Journal articles: 'Axial-bending coupling'

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Al-Janabi, Musab Aied Qissab. "Exact Stiffness Matrix for Nonprismatic Beams with Parabolic Varying Depth." Journal of Engineering 19, no. 10 (June 5, 2023): 1212–25. http://dx.doi.org/10.31026/j.eng.2013.10.02.

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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.

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Berger, Se´bastien, Olivier Bonneau, and Jean Fre^ne. "Influence of Axial Thrust Bearing on the Dynamic Behavior of an Elastic Shaft: Coupling Between the Axial Dynamic Behavior and the Bending Vibrations of a Flexible Shaft." Journal of Vibration and Acoustics 123, no. 2 (November 1, 2000): 145–49. http://dx.doi.org/10.1115/1.1355243.

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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.

3

Zhao, Guowei, and Zhigang Wu. "Effects of steady-state axial deformation on bending frequency of rotating cantilever beam." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 24 (September 19, 2016): 4521–27. http://dx.doi.org/10.1177/0954406216669534.

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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.

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MacArthur, Sandra L., Matthew D. Johnson, and Daniel D. Lewis. "Biomechanical Comparison of Two Conical Coupling Plate Constructs for Cat Tibial Fracture Stabilization." Veterinary and Comparative Orthopaedics and Traumatology 33, no. 04 (April 21, 2020): 252–57. http://dx.doi.org/10.1055/s-0040-1708497.

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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.

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Chen, Wen Yuan. "Analysis of Dynamic Characteristics of Pile-Soil Coupling Effect in Consideration of Large Span Cable-Stayed Bridge." Applied Mechanics and Materials 501-504 (January 2014): 1270–73. http://dx.doi.org/10.4028/www.scientific.net/amm.501-504.1270.

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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.

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Cui, Zhiming, Zihe Liang, and Jaehyung Ju. "A non-centrosymmetric square lattice with an axial–bending coupling." Materials & Design 216 (April 2022): 110532. http://dx.doi.org/10.1016/j.matdes.2022.110532.

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Lei, Dun Cai, and Jin Yuan Tang. "The Design Method of V-Tooth Coupling." Advanced Materials Research 871 (December 2013): 347–51. http://dx.doi.org/10.4028/www.scientific.net/amr.871.347.

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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.

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Baisden, Jamie L., Brian D. Stemper, David Barnes, Narayan Yognandan, and Frank A. Pintar. "Normative Lumbar Spine Coupling Relationships between Axial Rotation and Lateral Bending." Spine Journal 10, no. 9 (September 2010): S124. http://dx.doi.org/10.1016/j.spinee.2010.07.324.

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Wang, Chen, Hamed Haddad Khodaparast, Michael Ian Friswell, and Alexander David Shaw. "An equivalent model of corrugated panels with axial and bending coupling." Computers & Structures 183 (April 2017): 61–72. http://dx.doi.org/10.1016/j.compstruc.2017.01.008.

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Senouci, M., D. FitzPatrick, J. F. Quinlan, H. Mullett, L. Coffey, and D. McCormack. "Quantification of the coupled motion that occurs with axial rotation and lateral bending of the head-neck complex: An experimental examination." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 221, no. 8 (August 1, 2007): 913–19. http://dx.doi.org/10.1243/09544119jeim265.

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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.

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Wang, Fan, and Xing Wang. "Tangent Stiffness Matrix of Single-Layer Reticulated Shell’s Members with Rigid Ends." Advanced Materials Research 479-481 (February 2012): 1997–2000. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1997.

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In the paper, the axial stiffness and bending stiffness of single-layer reticulated shell’s joint are considering together, non-linear beam-column element with rigid springs and rigid ends is taken as the analysis model of members of single-layer reticulated shell, a tangent stiffness matrix of members of single-layer reticulated shell considering joint’s stiffness is derived on the basis of the beam-column theory. In this matrix, not only coupling effects of bending in two axes but also joint’s stiffness and joint’s size are considered, not only the effect of axial force on bending but also the effect of axial force on torsion are considered. All higher order terms in the displacement function are considered. So this matrix is perfect and more precise than the tangent stiffness matrix from C.Oran, and this model can be suited to the non-linear stablity analysis of single-layer reticulated shell.

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Huang, Jianyou, Chia-Ou Chang, and Chien-Cheng Chang. "Analysis of Structural Vibrations of Vertical Axis Wind Turbine Blades via Hamilton’s Principle — Part 1: General Formulation." International Journal of Structural Stability and Dynamics 20, no. 09 (August 2020): 2050098. http://dx.doi.org/10.1142/s0219455420500984.

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Energy harvesting by wind turbines is of great concern in many countries/areas, yet its safety is inevitably related to the structural vibration of the turbine system. In this study, we present a complete linear analysis of structural vibrations for vertical axis wind turbines (VAWTs) based on Euler’s beam theory by Lagrangian mechanics. The un-deformed blade is assumed to be vertically straight. There are several findings from solving the resultant equations which represent four dimensions of deformation, involving motion: lateral bending-chordwise bending-axial torsion-axial extension (BBTE) (1) There is no deformation coupling between axial tension and axial torsion. (2) The natural frequencies of the blade are mainly determined by lateral bending, and [Formula: see text] ([Formula: see text]) denote the natural frequencies determined solely by lateral bending. (3) The centrifugal force credited to blade deformation is the primary factor that modifies the natural frequencies. (4) The Coriolis force can exist only in the coupled system, but in any case, the Coriolis force will not be generated by coupling lateral bending and axial tension. (5) The Coriolis force, when lateral bending is coupled with chord bending or axial torsion, can only slightly modify the natural frequencies. (6) In the case of fixed speed of rotation, [Formula: see text], where [Formula: see text] is angular speed and [Formula: see text] is the distance from the rotation axis to the elastic center of the blade: given [Formula: see text]-the blade length to chord ratio, it is found that the natural frequencies [Formula: see text] of the blade are, in close approximations, inversely proportional to [Formula: see text], i.e. [Formula: see text], where [Formula: see text] is the base chord length and [Formula: see text] is the base blade length. (7) In the general case of rotating blade ([Formula: see text], we let [Formula: see text] denote the [Formula: see text]th natural frequency when [Formula: see text]. It is found that the natural frequencies [Formula: see text] are closely approximated by [Formula: see text] (8) The material damping yields the imaginary part of the modified system frequency [Formula: see text], which deteriorates the energy absorption rate of the blade. Perturbation analysis with a solvability condition is performed to determine the imaginary part of [Formula: see text]. Given the same material, [Formula: see text] is inversely proportional to [Formula: see text], i.e. [Formula: see text].

