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Three-to-one Internal Resonance of Suspended Cable Accounting for bending stiffness

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Three-to-one Internal Resonance of Suspended Cable Accountin...

Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

第九届全国动力学与控制学术会议

作者： H.J.Kang Y.Y.Zhao H.P.Zhu College of Civil Engineering Hunan University Changsha School of Engineering University of Western Sydney

The paper reports an investigation on a continuous model for dynamics of large-diameter cables,taking bending stiffness into account.Firstly,by making some simplifications,the frequencies and mode shape equations for in-plane and out-of-plane motion have been obtained in non-dimensional form.Secondly,by parametrical studies,the effect of bending stiffness on frequencies and mode shapes of symmetrical/antisymmetrical in-plane and out-of-plane modes are investigated in

关键词： cable internal resonance modal frequency bending stiffness key word

来源： cnki会议评论

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Applied Mathematics and Mechanics(English Edition) 2022年第10期43卷 1515-1530页

作者： M.H.B.M.Shariff J.Merodio R.Bustamante Department of Mathematics Khalifa University of Science and TechnologyAbu Dhabi127788United Arab Emirates Departamento de Matemática Aplicada a las TIC ETS de Ingeniería de Sistemas InformaticosUniversidad Politecnica de MadridMadrid28031Spain Departamento de Ingeniería Mecánica Universidad de ChileBeauchef 851Santiago CentroSantiago8370448Chile

Mechanical models of residually stressed fibre-reinforced solids,which do not resist bending,have been developed in the literature.However,in some residually stressed fibre-reinforced elastic solids,resistance to fibre bending is significant,and the mechanical behavior of such solids should be investigated.Hence,in this paper,we model the mechanical aspect of residually stressed elastic solids with bending stiffness due to fibre curvature,which up to the authors’knowledge has not been mechanically modeled in the past.The proposed constitutive equation involves a nonsymmetric stress and a couple-stress tensor.Spectral invariants are used in the constitutive equation,where each spectral invariant has an intelligible physical meaning,and hence they are useful in experiment and analysis.A prototype strain energy function is proposed.Moreover,we use this prototype to give results for some cylindrical boundary value problems.

关键词： fibre-reinforced solid residual stress bending stiffness spectral invariant second gradient finite elasticity

bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

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Frontiers of Mechanical Engineering 2020年第3期15卷 417-429页

作者： Heng LIU Jie HONG Dayi ZHANG School of Energy and Power Engineering Beihang UniversityBeijing 100191China State Key Laboratory of Laser Propulsion and Application Beijing Power Machinery InstituteBeijing 100074China

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.

关键词： discontinuous beam bending stiffness transverse vibration axial loads gyroscopic moments

A novel structural modification to eliminate the early coupling between bending and torsional mode shapes in a cable stayed bridge

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Frontiers of Structural and Civil Engineering 2017年第2期11卷 131-142页

作者： Nazim Abdul NARIMAN Institute of Structural Mechanics Faculty of Civil Engineering Bauhaus University Weimar Weimar 99423 Germany

In this paper, a novel structural modification approach has been adopted to eliminate the early coupling between the bending and torsional mode shapes of vibrations for a cable stayed bridge model generated using ABAQUS software. Two lateral steel beams are added to the middle span of the structure. Frequency analysis is dedicated to obtain the natural frequencies of the first eight mode shapes of vibrations before and after the structural modification approach. Numerical simulations of wind excitations are conducted for the 3D model of the cable stayed bridge with duration of 30 s supporting on real data of a strong wind from the literature. Both vertical and torsional displacements are calculated at the mid span of the deck to analyze both the bending and the torsional stiffness of the system before and after the structural modification. The results of the frequency analysis after applying lateral steel beams declared a safer structure against vertical and torsional vibrations and rarely expected flutter wind speed. Furthermore, the coupling between the vertical and torsional mode shapes has been removed to larger natural frequencies magnitudes with a high factor of safety. The novel structural approach manifested great efficiency in increasing vertical and torsional stiffness of the structure.

关键词： aeroelastic instability structural damping flutter wind speed bending stiffness torsional stiffness

Functional Morphology and bending Characteristics of the Honeybee Forewing

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Journal of Bionic Engineering 2017年第1期14卷 111-118页

作者： Yun Ma Huilan Ren Jianguo Ning Pengfei Zhang State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 China

