Effects Of Axial Deformations Research Articles

Axial deformation effects on hydrogen storage of Ni decorated (8,0) zigzag single-walled boron nitride nanotubes: a DFT study

The effect of axial deformation on tuning the hydrogen storage of nickel functionalised (8,0) zigzag boron nitride nanotube is investigated by using density functional theory calculations. The assessment has been carried out based on the adsorption of molecular hydrogen with the binding energy lying in the desirable energy window, charge transfer, the density of states, pairwise and nonpairwise additivty, frontier orbital band gaps, isosurface plots, polarizabilities and hyperpolarizabilities, simulated Infrared (IR) and Raman (R). The numerous changes in adsorption energy of H2 upon relaxation or compression of only (1%) strain points to the sensitivity of H2 binding to axial deformation effects. The calculated pairwise and non-pairwise additive components show that the role of the BNNT is not restricted to support the metal. Spectral analysis additionally as polarizability and hyperpolarizability calculations characterise the relaxed structure (Z = 1.01), that H2 adsorption energy (−0.552 eV) is within the suggested energy vary for hydrogen storage, to be energetically additional desirable than the compressed structure (Z = 0.99). The results provide some way to manage and characterise the hydrogenation process of metal functionalised BNNTs by strain loading.

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products, and are an active area of research. In this paper, according to the optimization of regular honeycomb structures, two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented. The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods, in which the axial deformation of the rods was considered. The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures. The elastic properties of the structure can be considered by the enclosed area of the unit structure, the shape of the unit structure, and the elastic properties of the original materials. The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.

Transient response of functionally graded non-uniform cylindrical helical rods

This paper have the objective of investigating forced vibration behaviour of axially functionally graded cylindrical helices with variable cross-section. An algorithm is developed in order to solve corresponding problems. The ordinary differential equations governing the dynamic behaviour of cylindrical helices are determined in Laplace domain by using Timoshenko beam theory. Then transfer matrix method is implemented for the solution, including shear and axial deformation effects. Obtained results are transferred to time domain using Durbin's modified numerical inverse algorithm for Laplace transform. A benchmark problem has been solved to check the accuracy of developed algorithm then a parametric study is conducted considering the effects of material gradient index (b_mat), section variation parameter (b-sec) and number of active turns (n). Results are compared with solutions attained from ANSYS for verification.

Physical-chemical properties of M@Fe3O4 core@shell nanowires (M = Cu, Co, CoO).

Interest in low dimensional magnetic systems has been growing due to the novel and dramatically differentiated effects of their physical properties, which give them special behaviors and uses in biomedical, environmental and technological fields. In this study we report extensive first-principles calculations on the geometric optimization as well as electronic, magnetic, mechanical and thermal properties of several quasi one-dimensional core/shell nanowires: Cu/Fe3O4, Co/Fe3O4, and CoO/Fe3O4. The main focus lies on the quantum confinement effects as well as on the effect of the interaction between the ferrimagnetic semiconductor shell material (magnetite nanotube) and core compounds with differentiated magnetic behavior such as (i) a ferromagnetic material (Co), (ii) an antiferromagnetic transition metal oxide (CoO) and (iii) a non-magnetic simple metal (Cu). The mechanical properties of the related nanosystems are studied through the effects of axial deformations, and their thermal behavior is evaluated by considering the electronic contribution of each sample to the heat capacity, and some potential technological applications are suggested.

Analysis of Large-Sag Extensible Catenary with Free Horizontal Sliding at One End by Variational Approach

A variational approach for the static equilibrium configuration analysis of a large-sag extensible catenary with free horizontal sliding at one end is developed, considering the virtual work done by the catenary self-weight and the horizontal tension at the free sliding end support. The virtual work of the cable system is expressed in terms of the vertical coordinate, which is a function of the unstrained arc length of the cable. The stationary condition is applied to the virtual work functional to obtain the equilibrium configuration of the catenary. The validity of the variational approach is ensured by Euler’s equation, which is identical to the one derived by the force equilibrium consideration of a catenary segment. The finite element method is used to evaluate the numerical results. A parametric study is performed to demonstrate the effect of axial deformation on the equilibrium configuration of a large-sag extensible free horizontal sliding catenary. The results indicate that as the axial deformation increases, the total arc-length and horizontal span length of the cable also increase. Particularly, the very large-sag catenary configurations are studied and exhibited in this study.

