Beam Of Circular Cross Section Research Articles

Large Deflection Analysis of Functionally Graded Beam by Using Combining Method

In this study, the large deflection behavior of a circular cross-section beam is examined using the Combining Method (CM). The CM is a numerical solution method that uses block diagrams in the Matlab-Simulink program and weighting coefficients in the Differential Quadrature Method (DQM). The beam material considered is Functionally Graded Material (FGM). Boundary conditions of the beam are taken as clamped-free (C-F) and a singular load is assumed to be applied from the free end of the beam. Geometric nonlinear analysis is performed while calculating the large deflection equations of the beam and performing numerical analysis. The effects of increasing the force applied to the beam, changing the beam cross-section in the longitudinal direction, and changing the material index of the FGM on the extreme deflection behavior of the beam were examined. For comparison purposes, the results obtained from CM are compared with the results obtained from both SolidWorks-Simulation and Ansys-Workbench programs. As a result of the analysis, increasing the applied force causes the x and y coordinates of the end point of the beam to decrease. The change in geometry and material index greatly affects the large deflection occurring in the beam.

ALE-ANCF circular cross-section beam element and its application on the dynamic analysis of cable-driven mechanism

ALE-ANCF circular cross-section beam element and its application on the dynamic analysis of cable-driven mechanism

Electromechanical response of boron nitride nanosheet reinforced nanocomposite beam: A finite element study

The objective of the present study is to investigate the electromechanical response of a piezoelectric boron nitride nanosheet reinforced nanobeam accounting for the surface and the flexoelectric effects using finite element analysis. The finite element model was developed by using the size-based Euler–Bernoulli beam model, modified piezoelectricity theory, and Galerkin's weighted residual method. The boron nitride nanosheet-reinforced nanobeam was loaded with uniformly distributed load and point-loading conditions. Three common boundary conditions for beams such as clamped-free, simply supported, and clamped-clamped have been considered here. The electromechanical behavior of the boron nitride nanosheet reinforced nanobeam has been studied under the pure surface, pure flexoelectric, as well as combined surface and flexoelectric effects. It is observed that the integrated surface and flexoelectric effects are mainly responsible for enhancing the electromechanical performance of the nanobeam. For the thickness H = 20 nm, the maximum deflection of the nanobeam was reduced by ∼50% when both the flexoelectricity and surface effects are combined together for all the support conditions. Moreover, the circular cross-section beam becomes ∼30% stiffer than the rectangular cross-section beam under the integrated effect of surface and flexoelectricity under all loading conditions. Hence, the highly size-dependent surface and flexoelectricity must be explored in the accurate electromechanical behavior of the nanostructure. Furthermore, beam stiffness is highly influenced by the flexoelectric effect irrespective of the beam boundary conditions whereas the surface effect is largely reliant on the beam boundary conditions. This research work provides a methodology to design efficient boron nitride nanosheet reinforced nanostructures that may potentially be applied in the design and development of several nanoelectromechanical systems such as force and pressure-based nanosensors and actuators.

Inhomogeneous Beam of Circular Cross-Section with Concentric Lengthwise Cracks: A Fracture Analysis with Considering Viscoplastic Behaviour

In this paper, a lengthwise fracture analysis of a viscoplastic inhomogeneous cantilever beam of circular cross-section acted upon by a torsion moment is presented. The beam is with an arbitrary number of concentric lengthwise cracks. The time-dependent mechanical behaviour of the beam is treated by a viscoplastic model representing a series of units which are combinations of springs, dashpots and frictional sliders. Due to the sliders, the model units start to deform one after another with increasing of the external load. Constitutive laws of the viscoplastic model are obtained and applied to treat the beam mechanical behaviour when deriving time-dependent strain energy release rates for the lengthwise cracks.

Dynamic, fatigue and harmonic analysis of a beam to beam system with various cross-sections under impact load

Contact of materials is inevitable in machine environment where a number of elements interact with each other causing impact force and consequent stress and strain at point of contact. The study of this behaviour is essential for machine design applications as it helps to predict life of a particular element as per the amount of stress it can sustain. This study is based on dynamic, fatigue and harmonic analysis of two-beams in contact with a combination of cross-section geometries of the beams. ANSYS, which is a Finite Element Analysis software is used for numerical modelling of stresses and deformations developed within the two-beam system. Three different combination of beam cross-sections were simulated: square-square, circular-circular and square-circular. Under dynamic and fatigue analysis, the results show that the least deformation coupled with the highest fatigue life and safety factor occurs when one beam is square and the other is circular (Square-circular), a slightly higher deformation occurs when two square beams (square-square) interact with each other while the highest deformation occurs when two circular beams interact with each other. This shows that Square cross-section beams have higher bending resistance while circular cross-section beams have low bending resistance and thus higher deformation. Under vibration analyses, due to higher natural frequencies, both the square-square and square-circular section beams show excellent durability and better margin of safety to the same extent during vibration. The results of this work will be useful in enlightening design engineers on the combination of beam cross sections that will give optimum performance in a beam-to-beam system for structural and machine design applications.

