Letteratura scientifica selezionata sul tema "Axial-bending coupling"

In this paper, an exact stiffness matrix and fixed-end load vector for nonprismatic beams having parabolic varying depth are derived. The principle of strain energy is used in the derivation of the stiffness matrix. The effect of both shear deformation and the coupling between axial force and the bending moment are considered in the derivation of stiffness matrix. The fixed-end load vector for elements under uniformly distributed or concentrated loads is also derived. The correctness of the derived matrices is verified by numerical examples. It is found that the coupling effect between axial force and bending moment is significant for elements having axial end restraint. It was found that the decrease in bending moment was in the range of 31.72%-42.29% in case of including the effect of axial force for the studied case. For midspan deflection, the decrease was 46.07% due to the effect of axial force generated at supports as a result of axial restraint.

This paper presents the nonlinear dynamic behavior of a flexible shaft. The shaft is mounted in two journal bearings and the axial load is supported by a hydrodynamic thrust bearing. The coupling between the axial thrust bearing behavior and the bending vibrations of the shaft is studied in particular. The shaft is modeled with typical beam finite elements. The dynamic behaviors of the fluid supports are considered as nonlinear. The dynamic behavior is analyzed using an unsteady time integration procedure. The paper shows the coupling between the axial dynamic behavior and the bending vibrations of the shaft.

A coupling dynamic model of a rotating cantilever beam is established by considering the effect of steady-state axial deformation on transverse bending deformation. The present method uses fully nonlinear Green strain–displacement relationship to derive the coupling terms in the equations of motion. The steady-state axial deformation is derived by analysing the equation of axial motion. An expression of the rotational speed limit is also obtained. The numerical results indicate that the steady-state axial deformation has a considerable effect on the transverse bending frequencies. A comparison of the present model with the absolute nodal coordinate formulation indicates that the two models are in good agreement, which proves the effectiveness and rationality of the present model.

Abstract Objective This study aimed to compare the biomechanical characteristics of two conical coupling plate (CCP) constructs in an ex vivo feline tibial fracture gap model. Study Design Paired tibiae harvested from eight recently euthanatized cats were alternately assigned to one of two stabilization groups. One tibia was stabilized with a standard, 6-hole, 2.5-mm CCP and the contralateral tibia was stabilized with a 6-hole, 2.5-mm prototype CCP (pCCP). Non-destructive cyclic four-point craniocaudal bending, mediolateral bending and axial compression testing were performed, and stiffness was recorded. The specimens were then loaded to failure in axial compression, and yield and failure loads were recorded. Results During non-destructive testing, the pCCP constructs were significantly stiffer than the CCP constructs in both modes of bending and axial loading. Both constructs demonstrated significantly greater craniocaudal bending stiffness compared with mediolateral bending. Yield load and failure load were significantly greater for the pCCP constructs. Conclusion The augmented design of the pCCP yielded superior mechanical characteristics during both non-destructive and destructive testings compared with constructs employing standard CCP. The more rigid design of the pCCP suggests that this implant may be better at withstanding greater loads, particularly when applied in a bridging fashion, during the postoperative convalescence. Further investigations are warranted to prospectively evaluate the clinical performance of the pCCP.

Using the viscouselastic artificial boundary, three conditions of long-span cable-stayed bridge are analyzed,such as pile cap consolidation, pile - structure and pile soil structure interaction. Natural frequency of bridge of pile - soil - structure coupling becomes small and cycle becomes long. The pile bottom reaction force decreased obviously, at the same time, the axial force , bending moment, axial force of cable, tower of axial force and bending moment is also reduced significantly. Cable-stayed bridge is a special flexible structure, so, static internal force calculation in the tower bottom consolidation pattern is safe, but the value is too large.

A lecture on the method to compute the the stress of V-tooth coupling under the actual operating conditions. the finite element analysis model of V-tooth coupling under the preload, axial load and torsion was established by used of the software ABAQUS,and the distribution of the bending stress at the root was obtained. The analytical method to compute the bending stress of V-tooth disk is deduced based on the basic principle of material mechanics, and the relative error within 10% compared with the results of finite element analysis.The paper work provide the reference for the precision design of V-tooth coupling.

