Axial Extension Research Articles

Transverse Vibration Response and Time-Varying Analysis of Axially Moving Beams Based on Choi–Williams Distribution

Cantilever beams with axial extension and contraction functions as time-varying parameter systems have attracted extensive research due to their prevalence in engineering structures. In this paper, the dynamic characteristics of the flat-push bridge mechanism are investigated from the theoretical aspect, firstly, it is simplified into a cantilever beam model with axial motion, and the transverse vibration equations of the cantilever beam are established based on the Euler–Bernoulli beam theory and D’Alembert’s principle, and the transverse displacements of the beam are discretized using the Galerkin truncation method and solved numerically by using the Newmark-[Formula: see text] method for the second-order vibration differential equations with variable coefficients; second-order vibration differential equations were solved numerically by the Newmark-[Formula: see text] method; then the structural examples in the existing literature are verified numerically, and the calculation results are consistent with the literature results, indicating that the transverse vibration equations derived in this paper are solved effectively; then a parametric analysis of the speed of the cantilever beam during axial extension/contraction was done, which showed that the faster the speed of axial motion, the faster the rate of change of the dynamic characteristics of the beam and the more pronounced the vibration; finally, the power signal is decomposed in the time-frequency domain by using the Choi–Williams Distribution (CWD), and the time-frequency characteristics of the system under different speeds are analyzed, and the results show that the use of CWD technique can accurately reflect the system’s transient vibration frequency and vibration energy with the change rule of time and speed, and the axial motion speed of ±0.05[Formula: see text]m/s, the transient frequency of the theoretical prediction and the average relative deviation between the finite element modal frequencies are kept within 5% and the recognition accuracy is high. This analysis provides flexible technical guidance for vibration control in engineering structures.

Understanding cervical spine instability: a finite element study on atypical hangman’s fractures

Recent reports have highlighted a notable prevalence of atypical hangman’s fractures, yet their biomechanical aspects remain underexplored. Using a validated finite element model, this study assesses changes in rotation-moment characteristics of the upper cervical spine due to fractures involving the superior and inferior articular process, pars interarticularis, and lamina. The results revealed that fractures affecting the superior articular process and pars interarticularis led to significant instability, particularly in axial rotation and extension. However, atypical hangman’s fractures did not necessarily produce greater instability than Levine-Edwards type II hangman’s fractures.

Effect of a uniform magnetic field on the nonlinear instability of double cylindrical interfaces concerning three magnetic liquids

The present manuscript relates to the movement of three immersed viscous magnetic liquids in porous media that are positioned between three concentric cylindrical interfaces. Every cylindrical layer has an axial extension that extends in both vertical directions to infinity. Moreover, the pressure gradients are the driving force behind the uniform motion of all fluids in a similar upward motion at varying velocities. Permanent magnetic fields are tangentially oriented exert stress on the system. The computations are rendered simpler by applying the viscous potential theory. The Maxwell equations are utilized for the magnetic field, while the Brinkman-Darcy equations define the fluid mobility. Moreover, the rise of the disturbance and the subsequent extraction of fuel from the tiny cracks of the reservoir stone can be managed through the implementation of engineering techniques such as electromagnetic field impacts and oil extraction engineering. Typically, the nonlinear strategy involves incorporating the applicable nonlinear boundary conditions and analyzing the linearized equations of motion. This research offers a framework for verifying theoretical models and simulations based on experimental observations. The inclusion of a homogeneous magnetic field introduces complexity to the system, rendering it a suitable candidate for validating and improving models in the field Magneto hydrodynamics. The originality of the problem lies in the dual nonlinear stability of cylindrical interfaces when subjected to uniform magnetic field. Accordingly, two nonlinear characteristic differential equations controlling the surface displacements are produced. The nonlinear stability prerequisite is met by applying the matrix concept and the multiple scale technique in conjunction with a theoretical analysis of stability. Additionally, the Routh-Hrutwitz criterion is encompassed to judge the stability cofiguration. A detailed examination of the associated nonlinear stability requirements is showed. Meanwhile, the estimated limited solutions of perturbed surfaces are achieved. For the cylindrical middle layer, it is found that the outer cylindrical interface has a more stabilizing effect than the inner one. The approximate solutions for displacements at the interface are calculated. The influence of Weber numeral of the problem on the stability profile is investigated.