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Kam, Wern, Yong Sheng Ong, Sinead O’Keeffe, Waleed S. Mohammed, and Elfed Lewis. "An Analytical Model for Describing the Power Coupling Ratio between Multimode Fibers with Transverse Displacement and Angular Misalignment in an Optical Fiber Bend Sensor." Sensors 19, no. 22 (November 14, 2019): 4968. http://dx.doi.org/10.3390/s19224968.

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The power coupling ratio between step-index multimode fibers caused by combined transversal and angular misalignment is calculated. A theoretical description of the coupling efficiency between two optical fibers based on geometrical optics is provided. The theoretical calculations are collaborated by experiments, determining the power coupling ratio between three output fibers with an axial offset and angular misalignment with a single input fiber. The calculation results are in good agreement with experimental results obtained using a previously fabricated optical fiber sensor for monitoring physiological parameters in clinical environments. The theoretical results are particularly beneficial for optimizing the design of optical fiber bending sensors that are based on power coupling loss (intensity) as the measurement interrogation requires either axial displacement, angular misalignment, or both.

14

Wang, Xing. "Elememt Stiffness Matrix of Members of Reticulated Shell with End Springs." Applied Mechanics and Materials 94-96 (September 2011): 289–92. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.289.

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In this paper, a tangent stiffness matrix of members with end springs of reticulated shell is derived on the basis of Timoshenko’s beam-column theory. In this matrix, joint’s axial stiffness and bending stiffness are considering together, non-linear beam-column element with end springs and rigid ends is taken as the analysis model of members of reticulated shell. In this matrix, not only coupling effects of bending in two axes but also joint’s stiffness and joint’s size are considered, not only the effect of axial force on bending but also the effect of axial force on torsion are considered. Higher order terms in the displacement function are considered. So this matrix is perfect and more precise than Oran’s tangent stiffness matrix. An example of a single layer reticulated shell is provided, which verified the correctness and good accuracy of the present model, and this model can be suited to the non-liner stablity analysis of reticulated shell.

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Hottmann, Natasha M., Matthew D. Johnson, Scott A. Banks, David Tuyn, and Daniel D. Lewis. "Biomechanical Comparison of Two Locking Plate Constructs for the Stabilization of Feline Tibial Fractures." Veterinary and Comparative Orthopaedics and Traumatology 33, no. 02 (December 13, 2019): 089–95. http://dx.doi.org/10.1055/s-0039-3399572.

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Abstract Objectives The aim of this study was to compare the biomechanical characteristics of locking compression plate (LCP) and conical coupling plate (CCP) constructs for the stabilization of experimentally induced gap fractures in cat tibiae. Materials and Methods Pelvic limbs were harvested from eight cat cadavers. Paired tibiae were stripped of all soft tissues, and randomly assigned to the LCP or CCP stabilization group. An eight-hole 2.7 mm LCP or a six-hole 2.5 mm CCP was applied to the medial surface of each tibia. A 1-cm segment of the tibia was excised centrally beneath the plate. The specimens were potted, then tested in non-destructive four-point craniocaudal and mediolateral bending, followed by non-destructive axial compression. Each construct was subsequently loaded to failure in axial compression. Bending and axial stiffness, yield load and failure load were calculated for each specimen. Results The LCP constructs were significantly stiffer than the CCP constructs when subjected to non-destructive bending and axial loading. Craniocaudal bending stiffness was significantly greater than mediolateral bending stiffness for both constructs. Yield load and failure load were significantly greater for LCP constructs compared with CCP constructs. Clinical Significance LCP may be a more suitable implant for stabilizing complex diaphyseal tibial fractures in cats. Additional supplemental fixation should be considered when using CCP to stabilize unreconstructed diaphyseal tibial fractures in cats. Further clinical investigation of both implants is recommended.

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Wu, Zhi-Yuan, Han Yan, Lin-Chuan Zhao, Ge Yan, Zhi-Bo Yang, Hai-Feng Hu, and Wen-Ming Zhang. "Axial-bending coupling vibration characteristics of a rotating blade with breathing crack." Mechanical Systems and Signal Processing 182 (January 2023): 109547. http://dx.doi.org/10.1016/j.ymssp.2022.109547.

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Kang, Ji, Tae-Jeong Lim, and Hyun-Woo Park. "Predicting the Modal Frequencies of a Cracked Beam Considering Axial-bending Coupling." Transactions of the Korean Society for Noise and Vibration Engineering 29, no. 2 (April 20, 2019): 270–72. http://dx.doi.org/10.5050/ksnve.2019.29.2.270.

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Gupta, Prakhar, and Ajeet Kumar. "Phonons in chiral nanorods and nanotubes: A Cosserat-rod-based continuum approach." Mathematics and Mechanics of Solids 24, no. 12 (June 30, 2019): 3897–919. http://dx.doi.org/10.1177/1081286519856407.

