Nonlinear Dynamic Behaviour of the Intervertebral Disc

2013 ◽  
Author(s):  
Giacomo Marini ◽  
Gerd Huber ◽  
Stephen J. Ferguson
Keyword(s):  
Dynamic Response ◽  
Intervertebral Disc ◽  
High Frequency ◽  
Nonlinear Dynamic ◽  
Mechanical Response ◽  
Numerical Models ◽  
Low Frequency ◽  
Upper Body ◽  
Highly Nonlinear ◽  
Flexion Extension

The intervertebral disc, like many collagen-based tissues, has a mechanical response which is highly nonlinear (1). This characteristic is due to both the arrangement and composition of the tissue constituents of the disc (2). Over the past decades several studies have reported the nonlinear response of the disc for different loading scenarios. In particular, past studies were focused on the quasi-static and low frequency (< 10Hz) response to pure and combined cyclic loading, such as axial compression, shear, flexion/extension moment (3–6). The information provided by these studies has been applied in several fields, from the validation of numerical models to the development of disc prostheses. However, such loading conditions are only partially representative of the in-situ load that the intervertebral disc normally experiences. High frequency dynamics stimuli, such as that experienced while driving a car on a rough surface or driving heavy industrial machinery, are also important. It is well known that long-term exposure to vibrational loading is detrimental to normal disc metabolism (7,8). Despite its relevance only a few studies have investigated the dynamic response of the disc to high frequency vibration (9,10) with sometimes different outcomes. In particular, no study has shown an asymmetric, nonlinear dynamic behavior of the system, even though it is evident in quasi-static testing — the well-known tension / compression asymmetry. This aspect is somehow neglected when building rigid body models of the upper body for impact simulation where a Kelvin-Voigt model with linear stiffness is normally used. The aim of this experimental study was therefore to investigate the nonlinear dynamic response of the intervertebral disc to high frequency loadings, taking different pre-loads and displacement amplitude into account.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Ghislain Maquer ◽  
Marc Laurent ◽  
Vaclav Brandejsky ◽  
Michael L. Pretterklieber ◽  
Philippe K. Zysset
Keyword(s):  
Mechanical Properties ◽  
Intervertebral Disc ◽  
Material Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Parameter Study ◽  
Nonlinear Normalization ◽  
Highly Nonlinear ◽  
Flexion Extension ◽  
Linear And Nonlinear

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

scholarly journals Rheology of rounded mammalian cells over continuous high-frequencies

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Gotthold Fläschner ◽  
Cosmin I. Roman ◽  
Nico Strohmeyer ◽  
David Martinez-Martin ◽  
Daniel J. Müller
Keyword(s):  
High Frequency ◽  
Mammalian Cells ◽  
Mechanical Response ◽  
Cell Mass ◽  
Low Frequency ◽  
Mass Measurements ◽  
High Frequencies ◽  
Polymer Relaxation ◽  
Continuous Frequency ◽  
Rheological Experiments

AbstractUnderstanding the viscoelastic properties of living cells and their relation to cell state and morphology remains challenging. Low-frequency mechanical perturbations have contributed considerably to the understanding, yet higher frequencies promise to elucidate the link between cellular and molecular properties, such as polymer relaxation and monomer reaction kinetics. Here, we introduce an assay, that uses an actuated microcantilever to confine a single, rounded cell on a second microcantilever, which measures the cell mechanical response across a continuous frequency range ≈ 1–40 kHz. Cell mass measurements and optical microscopy are co-implemented. The fast, high-frequency measurements are applied to rheologically monitor cellular stiffening. We find that the rheology of rounded HeLa cells obeys a cytoskeleton-dependent power-law, similar to spread cells. Cell size and viscoelasticity are uncorrelated, which contrasts an assumption based on the Laplace law. Together with the presented theory of mechanical de-embedding, our assay is generally applicable to other rheological experiments.

scholarly journals A Multi-Scale Approach for Nonlinear Dynamic Response Predictions With Fretting Wear

2016 ◽  
Author(s):  
J. Armand ◽  
L. Pesaresi ◽  
L. Salles ◽  
C. W. Schwingshackl
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Accurate Prediction ◽  
Fretting Wear ◽  
Contact Interface ◽  
Contact Conditions ◽  
Nonlinear Dynamic Response ◽  
Multi Scale ◽  
Highly Nonlinear ◽  
The Impact