A conserved regulation of cell expansion underlies notochord mechanics, spine morphogenesis, and endochondral bone lengthening.

Cell size is a key contributor to tissue morphogenesis 1 . As a notable example, growth plate hypertrophic chondrocytes use cellular biogenesis and disproportionate fluid uptake to expand 10-20 times in size to drive lengthening of endochondral bone 2,3 . Similarly, notochordal cells expand to one of the largest cell types in the developing embryo to drive axial extension 4-6 . In zebrafish, the notochord vacuolated cells undergo vacuole fusion to form a single large, fluid-filled vacuole that fills the cytoplasmic space and contributes to vacuolated cell expansion 7 . When this process goes awry, the notochord lacks sufficient hydrostatic pressure to support vertebral bone deposition resulting in adult spines with misshapen vertebral bones and scoliosis 8 . However, it remains unclear whether endochondral bone and the notochord share common genetic and cellular mechanisms for regulating cell and tissue expansion. Here, we demonstrate that the 5'-inositol phosphatase gene, inppl1a , regulates notochord expansion, spine morphogenesis, and endochondral bone lengthening in zebrafish. Furthermore, we show that inppl1a regulates notochord expansion independent of vacuole fusion, thereby genetically decoupling these processes. We demonstrate that inppl1a -dependent notochord expansion is essential to establish normal mechanical properties of the notochord to facilitate the development of a straight spine. Finally, we find that inppl1a is also important for endochondral bone lengthening in fish, as has been shown in the human INPPL1 -related endochondral bone disorder, Opsismodysplasia 9 . Overall, this work reveals a conserved mechanism of cell size regulation that influences disparate tissues critical for skeletal development and short-stature disorders.

A New Technology for Industrial Strain Mapping Using Single-Wall Carbon Nanotube Sensors

Measurements of mechanical strain are widely used in heavy industry to design and test new structures and to ensure the safety of installed infrastructure. However, the few practical methods for strain measurement all have serious limitations. To complement these methods, we have developed a new strain technology, called S4 for “strain-sensing smart skin,” which uses single-wall carbon nanotubes (SWCNTs) as microscopic sensors. Nanotubes dilutely embedded in a polymer are applied as a thin film to specimen surfaces of interest. Subsequent strains in the specimen are transmitted by load transfer through the film to the nanotubes, inducing axial compression or extension. Those small structural deformations of the SWCNTs alter the semiconducting band gaps in predictable ways, causing proportional shifts in the peak wavelengths of their near-infrared fluorescence emission. Shifts are quantified by optically exciting the specimen surface and spectrally analyzing the resulting fluorescence to deduce strain values at the probed locations. The S4 method has recently been implemented using hyperspectral imaging. We demonstrate measurements in less than one minute of strain maps containing hundreds of thousands of pixels with 50 microstrain noise levels and 0.2 mm spatial resolution. This technology has promising potential to become a large-scale commercialized application of carbon nanotechnology.

Shape and Size of the Annulus Fibrosus Excision Alters the Biomechanics of the Intervertebral Disc.

Biomechanical testings and finite element analysis. This study aims to investigate how annulus fibrosus (AF) incision size (RIS, Ratio of incision width to AF height) and shape affect intervertebral disc (IVD) biomechanics. A validated finite element model of lumbar spines simulated various incisions in the middle-right posterior region of the AF, with different sizes and shapes. Simulations included axial compression, flexion, extension, bending, and rotation. Parameters assessed included stability, re-herniation, and IVD degeneration by analyzing stress, height, Intradiscal pressure (IDP), and the range of motion (ROM). Incision increased AF stress and ROM under 3 Nm moment, with values rising as RIS increased. RIS exceeding 40% resulted in a 20% AF stress increase during compression and extension, while RIS over 50% led to over 20% AF stress increase during other motions. Incision stress also increased with higher RIS, particularly surpassing 50% RIS. IDP rose across all incision shapes. Endplate stress increased (9.9%-48.9%) with larger incisions, with average increases of 12.8%, 12.7%, 30.5%, and 22.8% for circular, oval, square, and rectangular incisions. Compression and rotation minimally affected NP pressure (<15%), while flexion (19.8%-38.8%) and bending (18.5%-43.9%) had a more pronounced effect. ROM increased with RIS (20.0% ∼ 77.4%), especially with an incision RIS exceeding 40%. AF injury elevates AF stress, reduces spine stability, heightens degeneration risk with increasing RIS. Reherniation risk rises when RIS exceeds 40%. Circular or oval incisions maintain spine biomechanics better than square or rectangular ones.