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A Cosserat-rod-based continuum approach is presented to obtain phonon dispersion curves of flexural, torsional, longitudinal, shearing, and radial breathing modes in chiral nanorods and nanotubes. Upon substituting the continuum wave form in the linearized dynamic equations of stretched and twisted Cosserat rods, we obtain an analytical expression of a coefficient matrix (in terms of the rod’s stiffnesses, induced axial force, and twisting moment) whose eigenvalues and eigenvectors give us frequencies and mode shapes, respectively, for each of the above phonon modes. We show that, unlike the case of achiral tubes, these phonon modes are intricately coupled in chiral tubes owing to extension–torsion–inflation and bending–shear couplings inherent in them. This coupling renders the conventional approach of obtaining stiffnesses from the long wavelength limit slope of dispersion curves redundant. However, upon substituting the frequencies and mode shapes (obtained independently from phonon dispersion molecular data) in the eigenvalue–eigenvector equation of the above-mentioned coefficient matrix, we are able to obtain all the stiffnesses (bending, twisting, stretching, shearing, and all coupling stiffnesses corresponding to extension–torsion, extension–inflation, torsion–inflation, and bending–shear couplings) of chiral nanotubes. Finally, we show unusual effects of the single-walled carbon nanotube’s chirality as well as stretching and twisting of the nanotube on its phonon dispersion curves obtained from the molecular approach. These unusual effects are accurately reproduced in our continuum formulation.

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Ku, C. P. Roger, J. F. Walton, and J. W. Lund. "Dynamic Coefficients of Axial Spline Couplings in High-Speed Rotating Machinery." Journal of Vibration and Acoustics 116, no. 3 (July 1, 1994): 250–56. http://dx.doi.org/10.1115/1.2930421.

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This paper provided the first opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in highspeed turbomachinery. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a nonrotating 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. The effects of external force and frequency were also 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 the experimental measurements.

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Wang, Guoxu, Yapeng Li, and Yegao Qu. "Effects of internal resonance on the nonlinear acoustic radiation induced by axial and bending vibration of hyperelastic cantilever beams." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 268, no. 7 (November 30, 2023): 1143–49. http://dx.doi.org/10.3397/in_2023_0173.

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This paper provides a numerical nonlinear vibro-acoustic study of a slender hyperelastic cantilever beam with 2:1 internal resonance condition. The model of beam includes geometric and material nonlinearities, while the model of acoustics includes the Arbitrary Lagrangian-Eulerian frame and the perfectly matched layers. The finite element method and the time integration method are used to discretize the structure and acoustic field. A loosely coupled serially staggered procedure is used to compute the variable values of structure and acoustic field. The results show that the transition from the axial mode to the bending mode of beam can be excited by the axial mode excitation. This leads to the alteration of acoustic directivity pattern and frequency components. Besides, due to the weak or strong coupling effects of axial and bending modes of beam, the symmetric or asymmetric acoustic directivity patterns can be witnessed in different frequency components.

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Lei, Zhiyang, Jinpeng Su, and Hongxing Hua. "Longitudinal and Transverse Coupling Dynamic Properties of a Timoshenko Beam with Mass Eccentricity." International Journal of Structural Stability and Dynamics 17, no. 07 (September 2017): 1750077. http://dx.doi.org/10.1142/s0219455417500778.

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Non-uniform mass distribution on a beam will lead to the coupling between lateral and axial vibrations of the beam. To simulate the mass eccentricity, a double-layered Timoshenko beam model is developed. Based on Hamilton’s principle, the coupled governing equations are derived and mass and stiffness coupling coefficients are also derived. Moreover, the spectral element method (SEM), with high frequency accuracy by employing the dynamic shape functions, is utilized to study the dynamic properties of the beam. In addition, a corresponding finite element model is established to verify the SEM model. The coupling vibration characteristics are investigated and the coupling mechanism is revealed. Furthermore, the effects of mass non--uniformity on the free vibration and forced vibration of the beam with classical and flexible boundary conditions are analyzed. Finally, an optimal control method for reducing the contributions of bending modes under the axial excitation is presented with the results displayed.

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Su, Jinpeng, Zhiyang Lei, and Hongxing Hua. "Axial–bending coupling vibration of mass eccentric double-beam system with discrete elastic connections." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 231, no. 2 (September 21, 2016): 555–68. http://dx.doi.org/10.1177/1475090216669890.

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The existence of mass eccentricity will lead to the energy transfer between axial and flexural vibrations of a beam. To study the coupling properties of a double-Timoshenko beam system, a non-uniform coupled double-beam system is modeled in which the upper beam is typical and the lower beam is mass eccentric simulated by a non-uniform two-layer Timoshenko beam. By incorporating Hamilton’s principle and spectral element method, the axial–bending coupled governing equations of the system are derived and the approach can also be easily used to analyze the influences of the parameters and other coupled beam systems. Both the free and forced vibration results of a double-beam system by this method are consistent with the corresponding finite element model’s and thus this method is validated. The coupled properties and their mechanism are revealed. The influences of axial and transverse flexible connection on the coupling properties including free and forced vibration are investigated. A systematic matching principle of reducing the vibration of the coupled system is proposed.

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Dong, Shi Min, Wan Sheng Zhang, Guo Hong Chai, Ming Ming Xing, and Hong Zhang. "Simulating Research on Rod String’s Gyro Effect Caused by Eccentric Rotation in Circular Tube." Applied Mechanics and Materials 130-134 (October 2011): 2294–300. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2294.

