Partial-interaction Composite Beams Research Articles

Bandgap analysis of partial-interaction composite beams periodically attached vibration absorbers

Elastic metamaterials with local resonant components exhibit unique bandgap behavior that can be utilized to control the vibration and noise of mechanical structures. This study aims to introduce the bandgap characteristics into the vibroacoustic control of partial-interaction composite beams (PICBs) widely adopted in civil engineering, aviation, and marine fields. Vibration absorbers are arranged periodically on the beam to generate a bandgap in PICBs, thereby transforming a conventional PICB into a metamaterial beam. An analytical approach is proposed to establish the spectral element (SE) matrix of a metamaterial beam based on the Timoshenko–Ehrenfest beam theory. Specifically, the governing equations of motion for PICBs follow Hamilton's principle. This model considers the effects of shear slip between two-layer sub-beams, shear deformations, and rotary inertia. The SE matrix of PICBs is then constructed and applied to obtain the SE matrix of the metamaterial beam by assembling the SE matrix of the vibration absorbers. Subsequently, the wave finite element (WFE) method is employed to predict the dispersion curve of the infinite metamaterial beam and the dynamic response of the finite metamaterial beam. In a benchmark example, the complex band structure and transmission indicated by the proposed approach are validated compared to those calculated by evaluation formulas of the literature and the finite element method. Lastly, the bandgap behavior for the vibration absorber parameters, lattice constants, and shear connector stiffness is investigated based on the defined dimensionless parameters. These results are valuable for optimizing vibration and noise reduction in PICBs equipped with attached vibration absorbers.

An accurate solution method for the dynamic characteristics of three-layered partial-interaction composite beams

In the dynamic analysis of three-layered partial interaction composite beams (PICBs), it is not clear whether the effects of shear deformation and rotary inertia all need to be considered, and the shear-locking problems often occurs in existing finite element methods. To improve computational efficiency, accuracy and stability, an analytical method is proposed by considering the shear slips at the interface and the independent rotary angles among the sub-elements. In the proposed method, a matrix containing the natural frequencies of the three-layered PICB is appropriately established by using the solutions to differential equations of motion rather than the shape function in finite element methods. The main improvement of the proposed method is the analyticity of solutions, which can effectively avoid shear-locking problems often mentioned in finite element methods and obtain accurate solutions due to no introduction of approximate shape functions. The present results agree well with the analytical and numerical results in the literature, which validates the accuracy of the proposed method. The effects of shear deformation and rotary inertia on the dynamic behaviors of three-layered PICBs are discussed. It reveals that the shear deformation can not be ignored but rotary inertia can be ignored in the dynamic analysis of three-layered PICBs, which can effectively reduce the computation complexity. In general, the proposed method has practical value in natural frequency analysis of the three-layered PICB with high computational efficiency, accuracy and stability.

Explicit Finite Element Formulations for the Free Vibrations and Buckling of Partial-Interaction Composite Beams with Two Sub-components

Explicit Finite Element Formulations for the Free Vibrations and Buckling of Partial-Interaction Composite Beams with Two Sub-components

Uniform Step Loading of a Partial Interaction Composite Beam

In the present paper, a one-dimensional finite element model for the analysis of composite beams of partial interaction is constructed. This model was verified against some analytical results available in the literature and achieved very good agreement with the natural frequencies and the time histories it was compared to. Then it was utilised to analyse partial interaction composite beams under the effect of uniform step loads and provided important information about the expected dynamic amplification factors, which turned out to be particularly high, and the effects of the linear stiffness ratio of the interface and the boundary conditions of the lower layer of the beam. The results, in particular, showed that even for extreme cases the orders of magnitude of the slip and the corresponding uplift remain the same. This pointed out an important finding that the uplift in the researched context, at least, is not negligible as it is widely assumed in the literature.

A numerically stable exact method for analysis of partial-interaction composite beams based on Timoshenko beam theory

The traditional direct stiffness matrix method may occur numerical instability for analysis of partial-interaction composite beams with long spans. To solve this problem, this paper proposes a numerically stable exact method called the coefficient matrix method for analysis of two-layered partial-interaction composite beams using the Timoshenko beam theory. By replacing the nodal displacements with the undetermined parameters of shape function obtained by the governing equation as primary unknown coefficients, the coefficient matrix method can avoid the inversion operation on the matrices in obtaining the direct stiffness matrix. Thus, numerical stability can be ensured. Finally, the coefficient matrix method is validated against experimental, ANSYS and other theoretical results in the literature with good agreement. And the effect of shear deformation on shear slips at the interface of the sub-beams by varying shear connector stiffness, shear-to-Young’s modulus ratios, and span-to-depth ratios are discussed.

