalent linearization method and by the numerical integration of asymmetric piecewise linear system equations. It is shown that the piecewise linear systems with asymmetrical damping and stiffness characteristics can provide a better vibration isolation (lower force transmissibility) than the linear system.

Reducing cost of transport in asymmetrical gaits: lessons from unilateral skipping.

Unilateral skipping is an asymmetrical gait only exceptionally used by humans, due to high energetic demands. In skipping, the cost of transport decreases as speed increases, and the spring-mass model coexists with the vaulting pendular one. However, the mechanisms of energy transfers and recovery between the vaulting and the bouncing steps are still unclear in this gait. The objective of this work is to study how spatiotemporal and spring-mass asymmetries impact on metabolic cost, lowering it despite speed augmentation. Kinematics and metabolic rates of healthy subjects were measured during running and skipping on a treadmill at controlled speeds. Metabolic power in skipping and running increased with similar slope but different intercepts. This fact determined the different behaviour of the cost of transport: constant in running, decreasing in skipping. In skipping the step time asymmetry remained constant, while the step length asymmetry decreased with speed, almost disappearing at 2.5m/s-1. Leg stiffness in trailing limb increased with higher slope than in leading limb and running; however, the relative leg stiffness asymmetry remained constant. Slow skipping presents short bouncing steps, even shorter than the vaulting, impacting the stride mechanics and the metabolic cost. Faster speeds were achieved by taking longer bouncing steps and a stiffer trailing limb, allowing to improve the effectiveness of the spring-mass mechanism. The step asymmetries' trends with respect to speed in skipping open the possibility to use this gait as an experimental paradigm to study mechanisms of metabolic cost reduction in locomotion.

Comparison of one-dimensional and three-dimensional glottal flow models in left-right asymmetric vocal fold conditions.

While the glottal flow is often simplified as one-dimensional (1D) in computational models of phonation to reduce computational costs, the 1D flow model has not been validated in left-right asymmetric vocal fold conditions, as often occur in both normal and pathological voice production. In this study, we performed three-dimensional (3D) and 1D flow simulations coupled to a two-mass model of adult male vocal folds and compared voice production at different degrees of left-right stiffness asymmetry. The flow and acoustic fields in 3D were obtained by solving the compressible Navier-Stokes equations using the volume penalization method with the moving vocal fold wall as an immersed boundary. Despite differences in the predicted flow pressure on vocal fold surface between the 1D and 3D flow models, the results showed reasonable agreement in vocal fold vibration patterns and selected voice outcome measures between the 1D and 3D models for the range of left-right asymmetric conditions investigated. This indicates that vocal fold properties play a larger role than the glottal flow in determining the overall pattern of vocal fold vibration and the produced voice, and the 1D flow simplification is sufficient in modeling phonation, at least for the simplified glottal geometry of this study.

Assessment of Vocal Fold Stiffness by Means of High-Speed Videolaryngoscopy with Laryngotopography in Prediction of Early Glottic Malignancy: Preliminary Report.

Simple SummaryThe method described in our manuscript can help to objectively assess the vibration of each vocal fold using larygotopographic analysis of high-speed videoendoscopy (HSV) recordings. We have developed image processing and analysis procedures to detect vocal fold regions in HSV films and quantitatively analyze their shape and kinematics. We proposed the term Stiffness Asymmetry Index which can provide valuable information on the texture and kinematic properties of individual vocal fold tissues, which can be important in the diagnosis of early glottis cancer. Our study showed that a low value of SAI indicated large, non-vibrating vocal fold areas, characteristic of infiltrative lesions such as invasive carcinoma. This important clinical information can help to assess the depth of vocal fold invasion before direct histologic examination and discriminate benign from malignant lesions.One of the most important challenges in laryngological practice is the early diagnosis of laryngeal cancer. Detection of non-vibrating areas affected by neoplastic lesions of the vocal folds can be crucial in the recognition of early cancerogenous infiltration. Glottal pathologies associated with abnormal vibration patterns of the vocal folds can be detected and quantified using High-speed Videolaryngoscopy (HSV), also in subjects with severe voice disorders, and analyzed with the aid of computer image processing procedures. We present a method that enables the assessment of vocal fold pathologies with the use of HSV. The calculated laryngotopographic (LTG) maps of the vocal folds based on HSV allowed for a detailed characterization of vibration patterns and abnormalities in different regions of the vocal folds. We verified our methods with HSV recordings from 31 subjects with a normophonic voice and benign and malignant vocal fold lesions. We proposed the novel Stiffness Asymmetry Index (SAI) to differentiate between early glottis cancer (SAI = 0.65 ± 0.18) and benign vocal fold masses (SAI = 0.16 ± 0.13). Our results showed that these glottal pathologies might be noninvasively distinguished prior to histopathological examination. However, this needs to be confirmed by further research on larger groups of benign and malignant laryngeal lesions.