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Based on the influences of eccentrical rotating inertial centrifugal force and axial force on the rod string’s lateral bending deformation, the finite beam element model of rod string’s bending deformation is established. The constraint to rod string’s bending deflection exerted by inwall of circular tube and the distinction of the constraint to rod string’s deflection because of the different gaps between rod string to circular tube and coupling to circular tube are both taken into account. Meanwhile, removable spring elements with two directions are adopted, by which the non-linear contact problem between the rod string and circular tube is well resolved. Combining space beam element and spring elements with two directions, the corresponding finite element simulating program is also developed. Several simulating results can be shown as follows: eccentric rotation of rod string is able to produce gyro effect in vertical circular tube; The shape of the rod string’s deformation is a spiral which is thin on the upper-part and dense on the under-part; Gyro wave numbers are affected obviously by rotating speed, eccentricity, axial concentrated force, axial distributed force and length of the rod string.

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Lee, Jung Woo. "Free Vibration Analysis of Three Layered Beams with a Soft-Core Using the Transfer Matrix Method." Applied Sciences 13, no. 1 (December 28, 2022): 411. http://dx.doi.org/10.3390/app13010411.

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In this study, the free vibration characteristics of symmetric three-layered beams with a soft core, whereby the mass of the core could be ignored, were investigated. The coupling effect of the axial and bending displacements owing to the presence of the soft core was considered. Classical beam theory was employed for analyzing the top and bottom layers, and only the shear deformation was applied for the core layer. The frequency determinant was deduced using the transfer matrix method. The efficacy of the method was demonstrated through a comparison with the natural frequencies obtained in previous studies. To determine the physical phenomena caused by the exchange process in the order of modes of such beams, a new analytical method is proposed. As an example, the dynamic behavior of a three-layered beam was analyzed by examining the changes in the strain energies related to the natural frequencies and mode shapes. All bending-dominated modes were accompanied by the axial displacements because of the existence of a core layer, whereas the axial-dominated modes were uncoupled with the bending displacements. In addition, the efficiency of the proposed method was demonstrated through relevant discussions of the predicted results.

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Tadeo, A. T., K. L. Cavalca, and M. J. Brennan. "Dynamic characterization of a mechanical coupling for a rotating shaft." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 3 (August 18, 2010): 604–16. http://dx.doi.org/10.1243/09544062jmes2214.

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This article concerns the dynamic characterization of a flexible coupling that connects two co-axial shafts. Four different lumped parameter coupling models from the literature are investigated to see which model could best predict the dynamic behaviour of the coupling. The finite-element method was used to model the rotor dynamic system incorporating the coupling. Frequency response functions from this model were compared with measured frequency response functions from the rotor test rig with the shaft and coupling rotating at a specific speed. Parameters from the model were adjusted to minimize an objective function involving the measured and predicted frequency response functions. It was found that the simplest model of the coupling that could reasonably represent the coupling involves rotational (bending) stiffness and damping.

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Scaccabarozzi, Diego, and Bortolino Saggin. "Measurement of Stress Waves Propagation in Percussive Drilling." Sensors 21, no. 11 (May 25, 2021): 3677. http://dx.doi.org/10.3390/s21113677.

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This work describes the results of a test campaign aimed to measure the propagation of longitudinal, torsional, and flexural stress waves on a drill bit during percussive rock drilling. Although the stress wave propagation during percussive drilling has been extensively modeled and studied in the literature, its experimental characterization is poorly documented and generally limited to the detection of the longitudinal stress waves. The activity was performed under continuous drilling while varying three parameters, the type of concrete, the operator feeding force, and the drilling hammer rotational speed. It was found that axial stress wave frequencies and spectral amplitudes depend on the investigated parameters. Moreover, a relevant coupling between axial and torsional vibrations was evidenced, while negligible contribution was found from the bending modes. A finite element model of the drill bit and percussive element was developed to simulate the impact and the coupling between axial and torsional vibrations. A strong correlation was found between computed and measured axial stress spectra, but additional studies are required to achieve a satisfactory agreement between the measured and the simulated torque vibrations.

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Jing, Zhao, Qin Sun, Ke Liang, and Jianqiao Chen. "Closed-Form Critical Buckling Load of Simply Supported Orthotropic Plates and Verification." International Journal of Structural Stability and Dynamics 19, no. 12 (December 2019): 1950157. http://dx.doi.org/10.1142/s0219455419501578.

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The buckling mode is important to determine the critical load of specially orthotropic rectangular plates under axial compression with simply supported boundary. However, in classical laminated plate theory (CLPT), the critical buckling mode can only be obtained by iterative or numerical methods. This paper derives the critical buckling mode mathematically and presents the critical buckling load in closed form. By taking advantage of the derived closed-form solution, it is convenient to investigate the effects of aspect ratio, load ratio, and fiber orientation on the buckling load, and the parameters affecting the buckling mode can be easily obtained. The first-order shear deformation theory (FSDT)-based finite element method is developed to verify the closed-form solution. The bending-torsional coupling effects are analyzed and discussed to assess the approximation of the buckling behavior of specially orthotropic plates to general laminates. The obtained finite element solutions of general laminates are compared with the closed-form solutions of specially orthotropic plates. The accuracy of approximation of the buckling behavior of specially orthotropic plates to the general laminates increases as the bending-torsional coupling coefficients decrease. The closed-form solution can be applied to laminates with small bending-torsional coupling coefficients.

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Fall, Massamba, Zhengguo Gao, and Becaye Cissokho Ndiaye. "Driven Pile Effects on Nearby Cylindrical and Semi-Tapered Pile in Sandy Clay." Applied Sciences 11, no. 7 (March 25, 2021): 2919. http://dx.doi.org/10.3390/app11072919.