Gradient Hierarchically Porous Ionic-Junction Fibers of Wet-Spun Carboxymethyl Cellulose Coagulated with Copper Sulfate.

Polyelectrolyte-based ionic-junction fibers newly serve as signal transmission and translation media between electronic devices and biological systems, facilitating ion transport within organic matrices. In this work, we fabricated gel filaments of carboxymethyl cellulose (CMC) chelated with Cu(II) ions through wet-spinning, using a saturated coagulant of CuSO4. Interestingly, the as-spun fibers exhibited dramatic 3D porous frameworks that varied with the temperature and precursor concentration. At 20 °C, the Cu(II) chelation networks favored the formation of well-organized cellular chambers or corrugated channels, displaying dense stacking patterns. However, critical transitions from cellular chambers to corrugated channels occurred at precursor dope concentrations of approximately 2 and 7 wt %, with the porous structure diminishing beyond 8 wt %. We have proposed schematic diagrams to mimic the 3D pore structure, dense porous stacking, and formation mechanism, according to electronic micrographs. Our investigations revealed that the distinct ion-junction channels or chambers are under the control of axial drawing extension as well as the outside-inside penetration of Cu(II) ions into the dope and inside-outside diffusion of water into coagulants. Therefore, controlling the metal chelation-water diffusion process at specific temperatures and concentrations will offer valuable insights for tailoring ionic-junction soft filaments with gradient hierarchically porous structures and shape memory properties.

Differential proliferation regulates multi-tissue morphogenesis during embryonic axial extension: integrating viscous modeling and experimental approaches.

A major challenge in biology is to understand how mechanical interactions and cellular behavior affect the shapes of tissues and embryo morphology. The extension of the neural tube and paraxial mesoderm, which form the spinal cord and musculoskeletal system, respectively, results in the elongated shape of the vertebrate embryonic body. Despite our understanding of how each of these tissues elongates independently of the others, the morphogenetic consequences of their simultaneous growth and mechanical interactions are still unclear. Our study investigates how differential growth, tissue biophysical properties and mechanical interactions affect embryonic morphogenesis during axial extension using a 2D multi-tissue continuum-based mathematical model. Our model captures the dynamics observed in vivo by time-lapse imaging of bird embryos, and reveals the underestimated influence of differential tissue proliferation rates. We confirmed this prediction in quail embryos by showing that decreasing the rate of cell proliferation in the paraxial mesoderm affects long-term tissue dynamics, and shaping of both the paraxial mesoderm and the neighboring neural tube. Overall, our work provides a new theoretical platform upon which to consider the long-term consequences of tissue differential growth and mechanical interactions on morphogenesis.

Folding Auxetic Polygonal Kirigami Tubes

Abstract Tubular auxetic structures have wide-ranging applications including medical stents, collapsible energy absorbers, and novel fasteners. To accelerate the development in these areas, and open up new application directions, an expanded range of design and construction methods for auxetic tubes is required. In this study, we propose a new method to construct polygonal cross-sectional auxetic tubes using the principles of origami and kirigami. These tubes exhibit useful global auxetic behavior under axial extension, despite the individual polygon faces not being auxetic themselves. In general, a flat kirigami sheet cannot be simply folded into a polygonal tube since this creates kinematic incompatibilities along the polygon edges. We resolve this issue by replacing the edge folds with an origami mechanism consisting of a pair of triangular facets. This approach eliminates the incompatibilities at the edges while maintaining a connection between faces. The proposed edge connection also introduces additional control parameters for the tube kinematics: for example, introducing a kinematic limit on tube extension and enabling non-uniform behavior along the length of the tube. The rich kinematic behavior possible with polygonal cross-sectional kirigami tubes has potential applications ranging from soft robotics to energy-dissipating devices.

Ciliary muscles contraction leads to axial length extension--The possible initiating factor for myopia.