The vertebrae of the cervical spine exhibit out-of-plane or coupled motion during axial rotation and lateral bending. Quantifying the range of motion (ROM) of this occurrence can aid the understanding of cervical spine injury mechanisms and disorders, as well as the development of new treatment methods. Previous studies have formulated ratios to describe coupled motion obtained from in-vitro examinations. The aim of the present study was to use in-vivo test data to develop mathematical relationships to quantify the coupled motion that occurs with axial rotation and lateral bending of the head-neck complex. Using a three-dimensional motion analyser it was possible to trace the coupling effect throughout the full range of unrestricted head-neck motion. Values for primary and coupled ROMs were obtained, showing no significant difference between male and female primary ROMs but a small disparity between male and female coupled ROMs. Regression equations were found to quantify coupled motion throughout the range of axial rotation and lateral bending. The present experimental study also examines the range of horizontally fixed axial rotation of the head to determine the minimum amount of coupled lateral bending that takes place, which has not been measured previously.

On propose par le biais de cette thèse un outil numérique pour l’étude statique et dynamique des structures viscoélastiques constituées de matériaux à gradient de propriétés (FGM) pour le contrôle des vibrations par amortissement passif. L’objectif est de mettre à la disposition des ingénieurs un code générique basé sur l’approche élément fini pour des calculs de dimensionnements sur des poutres sandwich FGM à âme viscoélastique destinées aux applications exigeant la légèreté et une bonne résistance thermique et mécanique comme le domaine de l’aérospatial, de l’automobile et du nucléaire. Pour atteindre cet objectif nous avons d’abord proposé un modèle numérique pour l’étude statique et des vibrations libres des poutres sandwich FGM à comportement élastique. Ce modèle élément fini est implémenté dans l’environnement du code Matlab. A l’aide de ce code nous comparons les différentes théories de poutre pour différentes configurations géométriques et différentes conditions aux limites. Ainsi, la limite de la théorie classique de poutre dans l’étude des structures courtes est soulignée. Aussi, avec ce modèle numérique, l’étude du couplage flexion membrane et rotation membrane est possible. De là, il est montré que les structures FGM sont très sensibles aux effets de couplages spatiaux et du gauchissement à cause de la répartition non symétrique de la matière dans leurs sections droites. Dans le code proposé, la résolution du problème de vibrations est possible grâce à des méthodes classiques de résolution des problèmes aux valeurs propres et vecteurs propres. Pour introduire de l’amortissement passif dans la structure sandwich FGM, nous avons proposé un modèle de poutre sandwich dont les faces sont en matériaux FGM et le cœur en matériaux viscoélastiques. Ce modèle est également implémenté dans le langage de programmation Matlab et proposé sous forme d’un outil générique. L’intérêt de cet outil numérique réside dans sa capacité à calculer les propriétés modales ainsi que le comportement de la structure sandwich FGM viscoélastique tout en prenant en compte la dépendance en fréquence du comportement viscoélastique, les conditions aux limites et le couplage membrane-flexion et membrane-rotation propres aux matériaux FGM. Le problème de vibrations libres est fortement non linéaire dans ce cas à cause de la non linéarité matériaux induite par la couche molle. Dans le code proposé, la résolution de ce problème est possible grâce au couplage de la technique d’homotopie, de la méthode asymptotique numérique et de la différentiation automatique. Par ce travail, l’apport des matériaux FGM dans l’amélioration du pouvoir amortissant des structures est démontré. Dans la suite du travail, nous proposons une formulation élément fini pour calculer l’amplitude des vibrations forcées des structures sandwich FGM viscoélastiques. La résolution du problème de vibration forcée est possible par utilisation de la méthode des bandes passantes. Une étude sur la contribution des matériaux FGM dans la réduction des amplitudes de vibrations est menée pour différentes lois viscoélastiques. Il est prouvé dans cette étude que par un contrôle direct du gradient de composition des matériaux FGM, il est possible d’optimiser le pouvoir amortissant des structures même pour les modes de basses fréquences pour lesquels les matériaux composites classiques présentent un pouvoir amortissant nécessitant des améliorations
This thesis proposes a numerical tool for the static and dynamic study of viscoelastic structures made of Functionally Graded Materials (FGM) for vibration control by passive damping. The objective is to make available to engineers a generic code based on the finite element approach for sizing calculations on FGM sandwich beam with viscoelastic core for applications requiring lightness and good thermal and mechanical resistance such as aerospace, automotive and nuclear. To reach this objective we first proposed a numerical model for the static and free vibration study of FGM sandwich beams with elastic behavior. This finite element model is implemented in the Matlab code environment. Using this code, we compare different beam theories for different geometric properties and boundary conditions. Thus, the limit of the classical beam theory in the study of short structures is highlighted. Also with this numerical model, the study of axial-bending and axial-rotation coupling is possible. From this, it is shown that FGM structures are very sensitive to spatial coupling and warping effects because of the non-symmetrical distribution of the material in their cross sections. In the proposed code, the resolution of the vibration problem is possible using classical eigenvalue and eigenvector problem solving methods. Then to introduce passive damping in the FGM sandwich structure, we proposed a sandwich beam model with FGM materials faces and viscoelastic materials core. This model is also implemented in the Matlab language and proposed as a generic tool. The interest of this numerical tool lies in its ability to compute the modal properties as well as the behavior of the viscoelastic FGM sandwich beam while taking into account the frequency dependence of the viscoelastic behavior, the boundary conditions and the axial-bending and axial-rotation coupling specific to FGM materials. The free vibration problem is non-linear in this case due to the material non-linearity induced by the soft layer. In the proposed code, the resolution of this problem is possible thanks to the coupling of the homotopy technical, the asymptotic numerical method and the automatic differentiation. Through this work, the contribution of FGM materials in the improvement of the damping power of structures is highlighted. In the continuation of the work, we propose a finite element formulation to compute the amplitude of forced vibrations of viscoelastic FGM sandwich structures. The resolution of the forced vibration problem is possible by using the bandwidths method. A study on the contribution of FGM materials in the reduction of vibration amplitudes is carried out for different viscoelastic laws. It is proved in this study that by a direct control of the composition gradient of FGM materials it is possible to optimize the damping power of structures even for low frequency modes for which classical composite materials have a damping power requiring improvement