Refined spatial beam-column element for second-order analysis of lattice shell structure

Considering the coupling effect of axial force, bending moment and shear force, the displacement interpolation functions of the spatial beam-column element under axial tension and axial compression are derived respectively based on the differential equilibrium equations of the deformed member. The different displacement interpolation functions of the tension and compression elements are unified by replacing the stability integration functions with the Maclaurin series, and the unified functions are completely equivalent to those expressed by stability integration functions. The second-order element tangent stiffness matrix considering the effect of axial deformation, shear deformation, biaxial bending and torsion is derived. The number of series expansion terms in unified displacement interpolation functions is determined from aspects of calculation accuracy and positive definiteness of the structural general stiffness matrixes. Numerical calculation results by this element model accord well with the experimental data, and it indicates the accurateness of this element. Different element models are used in the analyses of a single layer lattice shell, and calculation results indicate that the geometrical nonlinearity of the structure is well exhibited with good efficiency by the refined spatial beam-column element proposed in this paper.

Effect of axial deformation on flutter of cantilevered FGM cylindrical shells under axial follower forces

The effect of axial deformation of shell particles on the dynamic instability (flutter) of cantilevered cylindrical shells made of functionally graded materials (FGM) under an end axial follower force is addressed. To this end, at first, results for free vibration of FGM cylindrical shells were verified with previous outcomes and they were in very good agreement. Then, the effect of axial deformation of the shell, acting like a reducing linearly-distributed follower load, on the critical circumferential mode number and the flutter load of FGM shells was accounted for. Finally, the effect of axial deformation of the shell particles on the critical circumferential mode number and the flutter load of FGM shells were investigated. In this case, three homogeneous shells with different elasticity moduli and densities and two FGM materials were considered: nickel-stainless steel and stainless steel-alumina. Results include the increasing critical circumferential mode number and the increasing value of the flutter load due to axial deformation. The increase in the flutter load occurs in proportion to the whole elasticity modulus of the material, and thus it can be derived from the formula of mixture for an FGM.

Physical properties of quasi-one-dimensional MgO andFe3O4-based nanostructures

We have studied the properties of several representative one-dimensional structures---MgO nanowires, ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ hollow nanotubes, ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ nanowires, and $\mathrm{Mg}\mathrm{O}/{\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ core/shell nanotubes---by means of first-principles-based calculations. Each of these nanostructures reveals different electronic properties with novel electronic states due to the large surface/interface of the nanocylinders. Electronic states of the ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ nanowire are localized around small clusters of atoms, and its bands appear with almost no energy dispersion. Localization is not a direct consequence of structural disorder; instead, it seems to be induced by an enhanced charge transfer due to the undercoordination on the surface. The combined effect of the $\mathrm{Mg}\mathrm{O}/{\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ nanostructure shows that the MgO is well coated and even bulk-like states can be observed. However, the magnetite suffers important atomic reconstructions losing symmetries and increasing its atomic-like behavior. Effects of axial deformations on the properties and the relation of the results to potential technological applications are discussed.

Theoretical characterization of axial deformation effects on hydrogen storage of Ti decorated armchair (5,5) SWCNT

Theoretical calculations have been performed in the framework of density functional theory to characterize the effect of axial deformation on hydrogen storage of Ti decorated armchair (5,5) SWCNT. The theoretical characterization has been carried out in terms of H2 adsorption energies that are lying in the desirable energy window (−0.2 to −0.6 eV) recommended by DOE, as well as a variety of physicochemical properties. A remarkable and significant change in H2 adsorption energy is observed under the effect of only (1%) axial strain. Axial relaxation leads to H2 adsorption energies within the recommended energy range for hydrogen storage, in contrast to axial compression. Simultaneous weakening of π and σ interactions, due to the effect of axial relaxation and loss of spatial orbital overlap, is in favor of hydrogen adsorption in the recommended energy range, and dominates the effect of charge transfer from Ti 3d to C 2p of the SWCNT. The calculated pairwise and non pairwise additive components confirm that the role of the SWCNT is not restricted to supporting the metal. Polarizability and hperpolarizabilty calculations as well as spectral analysis characterize the relaxed structure (Z = 1.02), for which H2 adsorption energy (−0.34 eV) is in the recommended energy range for hydrogen storage, to be energetically more preferable than the compressed structure (Z = 0.99). The results offer a way to control and characterize the hydrogenation process of metal functionalized SWCNTs by strain loading.