Accurate prediction of the vibration response of aircraft engine assemblies is of great importance when estimating both the performance and the lifetime of its individual components. In the case of underplatform dampers, for example, the motion at the frictional interfaces can lead to a highly nonlinear dynamic response and cause fretting wear at the contact. The latter will change the contact conditions of the interface and consequently impact the nonlinear dynamic response of the entire assembly. Accurate prediction of the nonlinear dynamic response over the lifetime of the assembly must include the impact of fretting wear. A multi-scale approach that incorporates wear into the nonlinear dynamic analysis is proposed, and its viability is demonstrated for an underplatform damper system. The nonlinear dynamic response is calculated with a multiharmonic balance approach, and a newly developed semi-analytical contact solver is used to obtain the contact conditions at the blade-damper interface with high accuracy and low computational cost. The calculated contact conditions are used in combination with the energy wear approach to compute the fretting wear at the contact interface. The nonlinear dynamic model of the blade-damper system is then updated with the worn profile and its dynamic response is recomputed. A significant impact of fretting wear on the nonlinear dynamic behaviour of the blade-damper system was observed, highlighting the sensitivity of the nonlinear dynamic response to changes at the contact interface. The computational speed and robustness of the adopted multi-scale approach are demonstrated.

Jitter Transmission Analysis and Experimental Research for Frame Structure in the Median and High Frequency Regions

2012 ◽  
Vol 271-272 ◽  
pp. 981-985
Author(s):  
You Yi Wang ◽  
Yang Zhao ◽  
Wen Lai Ma
Keyword(s):  
Dynamic Response ◽  
Frequency Response ◽  
Dynamic Model ◽  
Experimental Research ◽  
High Frequency ◽  
Low Frequency ◽  
Frame Structure ◽  
Wave Method ◽  
Simulation Results ◽  
Theoretical Results

Frame structure is widely used in practical projects. For jitter of the frame structure excited by median and high frequency disturbances, firstly, the dynamic model of thin plate substructure is built by wave method, and then the dynamic model of frame structure is established by combining wave method and substructure technique. At last, the accurate dynamic response was obtained. The simulation of dynamic characteristic is made, and simulation results are compared with FEM results. On this basis, modal experiment and frequency response experiment is done to verify theoretical results. In comparison to FEM, the results by wave method are accurate in low frequency regions, and the results are more accurate in the median and high frequency regions. The experiment proves wave method is correct and effective for jitter transmission analysis of frame structure in the median and high frequency regions.

scholarly journals A Multiscale Approach for Nonlinear Dynamic Response Predictions With Fretting Wear

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
J. Armand ◽  
L. Pesaresi ◽  
L. Salles ◽  
C. W. Schwingshackl
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Accurate Prediction ◽  
Fretting Wear ◽  
Multiscale Approach ◽  
Contact Interface ◽  
Contact Conditions ◽  
Nonlinear Dynamic Response ◽  
Highly Nonlinear ◽  
The Impact

Accurate prediction of the vibration response of aircraft engine assemblies is of great importance when estimating both the performance and the lifetime of their individual components. In the case of underplatform dampers, for example, the motion at the frictional interfaces can lead to a highly nonlinear dynamic response and cause fretting wear at the contact. The latter will change the contact conditions of the interface and consequently impact the nonlinear dynamic response of the entire assembly. Accurate prediction of the nonlinear dynamic response over the lifetime of the assembly must include the impact of fretting wear. A multiscale approach that incorporates wear into the nonlinear dynamic analysis is proposed, and its viability is demonstrated for an underplatform damper system. The nonlinear dynamic response is calculated with a multiharmonic balance approach, and a newly developed semi-analytical contact solver is used to obtain the contact conditions at the blade–damper interface with high accuracy and low computational cost. The calculated contact conditions are used in combination with the energy wear approach to compute the fretting wear at the contact interface. The nonlinear dynamic model of the blade–damper system is then updated with the worn profile and its dynamic response is recomputed. A significant impact of fretting wear on the nonlinear dynamic behavior of the blade–damper system was observed, highlighting the sensitivity of the nonlinear dynamic response to changes at the contact interface. The computational speed and robustness of the adopted multiscale approach are demonstrated.

scholarly journals Multiscale modeling of mechanotransduction in the utricle

2019 ◽  
Vol 122 (1) ◽  
pp. 132-150 ◽  
Author(s):  
Jong-Hoon Nam ◽  
J. W. Grant ◽  
M. H. Rowe ◽  
E. H. Peterson
Keyword(s):  
High Frequency ◽  
Computational Models ◽  
Numerical Models ◽  
Low Frequency ◽  
Head Movements ◽  
Hair Bundle ◽  
Functional Requirements ◽  
Natural Behavior ◽  
Hair Bundles ◽  
Static Head