Abstract This paper presents the results of the second part of an investigation of the dynamic characteristics of an axial spline coupling in high-speed rotating machinery. In the experimental method described herein, the bending moments and angular deflections transmitted across the axial spline coupling were measured while the nonrotating shaft was excited by an external shaker. The effects of external force and frequency on the angular stiffness and damping coefficients were investigated. The angular stiffness and damping coefficients were used to perform a linear steady-state rotordynamics stability analysis, and the unstable natural frequency was calculated and compared to experimental measurements. In addition, the mechanism and source of internal rotor friction instability caused by the axial spline couplings was studied.

A novel hyperbolic composite coupling is proposed. In addition to enjoying the advantages of composite materials, the proposed coupling can be readily integrated with composite drive shaft into a single unit. A mathematical model of the coupling is developed based on the Timoshenko beam theory using the energy approach and the extended Lagrange’s equations. The corresponding discrete equation of vibration is obtained using the finite element method and solved for the natural frequencies using MATLAB. The dynamic characteristics of the coupling (Axial, torsional and bending natural frequencies) are studied in order to assess the merits and potential of the proposed coupling.

The contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A dynamic model of the drillstring including both drillpipe and drillcollars is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach together with the finite element method. The model accounts for the gyroscopic effect, the torsional/bending inertia coupling, the axial/bending geometric nonlinear coupling, and the stiffening effect due to the gravitational force field. Reduced order modal form of the dynamic equations is obtained using complex modal transformation. The developed model is integrated into a computational scheme to calculate time-response of the drillstring due to torsional excitations.

Abstract This paper provided the first opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in high-speed turbomachinery. A unique test methodology and data reduction procedures were developed. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a non-rotating shaft was excited by an external shaker. A rotordynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. In addition, sensitivity analyses were performed to demonstrate that the accuracy of the dynamic coefficients do not rely on the accuracy of the data reduction procedures.

This paper concerns the response of a single-layered strand cable of helical wires with wires-to-core contact under free and constant curvature constrained bending. The stranded cable under static-loading conditions experiences any combination of tension, torsion and bending. A linear finite element model for helical wire strand cable for both bending cases was developed and their bending response for various load steps was analyzed. The responses thus observed were compared with the theoretical prediction reported by the present authors in the literature. The present authors have developed a theoretical model using the thin rod theory and presented a linear stiffness matrix establishing the relationship between the axial, torsional and flexural rigidities and the coupling parameters of the cable.