Analyses of rigid-flexible coupling dynamic properties of a rotating internal cantilever beam

The rigid-flexible coupling dynamic properties of an internal cantilever beam attached to a rotating hub are studied in this paper. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model is derived from Hamilton theory and assumed mode method, taking into account the second-order coupling quantity of axial displacement caused by transverse displacement of the beam. The simplified first-order approximation coupling model which neglects the effect of axial deformation of a beam is presented. The simplified model is transformed into dimensionless form in which dimensionless parameters are identified. Firstly, the dynamic response of an internal cantilever beam is compared with that of an external cantilever beam, which are both in non-inertia system. Then, the stability of an internal cantilever beam is analyzed. Finally, the convergence of critical rotating speed of an internal cantilever beam is analyzed. Generally, it is pointed that an internal cantilever beam has a dynamic softening phenomenon, which is different from the dynamic stiffening phenomenon of an external cantilever beam. The critical ratio of the internal radius to the length of the beam for unconditional stability and the critical rotating speed of conditional stability of an internal cantilever beam are derived. When the first natural frequency decreases as the rotating speed increases, the dynamic system of the internal cantilever beam is conditionally stable. As the number of modes increases, the critical rotating speed of an internal cantilever beam decreases, and it has a convergent value.

旋转内接微梁的动力学建模及稳定性分析

The dynamic properties of the micro beam are obviously different from those of the traditional macro beam due to the size effect of material on a micro scale. The rigid-flexible coupling dynamic properties analysis of an internal micro beam attached to a rotating hub is studied in this paper. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model are derived from couple stress theory and Hamilton theory, taking the second-order coupling quantity of axial displacement caused by transverse displacement of the beam into account. The simplified first-order approximation coupling model which neglects the effect of axial deformation of a beam is presented. The simplified model is transformed into dimensionless form in which dimensionless parameters are identified. Firstly, the dynamic response of an internal micro beam is compared with that of an external micro beam, which are both in non-inertia system. Then, the influence of size effect on the dynamic properties of an internal micro beam is studied. Generally, it is pointed out that an internal micro beam has dynamic softening phenomena, which is different from the dynamic stiffening phenomena of an external micro beam. The critical ratio of the internal radius to the length of the beam for unconditional stability and the critical angular speed of conditional stability of an internal micro beam are derived. The size effect results in the descending of vibration amplitude and the increasing of vibration frequency and critical angular speed of conditional stability of the micro beam. As the number of modes increases, the critical rotating speed of an internal cantilever beam decreases, and it has a convergent value.

Stability and free vibration analyses of an orthotropic singly symmetric Timoshenko beam-column with generalized end conditions

The stability and free vibration analyses (i.e., buckling, natural frequencies and modal shapes) of an orthotropic singly symmetric 3D Timoshenko beam-column with generalized boundary conditions (i.e., with bending and torsional semirigid restraints and lateral bracings as well as lumped masses at both ends) subjected to an eccentric end axial load are presented in a classical manner. The five governing equations of dynamic equilibrium (i.e., two transverse shear equations, two bending moment equations and pure torsional moment equation) are sufficient to determine the natural frequencies and the corresponding modal shapes of the beam-column in the two principal planes of bending and torsion about its longitudinal axis. The proposed model includes the coupling effects among: (1) the deformations due to bending, shear and pure torsion; (2) inertias (translational, rotational and torsional) of all masses considered; (3) eccentric axial loads applied at the ends, and (4) restraints at the supports (bending, torsional and lateral bracings at both ends of the member). However, the effects of axial deformations and warping torsion produced by the axial load are not included; consequently the proposed model is not capable of capturing the phenomena of torsional buckling or combined lateral bending–torsional buckling. The proposed analytical model indicates that the stability and dynamic response of beam-columns are highly sensitive to the coupling effects, particularly in members with both ends free to rotate. The natural frequencies and modal shapes can be determined from the eigenvalues of a full 4×4 matrix for vibration in the plane of symmetry (using the uncoupled equations of transverse force and moment equilibrium at both ends) and from a full 6×6 matrix for the coupled shear–bending–torsional vibration (using the coupled equations of transverse shear, bending and torsional moment equilibrium at both ends). Also, it is shown that the proposed method reproduces the phenomena of modal interchanges (e.g. the second mode becoming the first mode and vise versa, etc.) when the bending and torsional restraints at the ends of the beam-column become very low. Four illustrative examples are presented showing the advantages and limitations of the proposed method.