This study aimed to investigate the underlying factors driving the onset of myopia, specifically the role of the ciliary muscle's contraction in the elongation of the axial length of the eye. The retrospective study was conducted utilizing data from three ophthalmic centers in Shanghai and Beijing. Both Chinese and Caucasian children were involved. The axial length of the subjects' eyes was measured in both relaxed and contracted state of the ciliary muscle. A comprehensive mechanical model was also developed to observe the influence of ciliary muscle contraction on the axial length. This study included a sample of 198 right eyes of 198 myopic children. Of these, 97 were male and 101 were female, 126 were of Chinese ethnicity and 72 were Caucasian. The age of onset for myopia ranged from 5.9 to 16.9 years old. The axial length of the eye decreased 0.028 ± 0.007mm following dilation, indicating relaxation of the ciliary muscle (t paired student = 15.16, p = 6.72 x 10-35). In contrast, ciliary muscle contraction resulted in an increase in axial length. Considering proportionality, a significant 90.4% (179 eyes) exhibited a reduced axial length, while a minor 9.6% (19 eyes) demonstrated an increase post-mydriasis. Finite element modeling demonstrated that muscle contraction caused a tension force that transmits towards the posterior pole of the eye, causing it to extend posteriorly. The contraction of the ciliary muscle leads to an extension of the axial length. This could potentially be the initiating factor for myopia.

Modulated illumination microscopy: Application perspectives in nuclear nanostructure analysis.

The structure of the cell nucleus of higher organisms has become a major topic of advanced light microscopy. So far, a variety of methods have been applied, including confocal laser scanning fluorescence microscopy, 4Pi, STED and localisation microscopy approaches, as well as different types of patterned illumination microscopy, modulated either laterally (in the object plane) or axially (along the optical axis). Based on our experience, we discuss here some application perspectives of Modulated Illumination Microscopy (MIM) and its combination with single-molecule localisation microscopy (SMLM). For example, spatially modulated illumination microscopy/SMI (illumination modulation along the optical axis) has been used to determine the axial extension (size) of small, optically isolated fluorescent objects between ≤ 200nm and ≥ 40nm diameter with a precision down to the few nm range; it also allows the axial positioning of such structures down to the 1nm scale; combined with laterally structured illumination/SIM, a 3D localisation precision of ≤1nm is expected using fluorescence yields typical for SMLM applications. Together with the nanosizing capability of SMI, this can be used to analyse macromolecular nuclear complexes with a resolution approaching that of cryoelectron microscopy.

Research on the Law of Affecting the Quality of forging Metallurgy Quality on the Quality of Wedge Horizontal Rolling Mold

Drawing on the traditional and mature cross wedge rolling forming technology for stepped shaft parts, it is innovatively applied to the high-efficiency and low-cost manufacturing of blade preforms with special-shaped sections. Under the action of the rollers, the material undergoes radial compression deformation and axial extension deformation, and the blank changes from a uniform cross-section to a variable cross-section, which is in the shape of a stepped shaft. Forming, to prepare a blade preform with deformed cross-section characteristics. Then, the cooled blade preform is heated again and placed in a precision forging die. Under the action of the unidirectional compressive stress of the upper and lower dies, the blade preform is compressed and deformed, filling the die cavity with the smallest volume, thereby realizing precision forming of blade forgings. In the process parameters of the horizontal wedge rolling mold, the effect of forming angle has the greatest impact on center damage.

An Origami Continuum Manipulator with Modularized Design and Hybrid Actuation: Accurate Kinematic Modeling and Experiments

Herein, this study contributes significantly to the advancement of continuum manipulators in two main aspects. First, a modularization concept and a hybrid actuation scheme to create a novel origami continuum manipulator with exceptional deformability are introduced. Second, an accurate model and framework for the forward and inverse kinematic analysis of origami manipulators are proposed. Specifically, each origami manipulator module can achieve axial extension and bending deformation by coordinated actuation of shape memory alloy (SMA) and pneumatic muscles, and the manipulator's end is equipped with a deformable gripper based on waterbomb origami and actuated by SMA. Through careful consideration of the self‐weight and torque balance, an accurate kinematic model based on the Denavit–Hartenberg method is established, which enables one to effectively predict the reachable extreme positions and spatial poses of the manipulator and solve the inverse kinematics using a genetic algorithm. Comprehensive experiments are conducted to validate the design's rationality and model's accuracy . In these tests, the rich spatial configurations are not only demonstrated that can be achieved by integrating hybrid actuators with origami modules but also the accuracy and reliability of the kinematic model are confirmed, opening up possibilities for the advancement and application of origami‐inspired robotics in various fields.