In this paper, an analytical model is proposed to describe the nonlinear vibration of blades on floating offshore wind turbine (FOWT). The bending-torsion coupling equations are derived based on Hamilton’s principle. Comparing with the classical Newtonian method, this approach is more mathematically rigorous and systematic. The flapwise and edgewise deformation, the torsion as well as axial extension of the blades are all included in the model. A set of partial differential equations governing the coupled nonlinear vibration is established, and the results are compared with the multi-body model. Some details about the solution of equations are discussed. The eigen values of a rotating blade is also calculated. The structural model proposed in this paper can be widely used in the future study. For example, it can be coupled with an aerodynamic model to study the aeroelastic properties of the wind turbine blades. The effect of platform motion on blade dynamic response can also be obtained based on this analytical model.

Abstract A finite-element stress analysis of a one-piece, integrated, all-composite shaft and coupling is presented. In addition to a brief discussion of design-driving parameters, some limitations of the analytical techniques used for design development are described. The 3D finite-element method (FEM) was then used to evaluate critical stresses and strains experienced by the shaft coupling. A comparison of the results from the finite-element analysis and those from static bending, axial, and torsional tests conducted on these prototype shafts yielded excellent correlation. Some important considerations in the development of the FE model and the correlation of results with tests, especially in the design of composite materials, are addressed.

In this paper, the limitations of the linear elasticity finite element solutions in describing the coupling between the extensional and bending displacements are discussed. The fact that incorrect unstable solutions are obtained for models with more than one finite element using the linear elasticity theory motivates the analytical study of the rotating beam presented in this paper. It is shown, as documented in the literature, that the instability of the incorrect solution is directly related to the singularity of the stiffness matrix, and such an instability occurs when the angular velocity reaches the first bending fundamental frequency of the beam. The increase in the number of finite elements only leads to an increase of the critical speed. Crucial in the analysis presented in this paper is the fact that the mass matrix and the form of the elastic forces obtained using the absolute nodal coordinate formulation remain the same under orthogonal coordinate transformation. The absolute nodal coordinate formulation, in contrast to conventional finite element formulations, does account for the effect of the coupling between bending and extension. A similar concept can be incorporated into the finite element floating frame of reference formulation in order to introduce coupling between the axial and bending displacements. Nonetheless, when the linear theory of elasticity is used and no special measures are taken to account for the coupling effect as proposed in the literature, there always exists a critical velocity regardless of the number of finite elements used.

The advantage of composite riser is more pronounced due to its light weight and reduced axial tension and bending moment. Its characteristics provide more flexibility in the design of riser system such as stress joint, tensioner or even the platform hull. The composite riser under study consists of alternative hoop and axial layers. There is a marginal coupling between these two orientations hence, the riser is spatially orthotropic. The pressure capabilities of riser are governed by the performance of hoop layers under combined fluctuating axial tension and bending moment. The internal steel liner provided to ensure no leakage often limits the composite riser capabilities. The steel liner provided for production inevitably carries major share of loads. An attempt has been made to carry out a detailed local analysis of a segmental length under critical loads. Damage analysis for various combinations of axial tension and bending moment are performed. The results of global analysis are used to act as boundary/initial condition for the local and detailed dynamic analysis of the segmental length modeled as finite element assemblage of shell elements. The critical stress time histories obtained by global analysis are applied at the local level. The composite layers sustained the random stresses that lead to the failure of the composite. Some realistic failure criteria are chosen to check the damage at local level.

Abstract In recent years, earthworm-like robots have been widely concerned by researchers because of their outstanding mobility in various environments. However, most of them only possess up to 2D locomotion owing to the limitation in their structures and materials. Origami springs, with extraordinary multi-mode deformation ability, have promising potential for 3D locomotion. In this study, an analytic model of the origami spring is established by introducing virtual creases to the facets. Four topologically different configurations of a single cell are therefore obtained by changing the mountain and valley assembly of the virtual creases. By iteratively stacking the cells, a rigid-folding model is derived. Besides the conventional axial stretch-twist-coupling, the proposed modeling can also describe the off-axial deformation, including the point-to-point bending, and line-to-line bending. In addition, the potential energy of the multi-mode deformations is investigated by specifying the torsional spring on the creases of the rigid-folding kinematic model. Mechanical properties, including the nonlinear restoring force under axial deformation, and the approximate linear bending moment under off-axial deformation is observed. What’s more, a mode switching phenomenon is for the first time revealed once the structure is folded to the kinematic bifurcation point, and is experimentally evaluated via PETE film-based prototypes. We believe these findings could inspire the avenue for the next generation of the earthworm-like robot with multi-modal motions.