Investigation of the Free Vibrations of Radial Functionally Graded Circular Cylindrical Beams Based on Differential Quadrature Method

In the current research, an effective differential quadrature method (DQM) has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient. Based on the high-order theory of transverse vibration of circular cross-section beams, lateral displacement equation was reconstructed neglecting circumferential shear stress. Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue. Then, differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue problems. Natural frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time, and corresponding modal functions were solved together. The obtained numerical results indicated that the natural frequencies of functionally graded (FG) circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related literatures. In addition, influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous studies. Numerical results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.

Asymptotic Behavior of Stable Structures Made of Beams

In this paper, we study the asymptotic behavior of an varepsilon -periodic 3D stable structure made of beams of circular cross-section of radius r when the periodicity parameter varepsilon and the ratio {r/varepsilon } simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

Parametric Stability Analysis of a Parabolic-Tapered Rotating Beam Under Variable Temperature Grade

The static and dynamic stability of a parabolic-tapered beam of circular cross-section subjected to an axial alive load and rotating in the X-Y plane about the Z-axis is analyzed cosidering a variable temperature grade along the centroidal axis of the beam as the beam is in steady state condition. The stability is analyzed for clamped-clamped and pinned-clamped boundary conditions. The parametric instability regions are acquired by means of Saito-Otomi conditions. The consequences of variation parameter, revolution speed, temperature grade and boundary conditions on the instability regions are examined for dynamic load and static buckling loads for 1st, 2nd and 3rd modes and are represented by a number of graphs. The results divulge that the stability is increased by increasing revolution speed; however, increase in thermal grade and the variation parameter leads to destabilize the converging system for all boundary conditions. This research can be useful for vibration isolation of rotating non-uniform beams with high surrounding temperature and moderate rotational speeds and the design of rotor blades with high strength to weight ratio by choosing the suitable parameters obtained from this computational analysis.

On fracture analysis of cracked curved beams

This paper focuses on evaluating stress intensity factors (SIFs), for a curved beam of circular cross section with an external ring crack, applying an approach on the basis of estimating the strain energy release rate. The out of plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach namely differential quadrature element method (DQEM) to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam.

Analysis of thermoelastic damping in the clamped-free microbeam with linearly tapered circular cross-section

An accurate estimation of thermoelastic damping (TED) is of significance and importance in the design for the microbeam resonators with variable cross-section operated in vacuum. TED determines the up limit of quality factor (Q-factor) used for evaluating the microresonator performance. However, in the past, the previous works focus on the TED modelling of uniform microbeam resonators with rectangular cross-section. There is lack of works aiming at the TED modelling of non-uniform microbeam resonators with circular cross-section. In addition, the previous TED model developed by Zener for uniformly circular cross-section beams is not suitable for calculating TED values of the non-uniform beams. Therefore, the TED model for clamped –free microbeam resonators with linearly tapered circular cross-section is meaningful to be derived in this work. The radius and length dependences of TED are investigated. The results of finite element method (FEM) model are calculated for purpose of comparison. Results indicate that for large aspect ratio (l/r0), TED values of linearly tapered microbeams with circular cross-section are larger than those of uniform microbeams, while for small aspect ratio (l/r0), TED values of linearly tapered microbeams are lower than those of uniform microbeams. Moreover, the maximum values of TED called Debye peaks in linearly tapered microbeams are lower than those of uniform microbeams.

Thermoelastic damping in circular cross-section micro/nanobeam resonators with single-phase-lag time

Estimating thermoelastic damping (TED) is a crucial and significant procedure for the design of the high quality-factor micro/nanobeam resonators operated in vacuum. However, most of the previous TED models were derived by employing the classical thermoelasticity theory established on the Fourier heat conduction. These existing models all focused on beam resonators with rectangular cross-section. In this work, employing the generalized thermoelasticity theory of single-phase-lag model, an analytical TED model is derived for circular cross-section micro/nanobeams considering the non-Fourier heat conduction. The influences of non-Fourier effect on TED behaviors and the temperature field of the circular cross-section beam are examined. The single- and multiple-peak phenomena of TED spectrum under the non-Fourier effect are studied. The results indicate that TED in circular cross-section beams is significantly dependent on the equilibrium temperature and the ratio of single-phase-lag time to thermal relaxation time. In addition, the temperature distribution in the beam exhibits distinct differences due to the non-Fourier effect.

