Elastic Composite Beams Research Articles

Flexural vibration of elastic composite beams using a third-order deformation kinematics

The present study introduces a one-dimensional finite element (FE) model that utilizes third-order deformation kinematics to analyze the flexural vibration of two-layered composite beams with partial shear slip. The proposed model incorporates a three-node straight beam element, utilizing the field-consistent approach and full numerical integration of the stiffness matrix. This approach is adopted to effectively address stress oscillation and shear locking issues, ensuring accurate and reliable results. The analysis focuses on the third-order deformation kinematics of longitudinal displacement within the beam depth, examining each of the two layers individually. The interface between the two material layers is joined using deformable shear connectors, which are represented as dispersed shear springs over the length of the beam. This study focuses on conducting a flexural vibration analysis of two-layered composite beams. The analysis includes the examination of both free vibration and forced vibration responses while considering or omitting the influence of damping under various loading conditions. The validity of the proposed FE model is assessed by the utilization of a two-dimensional model developed within the ABAQUS software. Additionally, the suggested model is evaluated through the process of verification by comparing it with previously published results.

Stability of delaminated composite beams subjected to retarded periodic follower force

This work deals with the stability problem of elastic composite cantilever beams subjected to a delayed, periodically changing follower force. The equation of motion of the periodic system with time delay is deduced based on some previous works. Composite beams with and without delamination are considered, and the finite element method is applied to carry out the spatial discretization of the structures. Besides, for the delaminated case further two cases are involved. The first case is when the delamination is in the midplane of the beam, while the second case involves an asymmetrically placed delamination, respectively. The Floquet theory is applied to derive the transition matrix of the periodic system. An important aspect is that the time delay and the principal period of the dynamic force are equal to each other. The discretization over the time domain is performed by using the Chebyshev polynomials of the first kind. Basically, there are five parameters governing the dynamic problem including among others the time delay and the static and dynamic forces. The stability behavior is shown for the intact and delaminated beams on the parameter planes for large number of cases by using the unit circle criteria. The presence and absence of structural damping is also analyzed in each case. The results indicate that some planes are sensitive to the mesh resolution, others are not. Moreover, on some planes significant differences may take place between the intact and delaminated beams from the standpoint of stable zones.

Two phase local/nonlocal thermo elastic waves in a graphene oxide composite nanobeam subjected to electrical potential

AbstractThe present article studies the two phase local/nonlocal deformation of thermo electrical composite nanobeam reinforced with graphene oxide powder (GOP). The controlling equation of motion and boundary conditions are derived via two phase elasticity in differential form in conjunction with Hamilton's principle and Euler‐Bernoulli beam theory. The effect of a thermal and piezo electric field is incorporated with the governing equations by convoluting field quantities and displacement components. Then, Navier method is adopted to observe the influence of simply supported boundary conditions on the dynamics of the beam. Comparison studies are performed to display the accuracy and efficiency of this analytical model. Further, the effects of GOP weight fraction, two phase parameter, external electric voltage and temperature difference on the dimensionless frequency of GOP reinforced piezo thermo elastic composite beams are thoroughly investigated and highlighted through tables and dispersion curves. The results obtained from the present work gained the important role of GOP and thermo‐ piezoelectricity in predicting the vibration behaviors of two phase local/ nonlocal nanostructures.

A new model for thermal buckling of an anisotropic elastic composite beam incorporating piezoelectric, flexoelectric and semiconducting effects

A new model for thermal buckling of an anisotropic elastic composite beam incorporating piezoelectric, flexoelectric and semiconducting effects

Two phase local/non local waves in a magneto thermo electrical composite nano beam reinforced with graphene oxide powder

The present article studies the two phase local/nonlocal deformation of magneto thermo electrical composite nano beam reinforced with graphene oxide powder (GOP). The controlling equation of motion and boundary conditions are derived via two phase elasticity in differential form conjunction with Hamilton’s principle and Euler-Bernoulli beam model. The effect of a non-uniform magnetic and piezo electric field is incorporated with the governing equations by convoluting field quantities and displacement components. Then, Navier method is adopted to observe the influence of various boundary conditions on the dynamics of the beam. Comparison studies are performed to display the accuracy and efficiency of this analytical model. Further, the effects of magnetic field, GOP weight fraction, two phase parameter, external electric voltage, nonlocal parameter and temperature difference on the dimensionless frequency of GOP reinforced magneto piezo thermo elastic composite beams are thoroughly investigated and highlighted through tables and dispersion curves.