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A pile foundation is commonly adopted for transferring superstructure loads into the ground in weaker soil. They diminish the settlement of the infrastructure and augment the soil-bearing capacity. This paper emphases the pile-driving effect on an existing adjacent cylindrical and semi-tapered pile. Driving a three-dimensional pile into the ground is fruitfully accomplished by combining the arbitrary Lagrangian–Eulerian (ALE) adaptive mesh and element deletion methods without adopting any assumptions that would simplify the simulation. Axial forces, bending moment, and lateral displacement were studied in the neighboring already-installed pile. An investigation was made into some factors affecting the forces and bending moment, such as pile spacing and the shape of the already-installed pile (cylindrical, tapered, or semi-tapered). An important response was observed in the impact of the driven pile on the nearby existing one, the bending moment and axial forces were not negligible, and when the pile was loaded, it was recommended to consider the coupling effect. Moreover, the adjacent semi-tapered pile was subjected to less axial and lateral movement than the cylindrical one with the same length and volume for taper angles smaller than 1.0°, and vice versa for taper angles greater than 1.4°.

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Zhu, Q. A., Y. B. Park, S. G. Sjovold, C. A. Niosi, D. C. Wilson, P. A. Cripton, and T. R. Oxland. "Can extra-articular strains be used to measure facet contact forces in the lumbar spine? An in-vitro biomechanical study." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 222, no. 2 (February 1, 2008): 171–84. http://dx.doi.org/10.1243/09544119jeim290.

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Experimental measurement of the load-bearing patterns of the facet joints in the lumbar spine remains a challenge, thereby limiting the assessment of facet joint function under various surgical conditions and the validation of computational models. The extra-articular strain (EAS) technique, a non-invasive measurement of the contact load, has been used for unilateral facet joints but does not incorporate strain coupling, i.e. ipsilateral EASs due to forces on the contralateral facet joint. The objectives of the present study were to establish a bilateral model for facet contact force measurement using the EAS technique and to determine its effectiveness in measuring these facet joint contact forces during three-dimensional flexibility tests in the lumbar spine. Specific goals were to assess the accuracy and repeatability of the technique and to assess the effect of soft-tissue artefacts. In the accuracy and repeatability tests, ten uniaxial strain gauges were bonded to the external surface of the inferior facets of L3 of ten fresh lumbar spine specimens. Two pressure-sensitive sensors (Tekscan) were inserted into the joints after the capsules were cut. Facet contact forces were measured with the EAS and Tekscan techniques for each specimen in flexion, extension, axial rotation, and lateral bending under a ±7.5 N m pure moment. Four of the ten specimens were tested five times in axial rotation and extension for repeatability. These same specimens were disarticulated and known forces were applied across the facet joint using a manual probe (direct accuracy) and a materials-testing system (disarticulated accuracy). In soft-tissue artefact tests, a separate set of six lumbar spine specimens was used to document the virtual facet joint contact forces during a flexibility test following removal of the superior facet processes. Linear strain coupling was observed in all specimens. The average peak facet joint contact forces during flexibility testing was greatest in axial rotation (71±25 N), followed by extension (27±35 N) and lateral bending (25±28 N), and they were most repeatable in axial rotation (coefficient of variation, 5 per cent). The EAS accuracy was about 20 per cent in the direct accuracy assessment and about 30 per cent in the disarticulated accuracy test. The latter was very similar to the Tekscan accuracy in the same test. Virtual facet loads (r.m.s.) were small in axial rotation (12 N) and lateral bending (20 N), but relatively large in flexion (34 N) and extension (35 N). The results suggested that the bilateral EAS model could be used to determine the facet joint contact forces in axial rotation but may result in considerable error in flexion, extension, and lateral bending.

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Scholten, P. J. M., and A. G. Veldhuizen. "The Influence of Spine Geometry on the Coupling between Lateral Bending and Axial Rotation." Engineering in Medicine 14, no. 4 (October 1985): 167–71. http://dx.doi.org/10.1243/emed_jour_1985_014_041_02.

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Ranzo, Giulio, Marco Petrangeli, and Paolo Emilio Pinto. "Vertical oscillations due to axial-bending coupling during seismic response of RC bridge piers." Earthquake Engineering & Structural Dynamics 28, no. 12 (December 1999): 1685–704. http://dx.doi.org/10.1002/(sici)1096-9845(199912)28:12<1685::aid-eqe890>3.0.co;2-7.

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Towliat Kashani, M. Tahmaseb, Supun Jayasinghe, and Seyed M. Hashemi. "On the Flexural-Torsional Vibration and Stability of Beams Subjected to Axial Load and End Moment." Shock and Vibration 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/153532.

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The free vibration of beams, subjected to a constant axial load and end moment and various boundary conditions, is examined. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the differential equations governing coupled flexural-torsional vibrations and stability of a uniform, slender, isotropic, homogeneous, and linearly elastic beam, undergoing linear harmonic vibration, are first reviewed. The existing formulations are then briefly discussed and a conventional finite element method (FEM) is developed. Exploiting the MATLAB-based code, the resulting linear Eigenvalue problem is then solved to determine the Eigensolutions (i.e., natural frequencies and modes) of illustrative examples, exhibiting geometric bending-torsion coupling. Various classical boundary conditions are considered and the FEM frequency results are validated against those obtained from a commercial software (ANSYS) and the data available in the literature. Tensile axial force is found to increase natural frequencies, indicating beam stiffening. However, when a force and an end moment are acting in combination, the moment reduces the stiffness of the beam and the stiffness of the beam is found to be more sensitive to the changes in the magnitude of the axial force compared to the moment. A buckling analysis of the beam is also carried out to determine the critical buckling end moment and axial compressive force.

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Xi, Jing Jing, Qing Ning Li, and Tian Li Wang. "Calculation of State Transfer of Curved Bridge." Advanced Materials Research 243-249 (May 2011): 1701–6. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.1701.