Closed orbits in axial symmetric Finslerian extension of a Schwarzschild black hole

Closed orbits in axial symmetric Finslerian extension of a Schwarzschild black hole

An axial mode magnetoelectric antenna: Radiation predictions via multiphysics modeling with experimental validations

This study investigates an axial extension mode magnetoelectric antenna designed for near-field communication in dielectric cluttered environments. The antenna configuration consists of two magnetostrictive Metglas-polymer composites bonded on opposite sides of a PZT-5A actuator, creating a dumbbell configuration. Operating at its 88 kHz mechanical resonance, the antenna emits electromagnetic radiation in the near field by applying an AC voltage to the piezoelectric material, generating an acoustic wave that propagates through the volume and induces oscillating magnetizations. The design uses a system of uncoupled models: an electrostatic finite element model to predict strain that feeds into a Landau–Lifshitz–Gilbert micromagnetic model to predict magnetic moment changes and, subsequently, a dipole model to forecast near-field radiation characteristics. Measurements were conducted on the antenna’s impedance, quality factor, mechanical resonance, transmitted magnetic signal strength, and radiation patterns, with variations in the bias magnetic field, frequency, and applied voltage. The results exhibit a strong correlation with model predictions, and the radiated signal strengths compare favorably with those of state-of-the-art pacemaker communication devices. Computational parametric studies using Galfenol and Terfenol-D suggest the potential for up to a three order of magnitude reduction in the antenna's volume, which is critical for implanted medical devices.

A model for residually stressed viscoelastic bodies and its application to some boundary value problems

A model for residually stressed viscoelastic bodies undergoing finite deformations is developed and applied to the study of time-dependent responses of spheres and cylinders to various stress and strain controlled tests. An approach based on the notion of natural configurations is employed. An appropriate free energy function is used, and a suitable dissipation function is adopted to obtain a constitutive model. This constitutive model is applied to the study of different boundary value problems of thick spheres and cylinders. The responses to various strain controlled tests are investigated, which includes the stress-relaxation test and a test for a time-dependent inflation–deflation cycle. Also, the response to creep test and step-stress test in thick viscoelastic spheres is investigated. Furthermore, the stretch-controlled responses of residually stressed viscoelastic cylinders to pure torsion and axial stretch are studied. Pure torsion involves an axial extension or compression known as the Poynting effect. The Poynting effect in residually stressed viscoelastic bodies, which does not appear to be studied in the literature, is investigated in detail here. It is noted that the magnitude of the angle of twist has a significant influence (sometimes involving a change of sign) on the observed Poynting effect.

Low-coherence optical profilometry with multi-reflection reference mirrors for large-depth object measurement.

A new, to the best of our knowledge, optical configuration for digital holographic profilometry for surface profile measurement of large-depth objects is proposed. Two multi-reflection mirrors were employed to extend the maximum axial measurable range by a factor of 2 without any degradation of the spatial resolution. By adjusting the distance and the position of the two multi-reflection reference mirrors, the system can be made more flexible for measuring different parts of the object. In addition to the axial extension, the two-mirror system also increases the visibility of the interference fringes so that the object profile can be measured with high accuracy.

Investigating nonlinear forced vibration of functionally graded nanobeam based on the nonlocal strain gradient theory considering mechanical impact, electromagnetic actuator, thickness effect and nonlinear foundation