We review recent progress in using numerical models to relate utricular hair bundle and otoconial membrane (OM) structure to the functional requirements imposed by natural behavior in turtles. The head movements section reviews the evolution of experimental attempts to understand vestibular system function with emphasis on turtles, including data showing that accelerations occurring during natural head movements achieve higher magnitudes and frequencies than previously assumed. The structure section reviews quantitative anatomical data documenting topographical variation in the structures underlying macromechanical and micromechanical responses of the turtle utricle to head movement: hair bundles, OM, and bundle-OM coupling. The macromechanics section reviews macromechanical models that incorporate realistic anatomical and mechanical parameters and reveal that the system is significantly underdamped, contrary to previous assumptions. The micromechanics: hair bundle motion and met currents section reviews work based on micromechanical models, which demonstrates that topographical variation in the structure of hair bundles and OM, and their mode of coupling, result in regional specializations for signaling of low frequency (or static) head position and high frequency head accelerations. We conclude that computational models based on empirical data are especially promising for investigating mechanotransduction in this challenging sensorimotor system.

SEA Subsystem Property Identification by Periodic FEM Approach

2011 ◽  
Vol 94-96 ◽  
pp. 1979-1982
Author(s):  
Jie Gao ◽  
Ke An Chen
Keyword(s):  
Dynamic Response ◽  
High Frequency ◽  
Periodic Structures ◽  
Low Frequency ◽  
Engineering Method ◽  
Complex Structures ◽  
High Frequency Range ◽  
Frequency Range ◽  
Remarkable Improvement ◽  
Property Identification

A study on SEA properties of periodically stiffened structure was accomplished based on the periodic theory. With application of certain software, a simulation was performed on a common periodically stiffened fuselage structure. The results indicate such modeling approach reflects relatively accurate property of subsystem in mid and high frequency range, while a remarkable improvement could also be expected in low frequency range, especially for complex structures. Such approach was approved as one reliable engineering method for solving dynamic response of periodic structures.

scholarly journals Accounting for Quasi-Static Coupling in Nonlinear Dynamic Reduced-Order Models

2020 ◽  
Vol 15 (7) ◽  
Author(s):  
Evangelia Nicolaidou ◽  
Venkata R. Melanthuru ◽  
Thomas L. Hill ◽  
Simon A. Neild
Keyword(s):  
High Frequency ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Low Frequency ◽  
Nonlinear Effects ◽  
Fe Model ◽  
Engineering Structures ◽  
Reduced Order ◽  
Modal Coupling ◽  
High Frequency Modes

Abstract Engineering structures are often designed using detailed finite element (FE) models. Although these models can capture nonlinear effects, performing nonlinear dynamic analysis using FE models is often prohibitively computationally expensive. Nonlinear reduced-order modeling provides a means of capturing the principal dynamics of an FE model in a smaller, computationally cheaper reduced-order model (ROM). One challenge in formulating nonlinear ROMs is the strong coupling between low- and high-frequency modes, a feature we term quasi-static coupling. An example of this is the coupling between bending and axial modes of beams. Some methods for formulating ROMs require that these high-frequency modes are included in the ROM, thus increasing its size and adding computational expense. Other methods can implicitly capture the effects of the high-frequency modes within the retained low-frequency modes; however, the resulting ROMs are normally sensitive to the scaling used to calibrate them, which may introduce errors. In this paper, quasi-static coupling is first investigated using a simple oscillator with nonlinearities up to the cubic order. ROMs typically include quadratic and cubic nonlinear terms, however here it is demonstrated mathematically that the ROM describing the oscillator requires higher-order nonlinear terms to capture the modal coupling. Novel ROMs, with high-order nonlinear terms, are then shown to be more accurate, and significantly more robust to scaling, than standard ROMs developed using existing approaches. The robustness of these novel ROMs is further demonstrated using a clamped–clamped beam, modeled using commercial FE software.

Locating Schumann Resonant Frequencies on a Single Particle Radiation Patterns Using Golden Ratio Spiral and Octave Relationship of Schumann Points.