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The field transfer matrixs and the point transfer matrixs can be established by the transfer matrix method, which can solve the internal forces and deformations problems of each cross-section, based on the solutions of deflection differential equation of the curved bridge. The bending-torsional coupling, horizontal bending and axial deformations should be considered into the structural analysis of the curved bridge, under the influence of curvature. To establish the general transfer equation requires the field transfer matrixs and the point transfer matrixs of the curved bridge in horizontal and vertical directions. The state vectors of each cross-section can be obtained depending on the general transfer equation.

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Le, Yun, Jiancheng Fang, and Jinji Sun. "An integrated passive magnetic damping system for high-speed compressor with flexible rotor." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 6 (June 30, 2014): 1150–61. http://dx.doi.org/10.1177/0954406214542038.

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To provide a more reliable rotor damping system for high-speed compressor with flexible rotor, a passive magnetic damping integrated with an active axial bearing (PMDAB) system is proposed. The PMDAB system can provide active force in axial direction and also can provide damping force without control system in radial direction. To enhance the damping ability of the system, an analytical model is set up especially for the high-speed vibration rotor, and the relation between resistance of radial coils and the provided damping force is discussed for the first time. The coupling characteristic between passive radial damping coefficient and active axial bearing stiffness is also analyzed; the result shows that the coupling is too small, therefore can be neglected. Finally, a design example for a high-speed compressor is given based on electromagnetic analysis of PMDAB and dynamic analysis of the flexible rotor. The analytical and design results, which are verified by the finite element method result, show that the PMDAB is effective in controlling the first bending vibration of flexible rotor.

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O’Brien, P. J., J. F. McNamara, and F. P. E. Dunne. "Three-Dimensional Nonlinear Motions of Risers and Offshore Loading Towers." Journal of Offshore Mechanics and Arctic Engineering 110, no. 3 (August 1, 1988): 232–37. http://dx.doi.org/10.1115/1.3257056.

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A method is developed for the three-dimensional nonlinear motions of marine risers, pipelines and offshore loading towers. The technique is based on the finite element method and the separation of the rigid body motions and deformations of elements under conditions of finite rotations. The position of the riser is defined by a set of co-rotational axes and the evaluation of the finite rotations of this convected system is detailed. The method includes all nonlinear effects including geometry changes, bending-axial and bending-torsional coupling and follower forces and pressures. The computation of Morison-type loads is described with respect to three-dimensional axes. In order to verify the procedure numerical results are presented for the case of a vertical cantilever under bi-directional loading and axial torque; the results are shown to agree exactly with independent calculations. Results are also presented for an example from the literature on the three-dimensional response of an articulated tower to noncollinear waves and current.

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Liu, Heng, Jie Hong, and Dayi Zhang. "Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces." Frontiers of Mechanical Engineering 15, no. 3 (April 13, 2020): 417–29. http://dx.doi.org/10.1007/s11465-019-0584-4.

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Abstract The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

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Li, Changchang, Zhengzhong Wang, and Quanhong Liu. "Numerical Simulation of Mudstone Shield Tunnel Excavation with ABAQUS Seepage–Stress Coupling: A Case Study." Sustainability 15, no. 1 (December 30, 2022): 667. http://dx.doi.org/10.3390/su15010667.

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To explore the influence of shield construction on the stress of tunnels surrounding rock and linings in deep, high groundwater and low-permeability soft rock strata, a 3D coupled hydro-mechanical model of a low permeability mudstone tunnel was established with ABAQUS, based on the effective stress principle and the Mohr–Coulomb elastoplastic constitutive model, taking the Bailuyuan Tunnel of the Hanjiang to Weihe River Valley Water Diversion Project Phase II in China as an example. The tunnel shield construction was simulated, and the spatial-temporal variation in the pore water pressure and the internal forces of the lining were studied. The results show that the central pore water pressure of the low-permeability mudstone face presents a V-shaped variation with the tunnel excavation. When the face was approximately 15 m from the representative section, the pore pressure on the linings basically varied between 192.7 and 182.5 m. The bending moment and axial force of the lining increased by 7.4% and 12.8%, respectively, with shield tunnelling. When the tunnel diameter was constant, the axial force and bending moment of the lining decreased quadratically as the lining thickness increased. The influence of shield construction decreased as the lining thickness increased. The research results provide a reference for the safe and optimal construction of the Hanjiang to Weihe River Valley Water Diversion Project.

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Šalinić, Slaviša, Marko Todorović, and Aleksandar Obradović. "An analytical approach for free vibration analysis of Euler-Bernoulli stepped beams with axial-bending coupling effect." Engineering Today 1, no. 4 (2022): 7–17. http://dx.doi.org/10.5937/engtoday2204007s.

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Free vibration of eccentrically stepped beams with one step change in cross-section is considered. It is assumed that the longitudinal symmetry axes of the beam segments are translationally shifted along the vertical direction with respect to each other. The effect of that arrangement of the segments on the coupling of axial and bending vibrations of the stepped beam is analyzed. The beam segments are modeled in the frame of the Euler-Bernoulli theory of elastic beams. Two numerical examples are presented.

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Seys, Jonas, Koenraad Roeygens, Jeroen Van Wittenberghe, Timothy Galle, Patrick De Baets, and Wim De Waele. "Failure behaviour of preloaded API line pipe threaded connections." International Journal Sustainable Construction & Design 2, no. 3 (November 6, 2011): 407–15. http://dx.doi.org/10.21825/scad.v2i3.20539.