The present study proposes an investigation to nonlinear vibration response of a functionally graded (FG) nanobeam based on nonlocal strain gradient theory (NSGT) taking into consideration the longitudinal magnetic field and the thickness effect. The nonlinear terms from the governing equation are associated with the curvature of the nanobeam, the nonlinear foundation, the mean axial extension of the nanobeam and electromagnetic actuator for pinned-pinned nanobeam and the effect of discontinuities marked by the presence of the Dirac function (mechanical impact).The governing differential equation of motion and the boundary conditions are modeled within the framework of a simple supported Euler-Bernoulli nanobeam which accounts for the nonlinear von-Kármán strain and using so-called Hamilton's principle. To truncate the continuous system having an infinite degree of freedom, the Galerkin-Bubnov procedure is applied. The resulting nonlinear differential equation is studied by Optimal Auxiliary Functions Method. An explicit analytical solution is proposed for a complex problem near the primary resonance. Our proper procedure is a powerful tool to solve a nonlinear problem without presence of any small parameters. The main characteristic of our technique consists in the existence of some auxiliary functions derived from the expressions of the solution formed for initial linear equation and the form of nonlinear terms calculated for the solution of the linear equation. Also, the presence of some convergence-control parameters assures the rapid convergence of the solutions after only a single iteration. These parameters can be evaluated by means of some rigorous mathematical procedures. We have a large freedom to select the auxiliary functions and the number of convergence-control parameters. The proposed approach is proved to be very accurate, simple, and easy to implement for complicated nonlinear problems. The potential energy is analyzed in detail for different values of the parameters. The local stability of motion near the primary resonance is established using homotopy perturbation method.

Localized necking and bulging of finitely deformed residually stressed solid cylinder

In this paper, we investigate the influence of residual stress on the stability of a solid circular cylinder subject to axial extension. The nonlinear theory of elasticity is used to derive the equations governing the linearized incremental deformations superimposed on a known finitely deformed configuration. Specialized to the neo-Hookean model with residual stress, the bifurcation analysis results in an exact bifurcation condition for zero and periodic modes, based on the Stroh formalism. An expansion technique is adopted to treat singularities in the governing equations. We investigate three loading scenarios, specifically, gradual increase in axial stretch with constant residual stress and gradual increase in residual stress with fixed axial length or fixed axial force. In each case, the zero mode, corresponding to a localized bifurcation, occurs first. An explicit bifurcation condition for the zero mode is derived, which accounts for the effect of geometric dimensions, the residual stress, and the axial elongation on the stability of the solid cylinder. The critical values of the residual stress and the axial force for localized necking or bulging to occur are identified. In particular, we show that a reduction in residual stress delays the onset of localized necking. At constant values of pre-stretch, with 1 . 5 < λ < 2 . 10692 , localized necking occurs at a critical residual stress, whereas localized bulging occurs when λ > 2 . 10692 . We use the Maxwell equal-area rule to characterize the “two-phase” deformation consisting of necked and bulged regions. It is shown that the Maxwell values of stretch identify the radii of the two regions, which are connected by a transition zone that translates along the cylinder. At the completion of “two-phase” deformation, the stretch is again uniform.

Regulatory changes associated with the head to trunk developmental transition

BackgroundDevelopment of vertebrate embryos is characterized by early formation of the anterior tissues followed by the sequential extension of the axis at their posterior end to build the trunk and tail structures, first by the activity of the primitive streak and then of the tail bud. Embryological, molecular and genetic data indicate that head and trunk development are significantly different, suggesting that the transition into the trunk formation stage involves major changes in regulatory gene networks.ResultsWe explored those regulatory changes by generating differential interaction networks and chromatin accessibility profiles from the posterior epiblast region of mouse embryos at embryonic day (E)7.5 and E8.5. We observed changes in various cell processes, including several signaling pathways, ubiquitination machinery, ion dynamics and metabolic processes involving lipids that could contribute to the functional switch in the progenitor region of the embryo. We further explored the functional impact of changes observed in Wnt signaling associated processes, revealing a switch in the functional relevance of Wnt molecule palmitoleoylation, essential during gastrulation but becoming differentially required for the control of axial extension and progenitor differentiation processes during trunk formation. We also found substantial changes in chromatin accessibility at the two developmental stages, mostly mapping to intergenic regions and presenting differential footprinting profiles to several key transcription factors, indicating a significant switch in the regulatory elements controlling head or trunk development. Those chromatin changes are largely independent of retinoic acid, despite the key role of this factor in the transition to trunk development. We also tested the functional relevance of potential enhancers identified in the accessibility assays that reproduced the expression profiles of genes involved in the transition. Deletion of these regions by genome editing had limited effect on the expression of those genes, suggesting the existence of redundant enhancers that guarantee robust expression patterns.ConclusionsThis work provides a global view of the regulatory changes controlling the switch into the axial extension phase of vertebrate embryonic development. It also revealed mechanisms by which the cellular context influences the activity of regulatory factors, channeling them to implement one of several possible biological outputs.