2021 ◽  
Author(s):  
Mert Yucemoz
Keyword(s):  
Radiation Pattern ◽  
Single Particle ◽  
High Frequency ◽  
Numerical Models ◽  
Golden Ratio ◽  
Lightning Discharge ◽  
Low Frequency ◽  
Radiation Patterns ◽  
Particle Radiation ◽  
Schumann Resonances

&lt;p&gt;Although lightning discharge is not the only source or only physical phenomenon that affects the Schumann resonances, they have the highest contribution to the Schumann resonances oscillating between the ground the ionosphere. Schumann resonances are predicted through several different numerical models such as the transmission-line matrix model or partially uniform knee model. This contribution reports a different prediction method for Schumann resonances derived from the first principle of fundamental physics combining both particle radiation patterns and the mathematical concept of the Golden ratio. This prediction allows the physical understanding of where Schumann resonances originate from radiation emitted by a particle that involves many frequencies that are not related to Schumann resonances. In addition, this method allows predicting the wave propagation direction of each frequency value in the Schumann frequency spectrum. Particles accelerated by lightning leader tip electric fields are capable of contributing most of the Schumann resonances. The radiation pattern of a single particle consists of many frequencies. There are only specific ones within this pattern that contribute to the Schumann radiation. The vast majority of Schumann resonances distribute quite nicely obeying the Golden ratio interval. This property, used in conjunction with the full single-particle radiation patterns, also revealed that high-frequency forward-backward peaking radiation patterns, as well as low-frequency radiation patterns, can contribute to Schumann resonances. This method allows to locate them on the full radiation pattern. A theoretical analysis using the Golden ratio spiral, predict that there are more Schumann resonances in the high-frequency forward-backward peaking radiation pattern of a relativistic particle than low-frequency dipole radiation pattern. Extending the idea to an octave that identifies the identical sounding notes with different frequencies in standing waves. By knowing the value of the initial Schumann resonant frequency, this method allows us to predict the magnitude of other Schumann resonances on the radiation pattern of a single accelerated charged particle conveniently. In addition, it also allows us to find and match Schumann resonances that are on the same radiation lobe, which is named electromagnetic Schumann octaves. Furthermore, it is important to find Schumann octaves as they propagate in the same direction and have a higher likelihood of wave interference.&lt;/p&gt;

Mechanical Effectiveness of Polyvinyl Alcohol/Polyvinyl Pyrrolidone (PVA/PVP) as an Intervertebral Disc Polymer

2013 ◽  
Author(s):  
Kooroush Azartash-Namin ◽  
Zheila Azartash-Namin ◽  
S. Ashton Williams ◽  
Khiet Tran ◽  
M. Khandaker
Keyword(s):  
Elastic Modulus ◽  
Intervertebral Disc ◽  
Polyvinyl Alcohol ◽  
Nucleus Pulposus ◽  
Low Frequency ◽  
Axial Rotation ◽  
Polyvinyl Pyrrolidone ◽  
Disc Disease ◽  
Flexion Extension ◽  
Hydrogel Polymer

The intervertebral disc is one of the body’s most vital structures. It provides support and enables six degree of freedom (6DOF) motions in the spine: flexion, extension, right and left lateral bending, compression, and axial rotation. When individuals suffer from degenerative disc disease, the nucleus pulposus deteriorates, causing a loss of articulation in the intervertebral disc. To address this problem, replacements for the nucleus pulposus can be used. The objective of this study was to evaluate a potential nucleus pulposus replacement consisting of a hydrogel polymer. The hydrogel was synthesized by physically cross-linking 95%-weight polyvinyl alcohol (PVA) and 5%-weight polyvinyl pyrrolidone (PVP). PVA and PVP were selected for the hydrogel implant due to the natural biocompatibility when the two are physically cross-linked. In order to evaluate the mechanical effectiveness of the hydrogel, a slider-crank mechanism was designed and constructed to create the 6DOF motions when interfaced with a Universal Mechanical Testing System. The viscoelastic properties of the polymer were obtained using a rheometer, which determined the elastic (G′) and viscous (G″) moduli of the PVA/PVP hydrogel polymer by calculating the complex shear modulus (G*) under low-frequency oscillating shear deformation. This allows for study of the viscoelastic performance of the isolated nucleus pulposus and hydrogel implant. The elastic modulus of the hydrogel was tested at parameters 5%, 10%, and 15% strain with results of 228.6 Pa, 988.8 Pa, and 1793 Pa, respectively. However, the elastic modulus tested for the natural bovine specimen at 5%, 10%, and 15% strain were 712.9 Pa, 522.1 Pa, and 363.3 Pa, respectively.

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