The present work aimed to reveal the functional morphology and bending characteristics of the worker honeybee （Apis mellifera） forewing. Honeybee wings including the forewing and hindwing, which are mainly composed of veins and membranes, are a kind of typical hierarchical biomaterials. We investigated the cross-sections of membranes, veins and wing hairs through Scanning Electron Microscopy （SEM）. Based on the microscopic observation, it was found that the vein is a thick-walled cylinder, and the membrane possesses multilayered structure and so does the wing hair which shows the thread surface. At the vein-membrane conjunctive position, membranes and veins are assembled seamlessly and veins are packed smoothly and tightly by membranes into a whole, allowing honeybees to perform excellent flapping flight. In such a case, we also conducted the cantilevered bending experiment of honeybee forewing to explore their bending characteristics using a MTS Tytron 250 micro force tester. Experiment results indicate that the anti-bending capacity of the forewing along the spanwise direction is higher than that along the chordwise direction which is partly caused by the wing corrugation along the wing span detected by the micro-Computed Tomography （micro-CT）, and ventral load bearing ability is better than dorsal one along the spanwise and chordwise direction of the wing which is due to the stress-stiffening of membranes. It could be concluded that the structural configuration of the wing is closely relevant to wing biomechanical behaviors. All results above would provide a significant support for the design of bioinspired wings for Flapping Micro Aerial Vehicles （FMAV）.

关键词： honeybee forewing functional morphology hierarchical structure bending stiffness

A Finite Element Cable Model and Its Applications Based on the Cubic Spline Curve

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China Ocean Engineering 2013年第5期27卷 683-692页

作者：方子帆贺青松向兵飞肖化攀何孔德杜义贤 College of Mechanical & Material Engineering China Three Gorges University

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.

关键词： tension stiffness bending stiffness torsion stiffness cubic spline curve Galerkin criterion finite element model

Deflection analysis of reinforced concrete beams strengthened with carbon fibre reinforced polymer under long-term load action

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2012年第8期13卷 571-583页

作者： Mykolas DAUGEVIIUS Juozas VALIVONIS Gediminas MAR IUKAITIS Department of Reinforced Concrete and Masonry Structures Vilnius Gediminas Technical University

This paper presents the results of an experimental research on reinforced concrete beams strengthened with an external carbon fibre reinforced polymer(CFRP) layer under long-term load action that lasted for 330 d.We describe the characteristics of deflection development of the beams strengthened with different additional anchorages of the external carbon fibre composite layer during the period of interest.The conducted experiments showed that the additional anchorage influences the slip of the external layer with respect to the strengthened element.Thus,concrete and carbon fibre composite interface stiffness decreases with a long-term load action.Therefore,the proposed method of analysis based on the built-up-bars theory can be used to estimate concrete and carbon fibre composite interface stiffness in the case of long-term load.

关键词： Carbon fibre composite Beam strengthening Beam deflection Long-term load bending stiffness Concrete and carbon fibre composite interface stiffness Effective inertia moment

Prediction on Deflection of Inflated Beam

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Journal of Harbin Institute of Technology(New Series) 2013年第1期20卷 8-11页

作者： Hui-Feng Tan Zhen-Yong Du Chang-Guo Wang Center for Composite Materials Harbin Institute of Technology Nanjing Resarch Institute of Electronic Technology

The bending stiffness of the inflated beam is considered as a constant before wrinkles appear, and it decreases obviously as wrinkles propagate. The formula of the bending stiffness is obtained based on the membrane theory in this paper. Furthermore, the definition of dimensionless bending stiffness factor is presented; the relationship of bending stiffness factor and wrinkling factor is derived; the bending stiffness factor is simplified as different linear functions with wrinkling factor, and the simplified model of bending stiffness of inflated beam under bending is also obtained. The bending stiffness including expression of wrinkling factor is substituted into the deflection differential equation, and then the slope and deflection equation of the inflated beam is deduced by integrating the deflection differential equation. Finally, the load-deflection curve is obtained, which is compared with the experimental data in a previous paper. It has a good agreement with each other.

关键词： membrane structure inflated beam bending stiffness wrinkle stiffness factor

Mortarless structures based on topological interlocking

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Frontiers of Structural and Civil Engineering 2012年第2期6卷 188-197页

作者： Arcady V.DYSKIN Elena PASTERNAK Yuri ESTRIN School of Civil and Resource Engineering The University of Western AustraliaCrawley WA 6009Australia School of Mechanical and Chemical Engineering The University of Western AustraliaCrawley WA 6009Australia Centre for Advanced Hybrid Materials Department of Materials EngineeringMonash UniversityClayton VIC 3800Australia

We review the principle of topological interlocking and analyze the properties of the mortarless structures whose design is based on this principle.We concentrate on structures built of osteomorphic blocks-the blocks possessing specially engineered contact surfaces allowing assembling various 2D and 3D structures.These structures are easy to build and can be made demountable.They are flexible,resistant to macroscopic fractures and tolerant to missing blocks.The blocks are kept in place without keys or connectors that are the weakest elements of the conventional interlocking structures.The overall structural integrity of these structures depends on the force imposed by peripheral constraint.The peripheral constraint can be provided in various ways:by an external flame or features of site topography,intemal prestressed cables/tendons,or self-weight and is a necessary auxiliary element of the structure.The constraining force also determines the degree of delamination developing between the blocks due to bending and thus controls the overall flexibility of the structure thus becoming a new design parameter.

关键词： topological interlocking fragmented structures segmented structures constraint delamination bending stiffness