Water entry of compliant slender bodies: Theory and experiments

Hydroelastic phenomena play a critical role on the dynamics of lightweight marine vessels, but a comprehensive understanding of their potential benefits and drawbacks in water impact remains elusive. In contrast with the literature on hydroelastic impact that focuses on plane strain deformations and two-dimensional fluid flows, we address the water entry of compliant slender bodies. We propose a mathematically-tractable framework to predict the rigid body motion and elastic deformation of a beam impacting the water surface in free fall. At each location on the beam, the hydrodynamic loading is determined from the level of submersion of the cross-section and its local velocity and acceleration. Slamming, added mass, and drag are all included in the model and cogently weighted based on the level of submersion of the cross-section. Edge effects are incorporated in the model through a shape function that modulates the hydrodynamic loading as a function of the distance from the edges. Model predictions are validated through experiments on compliant beams of circular cross-section, which detail both the structural response and the resulting flow physics, through the integration of high-speed imaging, direct acceleration measurement, and particle image velocimetry. Results of this study are expected to aid in the design of lightweight ship hulls, experiencing dynamic bending deformations during sailing and maneuvering.

Milling of Dielectric Ceramics by Fast Argon Atoms

A new method for dielectric materials milling has been developed. Instead of well-known ion milling used for metals the dielectrics were processed by broad beams of fast argon atoms. The fast atoms were produced due to charge exchange collisions of accelerated ions. Plasma emitter of the ions was generated in hollow cathode glow discharge. Emissive grid of a circular cross-section beam source consisted of six segments. Energy of the fast atoms ranged from 1 to 3 keV. The beam source was used for production of contoured grooves on flat surfaces of hard ceramic materials. On the surface of movable seal ring made of α-corundum were produced grooves with depth of 20±0.5 μm and roughness of Ra ≈ 0.4 µm. The rate of α-corundum etching amounted to 3 μm/h.

Vibration analysis of a carbyne-based resonator in nano-mechanical mass sensors

Carbyne is a chain of C atoms held together by double or alternating single and triple chemical bonds, and has twice the tensile stiffness of carbon nanotubes (CNTs) and graphene sheets (GSs). In this study, we propose a nano-mechanical mass sensor using a tensioned carbyne resonator. The carbyne resonator is modeled as an equivalent continuum circular cross section beam with diameter 0.772 Å, Young’s modulus 32.71 TPa, shear modulus 11.8 TPa, Poisson’s ratio 0.386 and density 32.21 g cm−3. We analyze the resonant frequency of the proposed sensor carrying with a concentrated mass based on the Timoshenko beam theory and verify the theoretical approach using Rayleigh’s energy method and molecular dynamics simulation. The results show that the proposed mass sensor can measure a tiny mass with weight below 10−5 zg, and provide much higher sensitivity than CNTs- and GSs- based nano-mechanical mass sensors. In addition, the effects of carbyne length, mass position and tensile load on the frequency shift are also analyzed in detail, and it is preferred to use shorter carbyne and higher tensile load in the proposed mass sensor.

Effect of static axial compression on the natural frequencies of helical springs

Purpose – The purpose of this paper is to address the practically important problem of the load dependence of transverse vibrations for helical springs. At the beginning, the author develops the equations for transverse vibrations of the axially loaded helical springs. The method is based on the concept of an equivalent column. Second, the author reveals the effect of axial load on the fundamental frequency of transverse vibrations and derive the explicit formulas for this frequency. The fundamental natural frequency of the transverse vibrations of the spring depends on the variable length of the spring. The reduction of frequency with the load is demonstrated. Finally, when the frequency nullifies, the side buckling spring occurs. Design/methodology/approach – Helical springs constitute an integral part of many mechanical systems. A coil spring is a special form of spatially curved column. The center of each cross-section is located on a helix. The helix is a curve that winds around with a constant slope of the surface of a cylinder. An exact stability analysis based on the theory of spatially curved bars is complicated and difficult for further applications. Hence, in most engineering applications a concept of an equivalent column is introduced. The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The transverse vibration is represented by a differential equation of fourth order in place and second order in time. The solution of the undamped model equation could be obtained by separation of variables. The fundamental natural frequency of the transverse vibrations depends on the current length of the spring. Natural frequency is the function of the deflection and slenderness ratio. Is the fundamental natural frequency of transverse oscillations nullifies, the lateral buckling of the spring with the natural form occurs. The mode shape corresponds to the buckling of the spring with moment-free, simply supported ends. The mode corresponds to the buckling of the spring with clamped ends. The author finds the critical spring compression. Findings – Buckling refers to the loss of stability up to the sudden and violent failure of seed straight bars or beams under the action of pressure forces, whose line of action is the column axis. The known results for the buckling of axially overloaded coil springs were found using the static stability criterion. The author uses an alternative approach method for studying the stability of the spring. This method is based on dynamic equations. In this paper, the author derives the equations for transverse vibrations of the pressure-loaded coil springs. The fundamental natural frequency of the transverse vibrations of the column is proved to be the certain function of the axial force, as well as the variable length of the spring. Is the fundamental natural frequency of transverse oscillations turns to be to zero, is the lateral buckling of the spring occurs. Research limitations/implications – The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The more accurate model is based on the equations of motion of loaded helical Timoshenko beams. The dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain) is to be derived. Unfortunately, that for the spatial beam models only numerical results could be obtained. Practical implications – The closed form analytical formulas for fundamental natural frequency of the transverse vibrations of the column as function of the axial force, as well as the variable length of the spring are derived. The practically important formulas for lateral buckling of the spring are obtained. Originality/value – In this paper, the author derives the new equations for transverse vibrations of the pressure-loaded coil springs. The author demonstrates that the fundamental natural frequency of the transverse vibrations of the column is the function of the axial force. For study of the stability of the spring the author uses an alternative approach method. This method is based on dynamic equations. The new, original expressions for lateral buckling of the spring are also obtained.