Free Vibration of Three-Dimensional Orthotropic Uniform Shear Beam-Columns with Generalized End Conditions

The free vibration analysis of asymmetrical three-dimensional (3D) uniform shear beam-columns with generalized boundary conditions (semirigid flexural and torsional restraints, lateral bracings, and lumped masses at both ends) subjected to an eccentric end axial load in addition to a linearly distributed eccentric axial load along its span is presented in a classic manner. The five coupled governing equations of dynamic equilibrium (i.e., two shear equations, two bending moment equations, and the pure torsion moment equation) are sufficient to determine the natural frequencies and modal shapes. The proposed model which is an extension of a 2D model presented previously by the writer includes the simultaneous 3D coupling effects among the lateral deflections, deformations of the cross section along the member (shear, torsional and rotational), the translational, rotational and torsional inertias of all masses considered, an eccentric end axial load in addition to a linearly distributed axial load along its span, and the end restraints. Deformations caused by shear forces and pure torsion are considered. The effects of axial deformations, warping torsion and torsional stability are not included. The proposed model shows that the dynamic behavior of 3D shear beam-columns is highly sensitive to the coupling effects just mentioned, particularly in members with both ends free to rotate. Analytical results indicate that except for doubly symmetric members with concentric axial loads and with perfectly clamped ends, the natural frequencies and modal shapes of 3D shear beam-columns are determined from the eigenvalues of a full 8×8 matrix, rather than from the uncoupled equations of transverse (or shear-wave equations) and torsional moment equilibrium. Two comprehensive examples are presented that show the effectiveness of the proposed method.

Higher-Order Nonlinear Vibration Analysis of Timoshenko Beams by the Spline-Based Differential Quadrature Method

Higher-order nonlinear vibrations of Timoshenko beams with immovable ends are studied. The nonlinear effects of axial deformation, bending curvature and transverse shear strains are considered. The nonlinear governing differential equations are solved using a spline-based differential quadrature method (SDQM), which is constructed based on quartic B-splines. Ratios of the nonlinear to the linear frequencies are extracted and their variations with the ratio of amplitude to radius of gyration are examined. In contrast to the well-recognized finding for the nonlinear fundamental frequency of beams, some higher-order nonlinear frequencies decrease with the increase of ratio of amplitude to radius of gyration.

Active control of a flexible hub-beam system using optimal tracking control method

In this paper, active control of a flexible hub-beam system is investigated using optimal tracking control method and a first-order approximation coupling (FOAC) model. Using the Hamilton theory and assumed mode method (AMM) for discretization, the FOAC model considering second-order coupling quantity of axial displacement caused by transverse displacement of beam is first investigated. Subsequently a simplified FOAC model (or the SFOAC model) which neglects the effect of axial deformation of beam is presented in this paper. Active position control for the system is then studied by optimal tracking control theory. Since the controller obtained is a function of mode coordinate, an extraction method of modal coordinate from actual physical measurements is developed. Numerical simulations are carried out to demonstrate effectiveness of the proposed method. Simulation results indicate that the SFOAC model is valid for dynamic description of flexible hub-beam system and thus is available for control design. Modal filter proposed is effective in extracting modal coordinate from physical measurements. Desired position of system may be achieved by the proposed controller. Residual vibration of beam may be suppressed by this controller as well.