Stability of a Cross-Flow Heat-Exchanger Tube With Asymmetric Supports

Abstract Heat-exchanger tubes subjected to cross-flow experience a fluid elastic instability (FEI) at a critical flow velocity. Baffle plates are often used to provide additional stiffness to long tubes. A cladding is provided between the baffle plates and the tubes to allow for thermal expansion, and the cladding acts like a soft spring. In this paper, we study the contact between the cladding and the tube when the stiffness of the cladding is asymmetric. The tube is modeled as a cantilever Euler–Bernoulli beam, and the fluid forces are represented using an added mass, added damping and a time-delayed displacement term. This results in a partial delay differential equation model for the tube vibration. Using the Galerkin approximation and considering only a single mode, a delay differential equation (DDE) model is developed. However, due to the presence of the delay, the single mode model is also infinite-dimensional. This model contains sign function nonlinearity due to the asymmetry in the contact stiffness of the cladding. The DDE model is essentially nonlinear—that is, no linear approximation exists. However, its solutions are scalable: if q(t) is a solution, then α q(t) is also a solution for any α&amp;gt;0. By exploiting this scalability property of solutions, we use Lyapunov-like exponents to probe the stability of the nonlinear DDE. Further, by numerical continuation, we numerically demonstrate the existence of periodic solutions on the stability boundary. Our stability charts will be beneficial to the designers of heat-exchangers.

Динамическая диагностическая 3D-модель шпинделя шлифовального станка. Гибридный способ моделирования

We use a grinding machine spindle as an example to consider a hybrid (numerical and analytical) method of simulating a rotor with a rigid shaft. The paper describes a spatial dynamic model of the rotor constructed via this method that takes into account support stiffness asymmetry. We show that introducing support stiffness asymmetry allows the spatial simulation to explain a number of physical phenomena, including spectrum frequency splitting, which are fundamentally impossible to explain when using flat axially symmetric models.

Computational modelling of ankle-foot orthosis to evaluate spatially asymmetric structural stiffness: Importance of geometric nonlinearity.

An ankle-foot orthosis (AFO) constructed as a single piece of isotropic elastic material is a commonly used assistive device that provides stability to the ankle joint of patients with spastic diplegic cerebral palsy. The AFO has asymmetric stiffness that restricts plantarflexion during the swing phase while it is flexible to allow dorsiflexion during the stance phase with a large deflection, including buckling originating from geometric nonlinearity. However, its mechanical implications have not been sufficiently investigated. This study aims to develop a computational model of an AFO considering geometric nonlinearity and examine AFO stiffness asymmetry during plantarflexion and dorsiflexion using physical experiments. Three-dimensional AFO mechanics with geometric nonlinearities were expressed using corotational triangle-element formulations that obeyed Kirchhoff-Love plate theory. Computational load tests for plantarflexion and dorsiflexion, using idealised AFOs with two different ankle-region designs (covering or not covering the apexes of the malleoli), showed that plantarflexion moment-ankle angle relationships were linear and dorsiflexion moment-ankle angle relationships were nonlinear; increases in dorsiflexion led to negative apparent stiffness of the AFO. Both ankle-region designs resisted both plantarflexion and dorsiflexion, and out-of-plane elastic energy was locally concentrated on the lateral side, resulting in large deflections during dorsiflexion. These findings give insight into appropriate AFO design from a mechanical viewpoint by characterising three-dimensional structural asymmetry and geometric nonlinearity.

In-Run Automatic Mode-Matching of Whole-Angle Micro-Hemispherical Resonator Gyroscope Based on Standing Wave Self-Precession

This paper reports an in-run automatic mode-matching method of whole-angle (WA) micro-hemispherical resonator gyroscope ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG) based on standing wave self-precession. When the standing wave precesses in real-time by self-precession, all information of frequency mismatch contained in the output force of the quadrature suppression loop is identified by the least mean square algorithm (LMS). Then the electrostatic negative stiffness effect is used to realize online real-time mode matching to eliminate the angle bias error of WA <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG caused by the asymmetry of stiffness. Self-precession rate overcomes the limitation of rotation rate requirement so that the LMS algorithm can work without rate turntable. The physical input angular rate can still be measured when the proposed mode matching loop works normally. The mechanical gain loss caused by frequency mismatch is investigated, distorting the measured angle relative to the forced angle. The expression of the angle error caused by mechanical gain loss is derived. The electrostatic tuning theory of WA <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG, the proposed information identification method for frequency mismatch, and the realization principle of mode matching are analyzed and introduced. Experiment results show that the automatic mode-matching method in whole-angle mode is effective. After mode matching, the final mode matching accuracy of 28.7mHz is realized, with a reduction of about 95% from 570.7mHz (original frequency mismatch). And the WA <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG realized the angle-dependent bias (ADB) error decreased from 25.8° to 7.3° after mode matching. For the mode-matched WA <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG, the ADB is improved by nearly 3.5 times.

Comparison of one-dimensional and three-dimensional glottal flow models in left-right asymmetric vocal fold conditions

While the glottal flow is often simplified as one-dimensional (1D) in computational models of phonation to reduce computational costs, the 1D flow model has not been validated in left-right asymmetric vocal fold conditions, as often occur in both normal and pathological voice production. It is unclear to what extent the 1D model approximates the effect of three-dimensional (3D) flow phenomena and fluid-structure interaction. In this study, we performed 1D and 3D flow simulations coupled with the two-mass vocal fold model and compared vocal fold vibration patterns at different degrees of left-right stiffness asymmetry. The flow and acoustic fields in 3D were predicted by solving the compressible Navier-Stokes equations using the volume penalization method and considering the moving vocal fold wall as an immersed boundary. The results showed that vocal fold vibration amplitudes and left-right phase differences in the 3D flow were predicted by the 1D flow model under conditions of small left-right asymmetry, while vocal fold vibration amplitudes were underestimated at conditions of large left-right asymmetry. This indicates that 1D flow models may be sufficient in modeling phonation under left-right asymmetric conditions, although the performance can be further improved by more accurately predicting air pressure on vocal fold surface.