Vibration Analysis of Hollow Tapered Shaft Rotor

Shafts or circular cross-section beams are important parts of rotating systems and their geometries play important role in rotor dynamics. Hollow tapered shaft rotors with uniform thickness and uniform bore are considered. Critical speeds or whirling frequency conditions are computed using transfer matrix method and then the results were compared using finite element method. For particular shaft lengths and rotating speeds, response of the hollow tapered shaft-rotor system is determined for the establishment of dynamic characteristics. Nonrotating conditions are also considered and results obtained are plotted.

FFT Analysis on Coupling Effect of Axial and Torsional Vibrations in Circular Cross Section Beam of Steam Turbine Generators

This paper presents a novel method to nonlinearly investigate the dynamics of the coupled axial and torsional vibrations in the circular cross section beam of the steam turbine generator using the FFT analysis. Firstly, the coupled axial and torsional vibrations of a beam are proved by equivalent law of shearing stress and different boundary conditions. Then, a nonlinear mathematical model of the coupled axial and torsional vibrations is established by the Galerkin method. Lastly, the fast Fourier transform (FFT) is employed to investigate the coupled effect of the beam vibration. A practical calculation example is calculated numerically and the coupled mechanism of the beam’s axial and torsional vibrations is analyzed in detail. The analysis results show that the frequencies of the coupled response would be existed in some special orders and the coupled response frequencies are smaller than the single vibration. Since for the first time the coupled mechanism of the beam’s axial and torsional vibrations is theoretically analyzed, the findings in this work may provide directive reference for practical engineering problems in design of steam turbine generators. DOI : http://dx.doi.org/10.11591/telkomnika.v12i2.4379

Contact between rolling beams and flat surfaces

SUMMARY This work presents a new approach to model the contact between a circular cross section beam and a flat surface. In a finite element environment, when working with beam elements in contact with surfaces, it is common to consider node or line to surface approaches for describing contact. An offset can be included in normal gap function due to beam cross section dimensions. Such a procedure can give good results in frictionless scenarios, but the friction effects are not usually properly treated. When friction plays a role (e.g., rolling problems or alternating rolling/sliding) more elaboration is necessary. It is proposed here a method that considers an offset not only in normal gap. The basic idea is to modify the classical definition of tangential gap function in order to include the effect of rigid body rotation that occurs in a rolling scenario and, furthermore, consider the moment of friction force. This paper presents the new gap function definition and also its consistent linearization for a direct implementation in a Newton-Raphson method to solve nonlinear structural problems modeled using beam elements. The methodology can be generalized to any interaction involving elements with rotational degrees of freedom. Copyright © 2013 John Wiley & Sons, Ltd.

A new approach for simple calculation of shear stresses in steel beams of circular cross section

A new approach for simple calculation of shear stresses in steel beams of circular cross section

Shear strength of reinforced concrete circular cross-section beams

A proposed adequation of NBR 6118, Item 7.4, related to shear strength of reinforced concrete beams is presented with aims to application on circular cross-section. The actual expressions are most suitable to rectangular cross-section and some misleading occurs when applied to circular sections at determination of VRd2, Vc and Vsw, as consequence of bw (beam width) and d (effective depth) definitions as well as the real effectiveness of circular stirrups. The proposed adequation is based on extensive bibliographic review and practical experience with a great number of infrastructure elements, such as anchored retaining pile walls, where the use of circular reinforced concrete members is frequent.