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This paper reports on numerical and experimental work concerning the fatigue behaviour andsealing capacity of threaded pipe connections (1” API Line Pipe). Numerical simulations are performedusing Abaqus®in combination with ThreadGen©. The fatigue life of a thick-walled standard coupling isdetermined using a four-point bending test. The corresponding S-N curve is compared to results of previouswork on thin-walled specimens. It can be concluded that the standard thick-walled connection has a higherfatigue life than thin-walled ones. In future work, the prediction of fatigue life using established multi-axialcriteria will be evaluated. Further, the sealing capacity of several couplings will be investigated bysubmitting them to different combinations of internal pressure and axial force. Hereto, a specific test setupis designed. The results will then be presented as a test load envelope

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Hu, F. L., and A. G. Ulsoy. "Dynamic Modeling of Constrained Flexible Robot Arms for Controller Design." Journal of Dynamic Systems, Measurement, and Control 116, no. 1 (March 1, 1994): 56–65. http://dx.doi.org/10.1115/1.2900681.

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The modeling for controller design of a constrained rigid-flexible robot arm is considered. The mathematical model is obtained as a set of nonlinear hybrid ordinary-partial differential equations and an algebraic constraint equation. Galerkin’s method is employed to discretize the partial differential equations. Because of the constrained environment of the robot arm, the choice of approximating functions in the spatial discretization is crucial for obtaining accurate simulation results from a low order model. Several candidate approximating functions are evaluated through convergence and accuracy studies. This work also investigates the effects of coupling between rigid- and flexible-body motion, and the effects of axial force (due to the contact force) on bending vibrations through axial shortening. It is shown that the use of inappropriate spatial approximating functions with a low order model can result in faulty predictions of the dynamic response, especially, the axial force effects due to the contact force.

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Zhang, Xuping, James K. Mills, and William L. Cleghorn. "Investigation of axial forces on dynamic properties of a flexible 3-PRR planar parallel manipulator moving with high speed." Robotica 28, no. 4 (August 11, 2009): 607–19. http://dx.doi.org/10.1017/s0263574709990282.

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SUMMARYThe effect of axial forces on the dynamic properties is formulated and investigated for a 3-PRR planar parallel manipulator with three flexible intermediate links. A dynamic model of the manipulator system is developed based on the assumed mode method with the consideration of the effect of longitudinal forces on lateral stiffness is included. The flexible intermediate links are modeled as Euler–Bernoulli beams with pinned-pinned boundary conditions, which are verified by experimental modal tests. Natural frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Dynamic behavior including the effect of axial forces on lateral deformation is investigated, and configuration-dependant frequencies are analyzed. Numerical simulations of configuration-dependent frequency properties and axial forces are performed to illustrate the effect of axial forces on the dynamic behaviors of the flexible parallel manipulator. Simulation results of mode amplitudes, deformations, axial forces, inertial, and coupling forces are presented, and further validate the theoretical derivations. These analyses and results provide a new and valuable insight to the design and control of the parallel manipulators with flexible intermediate links.

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Ren, Fei, Da Tong Qin, and Xiao Ling Wu. "Research on the Dynamics of the Double Helical Gear Transmission." Applied Mechanics and Materials 456 (October 2013): 256–59. http://dx.doi.org/10.4028/www.scientific.net/amm.456.256.

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Against the transmission characteristics of the double helical gear pair, considering the time-varying mesh stiffness, the bearing radial and axial stiffness, the tensile and compressive stiffness of the transmission shaft, the bending stiffness of that, error excitations, and corresponding dampings, a double helical gear pair bending-torsion-axis coupling dynamic model was established by using the lumped parameter method based on the gear meshing theory and Lagrange equations. Based on the model, the dynamic response of double helical gear pair was solved, and taking the right side of helical gear as an example, the frequency spectrum characteristics of dynamic meshing force of the right side of helical gear were mainly analyzed. This research establishes the foundation for dynamic performance optimizations and reliability designs of the double helical gear pair transmission system in the future.

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Bösch, Nadja, Martin Hofstetter, Alexander Bürki, Beatriz Vidondo, Fenella Davies, and Franck Forterre. "Effect of Facetectomy on the Three-Dimensional Biomechanical Properties of the Fourth Canine Cervical Functional Spinal Unit: A Cadaveric Study." Veterinary and Comparative Orthopaedics and Traumatology 30, no. 06 (2017): 430–37. http://dx.doi.org/10.3415/vcot-17-03-0043.

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Abstract Objective To study the biomechanical effect of facetectomy in 10 large breed dogs (>24 kg body weight) on the fourth canine cervical functional spinal unit. Methods Canine cervical spines were freed from all muscles. Spines were mounted on a six-degrees-of-freedom spine testing machine for three-dimensional motion analysis. Data were recorded with an optoelectronic motion analysis system. The range of motion wasdetermined inall threeprimary motionsaswellasrange of motion of coupled motions on the intact specimen, after unilateral and after bilateral facetectomy. Repeated-measures analysis of variance models were used to assess the changes of the biomechanical properties in the three treatment groups considered. Results Facetectomy increased range of motion of primary motions in all directions. Axial rotation was significantly influenced by facetectomy. Coupled motion was not influenced by facetectomy except for lateral bending with coupled motion axial rotation. The coupling factor (coupled motion/primary motion) decreased after facetectomy. Symmetry of motion was influenced by facetectomy in flexion–extension and axial rotation, but not in lateral bending. Clinical Significance Facet joints play a significant role in the stability of the cervical spine and act to maintain spatial integrity. Therefore, cervical spinal treatments requiring a facetectomy should be carefully planned and if an excessive increase in range of motion is expected, complications should be anticipated and reduced via spinal stabilization.

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Leen, S. B., T. H. Hyde, C. H. H. Ratsimba, E. J. Williams, and I. R. McColl. "An investigation of the fatigue and fretting performance of a representative aero-engine spline coupling." Journal of Strain Analysis for Engineering Design 37, no. 6 (August 1, 2002): 565–83. http://dx.doi.org/10.1243/030932402320950161.