Lumped system model for elastic steel-concrete beams with partial interaction

PurposeThe purpose of this paper is to introduce a numerical model to investigate static response of elastic steel-concrete beams. The numerical model is based on the lumped system with the combination of the transfer matrix and the analog beam methods (ABM). The beams are composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. This type of beam is widely used in constructions especially for highway bridges. The static field and point transfer matrices for the element of the elastic composite beam are derived. The present model is verified and is applied to study the static response of elastic composite beams with intermediate conditions. The intermediate condition is considered as an elastic support with various values of stiffness. The elastic support can be considered rigid when the stiffness has very high values. The influence effect of shear stiffness between the upper slab and lower beam, and the end shear restraint on the static behavior of the composite beams is studied. In addition, the change in the stiffness of the elastic support is also highlighted.Design/methodology/approachThe objective of this study is to introduce a numerical model based on lumped system to calculate the static performance of elastic composite bridge beams having intermediate elastic support by combining the ABM with the transfer matrix method (TMM). The developed model is applicable for studying static and dynamic responses of steel-concrete elastic composite beams with different end conditions taking into account the effect of partial shear interactions. The validity of the lumped mass model is checked by comparing its results with a distributed model and good agreements are achieved (Ellakany and Tablia, 2010).FindingsA model based on the lumped system of the elastic composite steel-concrete bridge beam with intermediate elastic support under static load is presented. The model takes into consideration the effect of the end shear restraint together with the interaction between the upper slab and the lower beam. Combining the analogical beam method with the TMM and analyzing the behavior of the elastic composite beam in terms of shear studs and stiffness, the following outcomes can be drawn: end shear restraint and stiffness of the shear layer are the two main factors affecting the response of elastic composite beams in terms of both the deflection and the moments. Using end shear restraint reduces the deflection extensively by about 40 percent compared to if it is not used assuming that: there is no interaction between the upper slab and the lower beam and the beam is acting as simply supported. As long as the shear layer stiffness increases or interaction exists, the deflection decreases. This reduced rate in deflection is smaller in case of existence of end shear restraint. The effect of the end shear restraint is more prevailing on reducing the deflections in case of partial interactions. However, its effect completely diminishes in case of complete interaction. Presence of the end shear restraint and shear layer stiffness produces almost the same variations in the components of the bending moments of the composite beam. Finally, for a complete interaction, comparing the case of using end shear restraint or the case without it, the differences in the values of the deflections and moments are almost negligible.Research limitations/implicationsThe following assumptions related to the theory of ABM: shear studs connecting both sub-beams are modeled as a thin shear layer, each sub-beam has the same vertical displacement and the shear deformation in the sub-beams is neglected.Practical implicationsThe developed model can be effectively used for a quick estimation of the dynamic responses of elastic composite beams in real life rather than utilizing complicated numerical models.Social implicationsThe applications of this model can be further extended for studying the behavior of complex bridge beams that will guarantee the safety of the public in a quick view.Originality/valuePrevious models combined the TMM with the ABM for studying the static and free-vibration behaviors of elastic composite beams assuming that the field element is subjected to a distributed load. To study the dynamic response of elastic composite beams subjected to different moving loads using transfer matrix ABM, it was essential to use a massless field element and concentrate the own weight of the beam at the point element. This model is considered a first step for studying the impact factors of elastic composite beams subjected to moving loads.

Experimental and numerical study on static behavior of elastic concrete-steel composite beams

Elastic concrete (rubber-filled concrete) is employed into the steel-concrete composite structures due to its good ductility and crack resistance. Bending test and numerical simulation were conducted to investigate the static behavior of partial shear connected elastic concrete-steel composite beam with different section size, studs and degrees of shear connection. The results of the tests show that elastic concrete could improve the ductility behavior of stud and composite beam, and reduce the width of concrete cracks efficiently. Larger degree of shear connection can lengthen the elastic stage and retard the development and spread of slip, but may lead to a decrement of ductility. With the degree of shear connection unchanged, stud with large diameter of 22mm may cause 9% lower ultimate bearing capacity, and even worse deformability and ductility of composite beam compared with the smaller stud. Moreover, the analysis results exhibited a good behavior and applicability of the elastic concrete in the partial shear connected composite beams. With the help of elastic concrete, ductility of composite beam has been improved effectively so that it is possible to apply large studs into practice.