Nonlinear dynamics of an elastic cable during laying operations in rough sea

A numerical approach for predicting motion and tension of extensible marine cables during laying operations in a rough sea is presented here. The solution methodology consists of dividing the cable into straight elements, which must satisfy an equilibrium equation and compatibility relations. The system of nonlinear differential equations is solved by the Runge–Kutta method, taking the effect of regular and/or irregular waves into account explicitly. Illustrative applications of the method are given for a typical cable laying ship. The results are presented as rms values of the cable dynamic tension and corresponding dynamic factor for two different types of cable and several values of cable stiffness. The effect of axial deformation on the maximum tension at the shipboard pulley location is highlighted.

Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes

The research in the paper proposes the effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes (CNTs) through the analysis of a representative volume element (RVE) of the graphene layer via continuous elastic models. The bonds in the RVE are modeled with corresponding stretching and rotating springs. The in-plane stiffness of CNT in the equivalent elastic plate model is first obtained by equating the energy stored in the RVE and the strain energy induced in the continuous plate model under a uniaxial stretching subjected to CNT. The corresponding bending rigidity of CNT is derived by considering the inversion contributing to the bending resistance of the graphene sheet from a large deflection analysis in the elastic plate model of CNT. The results show that the in-plane stiffness of zigzag nanotube is more sensitive to the size of the tube than that of armchair nanotube. Besides, the in-plane stiffness of armchair nanotube is almost twice as big as that of zigzag nanotube at small size. Furthermore, the results also show that the effect of axial deformation on the derivation of bending rigidity is more obvious in armchair nanotube than that in zigzag nanotube at bigger curvature of bending. In addition, the explanation on the result that the bending rigidity of zigzag nanotubes is bigger than that of armchair tubes is provided from a mechanics analysis. In the end, the effect of radius on the bending rigidity is discussed in the research. It is hoped that the research in this paper may provide a benchmark on the derivation of mechanical properties of CNT from continuum models.

A parametric study on the natural frequencies of unidirectional composite conical springs

AbstractThis paper deals with the combined influences of the vibrational parameters chosen as the material types, number of active turns, helix pitch angle, minimum to maximum radii of the cylinder and maximum cylinder to wire diameters on the first six resonance frequencies of unidirectional composite conical helical springs with solid circle section and fixed–fixed ends. The transfer matrix method based on the distributed parameter model is used for the determination of the fundamental natural frequencies. The rotary inertia, the shear and axial deformation effects are taken into account in the solution based on the first‐order shear deformation theory. Variation of the natural frequencies with the chosen vibrational parameters is given in non‐dimensional graphical forms. Using these charts, a numerical prediction of the first six linear dimensional free vibration frequencies of composite conical springs and their upper and lower limits with respect to the geometrical and material properties of the spring can be made with a good approximation. Copyright © 2004 John Wiley & Sons, Ltd.

Large strain formulations of extensible flexible marine pipes transporting fluid

This paper develops mathematical formulations for large strain analysis of extensible flexible marine pipes transporting fluid in two different coordinates: Cartesian and natural coordinates. Both the virtual work method and the vectorial method are applied to generate the large strain formulations, in which deformation descriptions based upon the total Lagrangian, the updated Lagrangian, and the Eulerian mechanics are taken into consideration. The new ideas used in the model formulations deal with applications of the extensible elastica theory and the apparent tension concept to handle combined action of the effect of axial deformation with large strain and behaviour of flow of transported fluid inside the pipe including the effect of Poisson's ratio. The present models cover nonlinear statics and nonlinear dynamics, and provide flexibility in the choice of the independent variables used to define the elastic curves.

The effects of axial deformation and axial force on vibration characteristics of tall buildings

AbstractA tall building comprising frames and shear walls coupled together is idealized as a shear–flexure cantilever through the continuum approach. The effects of axial deformation as well as axial force in the frames are considered and incorporated in the formulation of the governing equations. Numerical examples are solved through the Galerkin method and the results compared with finite element solutions. The study indicates that the effect of axial deformation in the frame should be considered for tall and/or slender buildings while the effect of axial force in the column should be included for buildings with soft‐storeys resulting from the termination of core walls in the lower portion of the building. Copyright © 2002 John Wiley & Sons, Ltd.