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The fatigue behaviour of a representative high-performance aero-engine spline coupling is investigated under test conditions designed to simulate in-service conditions. The test load cycles consist of major cycle torque and axial load, simulating maximum thrust, combined with minor cycle rotating bending moment and fluctuating torque, simulating life-limiting conditions at take-off. The objective of the study is to develop understanding of the fatigue behaviour of the coupling over a range of loading conditions, including interaction between low-cycle fatigue, fretting fatigue and fretting wear. This information is necessary for the development of fatigue and fretting-fatigue life prediction techniques. The test results are interpreted with the help of three-dimensional finite element models, which include the frictional contact between the spline teeth.

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Eroglu, Ugurcan, and Ekrem Tufekci. "Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution." International Journal of Structural Stability and Dynamics 17, no. 10 (November 20, 2017): 1750111. http://dx.doi.org/10.1142/s0219455417501115.

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In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

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Hui, David, and I. H. Y. Du. "Effects of Axial Imperfections on Vibrations of Anti-Symmetric Cross-Ply, Oval Cylindrical Shells." Journal of Applied Mechanics 53, no. 3 (September 1, 1986): 675–80. http://dx.doi.org/10.1115/1.3171830.

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This paper examines the effects of axial geometric imperfections on the fundamental vibration frequencies of cross-ply simply-supported oval cylindrical shells. It is found that the presence of such imperfection with small amplitudes may significantly raise or lower the fundamental frequencies, depending on the wave numbers of the imperfection and vibration mode. The effects of oval eccentricity, bending-stretching coupling of the material, the reduced-Batdorf parameter and Young’s moduli ratio are examined. It appears that the present problem has not been examined, even in the simplified case of oval cylindrical shells made of isotropic-homogeneous material.

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Al-Solihat, Mohammed Khair, Meyer Nahon, and Kamran Behdinan. "Three-dimensional nonlinear coupled dynamic modeling of a tip-loaded rotating cantilever." Journal of Vibration and Control 24, no. 22 (January 19, 2018): 5366–78. http://dx.doi.org/10.1177/1077546317753058.

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This paper presents a general three-dimensional flexible dynamic model of a tip-loaded rotating cantilever beam. For generality, the beam tip is assumed to be loaded with a rigid body with an arbitrary center of mass position, and subject to external force and moment. The coupled longitudinal (axial), bending–bending, and twist elastic motions are considered to formulate the system dynamics. The beam structural internal damping is modeled utilizing Rayleigh’s dissipation function. As well, the influence of gravity is considered. A symbolic code is developed to derive the equations of motion, and it is subsequently used to simulate the dynamics of two numerical case studies. The time response results are found to be in an excellent agreement with those reported from the literature. The effects of internal damping and coupling among the elastic motions on the system dynamic response are then investigated.

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Taeprasartsit, S. "Using a homogeneous beam element to analyse functionally graded beams." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 4 (April 1, 2010): 789–95. http://dx.doi.org/10.1243/09544062jmes1712.

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When an appropriate reference plane is used, the coupling between axial and bending deformations in the stiffness matrix of a functionally graded beam (FGB) element vanishes. Then the stiffness matrix of the FGB element reduces to the same form as that of the homogeneous beam element. However, the coupling in the mass matrix of the FGB element cannot be eliminated at the same time. Consequently, in an analysis that does not involve mass, it is possible to use a homogeneous beam element to obtain the same results as would be achieved with an FGB element. This paper focuses on explaining a procedure to use ANSYS's BEAM3 element to analyse FGBs. The BEAM3 element has the ability to deal with a linear temperature gradient that is sufficient to analyse any arbitrary temperature distribution shape through thickness.

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Zhao, Wu, Wei Tao Jia, Quan Bin Zhang, and Zhan Qi Hu. "Precise Frequency Calculation Model on BTA Boring Bar." Applied Mechanics and Materials 532 (February 2014): 398–401. http://dx.doi.org/10.4028/www.scientific.net/amm.532.398.

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For the purpose of precise calculation on intrinsic frequency of the deep-hole boring bar in trepanning heavy-duty processing, a new frequency calculation model is proposed, based on the synthetically investigation of the axial press effects, intermediate supported, Coriolis inertia effects induced by cutting fluid and other relevant various factors of boring bar. The boring bar can be decomposed into the two parts, corresponding to the liquid-solid coupling vibration model inside the work part and Timoshenko beam model outside the work part, respectively. Then assume the whole system as continuous equal span beam model to combine these two parts. Through nesting liquid-solid coupled vibration model (considering cutting fluid velocity) and Timoshenko beam model (containing axial pressure and lateral bending) among the continuous beam model (considering equal span), the precise calculation on intrinsic frequency of the boring system can be completed.

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Martin, Tobias, and Hans Bihs. "A Numerical Solution for Modelling Mooring Dynamics, Including Bending and Shearing Effects, Using a Geometrically Exact Beam Model." Journal of Marine Science and Engineering 9, no. 5 (April 30, 2021): 486. http://dx.doi.org/10.3390/jmse9050486.

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During the operation of moored, floating devices in the renewable energy sector, the tight coupling between the mooring system and floater motion results in snap load conditions. Before snap events occur, the mooring line is typically slack. Here, the mechanism of energy propagation changes from axial to bending dominant, and the correct modelling of the rotational deformation of the lines becomes important. In this paper, a new numerical solution for modelling the mooring dynamics that includes bending and shearing effects is proposed for this purpose. The approach is based on a geometrically exact beam model and quaternion representations for the rotational deformations. Further, the model is coupled to a two-phase numerical wave tank to simulate the motion of a moored, floating offshore wind platform in waves. A good agreement between the proposed numerical model and reference solutions was found. The influence of the bending stiffness on the motion of the structure was studied subsequently. We found that increased stiffness increased the amplitudes of the heave and surge motion, whereas the motion frequencies were less altered.

Journal articles on the topic 'Axial-bending coupling'

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