Nonlinear free dynamics of a two-layer composite beam with different boundary conditions

The nonlinear free vibrations of a two-layer elastic composite beam are investigated. Different boundary conditions, both symmetric and not symmetric with respect to the beam midpoint, equal on both layers and different on each layers, are considered. The analysis is developed by means of the multiple time scale method, and at each order of the asymptotic development, we obtain different information. The first order terms provide the linear natural frequencies. The first, the second and the third natural frequencies are computed explicitly. The next order terms, on the other hand, provide the nonlinearity coefficients measuring the nonlinear amplitude dependence of the natural frequencies, i.e. the curvature of the backbone curve. Both the linear frequencies and the nonlinear coefficients are found to be dependent on two dimensionless parameters only and, for boundary conditions different on each layer, also of the ratio between the axial stiffnesses of each layer.

Fatigue Behavior of Elastic Concrete-Steel Composite Beams

As a new material type, elastic concrete has been used in pavement and bridge deck paving due to its superior properties to ordinary concrete. Nowadays, fatigue behavior of steel-concrete composite beams has become the focus in engineering design. This paper summarized the research status, methods, influence factors on fatigue behavior of elastic concrete and steel-concrete composite beams and compared various fatigue specifications among different countries. The result shows that elastic concrete has longer fatigue life than ordinary concrete, so we can solve fatigue problems by using elastic concrete instead of ordinary concrete in composite beams. Finally the author puts forward suggestions for further advanced study in this area.

BUCKLING OF COMPOSITE NONLOCAL OR GRADIENT CONNECTED BEAMS

The buckling of an axially loaded elastic composite beam with a nonlocal core or a nonlocal connection system is studied in this paper. The composite beam or the sandwich beam is composed of two Euler–Bernoulli beams with a nonlocal elastic interaction. This nonlocal interaction is physically based on the Reissner's model based on three-parameters' interaction function. The energy equations are first presented, and the differential equations are rigorously obtained from a variational principle. We show that the connection model can be expressed in an integral format, therefore, inducing the nonlocal character of this beam elastic interaction model. Furthermore, the variational format of this nonlocal composite model is given, leading to meaningful natural and higher-order boundary conditions. The system of these differential equations can be reduced to a single 10th-order differential equation. We present an exact method to solve this stability problem, based on Ferrari or Cardano's method. The solution can be fully simplified in case of specific boundary conditions with symmetrical considerations. The stability domain is analytically characterized in the loading space for the pinned–pinned boundary conditions. The correspondence between the buckling of the nonlocal composite column and the shear composite column is discussed. Finally, it is shown that the Timoshenko beam model is a nonlocal integral model.

Nonlinear analysis of the dynamics of articulated composite rotor blades

The general nonlinear intrinsic equations of motion of an elastic composite beam are solved in order to obtain the elasto-dynamic response of a rotating articulated blade. The solution utilizes the linear Variational-Asymptotic Method (VAM) cross-sectional analysis, together with an improved damped nonlinear model for the rigid-body motion analysis of helicopter blades in coupled flap and lead-lag motions. The explicit (direct) integration algorithm implements the perturbation method in order to solve the transient form of the nonlinear intrinsic differential equations of motion and obtain the elasto-dynamic behavior of an accelerating composite blade. The specific problem considered is an accelerating articulated helicopter blade of which its motion is analyzed since it starts rotating from rest until it reaches the steady-state condition. It is observed that the steady-state solution obtained by this method compares very well with other available solutions. The resulting simulation code is a powerful tool for analyzing the nonlinear response of composite rotor blades; and for serving the ultimate aim of efficient noise and vibration control in helicopters.

A numerical model for static and free vibration analysis of elastic composite beams with end shear restraint

The end shear restraint, which is an un-classical type of end support, has a significant effect on the behavior of elastic composite beams. The principal aim of this paper is to present a numerical model for studying the effect of end shear restraint on static and free vibration behavior of elastic composite beams with various end conditions. The elastic composite beam, considered in this study, is composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. This type of beam is widely used in constructions especially for highway bridges. The three types of end conditions considered in this study are simple, fixed and free supports. The numerical model is based on the combination of transfer matrix and analog beam methods. The field transfer matrices for the element of the elastic composite beam are derived. The present model is applied to the beam systems with and without end shear restraint and the static response and natural frequencies are calculated. the effect of shear stiffness between the upper slab and lower beam is also demonstrated.

On lateral–torsional vibrations of elastic composite beams with interlayer slip

The lateral–torsional vibrations of composite beams are investigated in this paper, based on a variational approach. Composite beams studied in this paper are classified as composite beams with interlayer slip (composite beams with partial interaction or layered wood beams) or three-layer sandwich beams. It will be shown in this paper that both structural systems are governed by the same nature of differential equations. The theoretical framework of lateral–torsional vibrations of composite beams is given, and some engineering results are presented for the pinned–pinned strip composite beam. A simple closed-form solution is achieved for the lateral–torsional natural frequencies. The results are analogous to the ones obtained for the in-plane vibrations of composite beams (sandwich beam or composite beams with partial interaction) where the natural frequencies increase with the stiffness of the connection. Extension of these results to some more complex loading cases is envisaged, and a numerical procedure will be probably needed in the general case.

Calculation of higher natural frequencies of simply supported elastic composite beams using Riccati matrix method

A composite beam is composed of an upper slab and a lower beam connected at the interface by shear transmitting studs. In this paper, an improved and efficient numerical model for the calculation of higher natural frequencies of an elastic composite beam is presented. The numerical model uses the Riccati transfer matrix method. First, the exact field transfer matrix for an element of the beam is represented using the combination of the Analog Beam Method and the transfer matrix method. Second, applying Riccati method to the beam system, the natural frequencies can be easily calculated. The advantage of the present model is to overcome the numerical instabilities of the ordinary transfer matrix method, especially when calculating the higher natural frequencies of structures. A numerical example is given to illustrate and compare the results with those available from other methods. Finally, a parametric study is given to examine the effect of various parameters of the elastic composite beam on its free vibration behavior.

Static Analysis of Non-Uniform Elastic Composite Beams

Static Analysis of Non-Uniform Elastic Composite Beams

Transfer Matrix-analog Beam Method To Calculate Natural Frequencies Of Elastic Composite Beams

The principal aim of this paper is to present a numerical model for predicting the natural frequencies of elastic composite beams, like bridges: with different intermediate conditions. The prediction of natural frequencies is carried out using the Transfer Matrix- Analog Beam Method [TMABM]. The effects of intermediate conditions such as elastic supports and hinge have been included in the presented model. Elastic composite beams are composed of an upper slab and a lower beam connected at the interface by shear transmitting studs. Parametric studies on the effects of various geometric and material parameters on the fundamental natural frequencies of elastic composite beam are conducted. The obtained results show that these parameters must be taken into account when analyzing the free and forced vibrations or designing these types of composite beams. The developed model can also be applied to calculate the natural frequencies of multi span composite bridges with various intermediate conditions.

Flexural vibrations of elastic composite beams with interlayer slip

The objective of the present paper is to analyze the dynamic flexural behavior of elastic two-layer beams with interlayer slip. The Bernoulli-Euler hypothesis is assumed to hold for each layer separately, and a linear constitutive equation between the horizontal slip and the interlaminar shear force is considered. The governing sixth-order initial-boundary value problem is solved by separating the dynamic response in a quasistatic and in a complementary dynamic response. The quasistatic portion that may also contain singularities or discontinuities due to sudden load changes is determined in a closed form. The remaining complementary dynamic part is non-singular and can be approximated by a truncated modal series of fast accelerated convergence. The solution of the resulting generalized decoupled single-degree-of-freedom oscillators is given by means of Duhamel,s convolution integral, whereby the velocity and acceleration of the loads are the driving terms. Light damping is considered via modal damping coefficients. The proposed procedure is illustrated for dynamically loaded layered single-span beams with interlayer slip, and the improvement in comparison to the classical modal analysis is demonstrated.

Shear center for elastic thin-walled composite beams

An analysis to determine shear centers for anisotropic elastic thin-walled composite beams, cantilevered and loaded transversely at the free end is presented. The shear center is formulated based on familiar strength of material procedures analogous to those for isotropic beams. These procedures call for a balancing of torsional moments on the cross sectional surface and lead to a condition of zero resultant torsional couple. As a consequence, due the presence of anisotropic coupling, certain non-classical effects are manifested and are illustrated in two example problems. The most distinguishing result is that twisting may occur for composite beams even if shear forces are applied at the shear center. The derived shear center locations do not depend on any specific anisotropic bending theories per se, but only on the values of bending and shear stresses which such theories produce.