Composite finite elements on dynamic and buckling responses of composite beams with independent rotations

To better understand the structural dynamic response and integrity under complex engineering situations, displacement-based variational principles and corresponding composite finite elements (CFEs) are developed for the simulation of vibration and buckling behavior of partial-interaction composite beams. The accuracy of the composite FEs are validated against the analytical and numerical results in the literature where good agreement is always generated. More importantly, the effect of independent-rotation assumption is investigated in the simulation which is tested to have significant impact on the natural frequencies and buckling loads of composite structures with distinct components and generally lead closer results to the plane-stress FE results. The influence of the rotation of sub-structure on the relative slips between sub-structures is discussed. This explains the discrepancies observed in the literature. The construction of CFEs also considers the internal degrees of freedom (DoFs), which are then eliminated through static condensation, to alleviate the shear/curvature locking phenomenon. The convergence of the proposed FEs are tested, along with the capability of the present FEs in avoiding the locking phenomenon. The final explicit expressions of the elements are also offered and can be readily implemented into the commercial packages with high computational efficiency.

Dynamic Amplification Factors of Partial-Interaction Composite Beams Acted Upon by the Moving Load

This paper focuses on the dynamic response, mainly dynamic amplification factors (DAFs), of partial-interaction composite beams (PICBs) based on the Timoshenko beam theory (TBT). By assuming that each sub-beam behaves as an independent Timoshenko beam, the governing differential equations of motion of the PICBs are derived under the action of dynamic load. The natural frequencies and modal shapes for simply supported PICBs are also extracted. For decoupling the governing differential equations of motion, the orthogonality property of two distinct vibration modes is checked and applied for further analysis. The modal superposition method is then utilized to derive the analytical expressions of transverse deflection, interfacial shear slip, and normal stresses of the PICBs subjected to the moving load. Finally, two test beams are organized to validate the proposed methodology. For this purpose, the results which are calculated by ANSYS and obtained from available methods are appropriately compared. The effects of shear connector stiffness and speed of the moving load on the DAFs of the PICB acted upon by the moving constant load are discussed.

Static and dynamic analysis of three-layered partial-interaction composite structures

The static and dynamic behavior of three-layered composite structures is investigated in the present work through the presently proposed finite-element (FE) expressions. Relative to most research on partial-interaction composite beams, the present numerical method is developed through considering independently assumed interlayer slips and transverse shear deformations among sub-elements, the latter of which are based on the Timoshenko’s beam theory. Variational method based on the minimum potential energy principle is delivered to establish the static and dynamic stiffness (and mass) matrices for the partial-interaction composite beams. The present results are validated against the analytical and numerical results from limited data presented in the literature where good agreement is generally obtained, giving credence of the present technique. What’s more, the present FE technique is also demonstrated to be advantageous in the following sense: 1) The introduction of the internal degrees of freedom significantly alleviates the locking phenomenon that is frequently mentioned in the literature; 2) Independently assumed rotations for three layers are necessary in predicting the global behavior of composite structures with significantly distinct material properties. It is finally concluded that the developed FE framework provides a stable and efficient tool in investigating the three-layered composite beams/columns in various perspectives and could be readily extended to composite structures with more complex geometries or loading conditions.

A dynamic stiffness matrix method for free vibrations of partial-interaction composite beams based on the Timoshenko beam theory

This paper focuses on the development of a dynamic stiffness matrix method for analyzing the dynamic behavior of geometrically and materially linear two-layer partial-interaction composite beams based on the Timoshenko beam theory. The proposed model considers the effect of shear slip between concrete slab and steel beam as well as the shear deformations and rotary inertia. The main improvement offered by the proposed model compared to the existing methods is that each sub-beam is assumed to have an independent rotary angle, which is more realistic. The proposed model is compared to experimental and finite element results and other theoretical models, and the effects of shear deformations and rotary inertia on eigenfrequencies are discussed in detail.

Variational Principles and Explicit Finite-Element Formulations for the Dynamic Analysis of Partial-Interaction Composite Beams

AbstractIn this paper, we conduct a systematic dynamic investigation of partial-interaction composite beams under various sophisticated loading conditions that have seldom been presented in the lit...

A numerically stable dynamic coefficient method and its application in free vibration of partial-interaction continuous composite beams

It has long been recognized that traditional exact methods may encounter numerical instability when analyzing the free vibration of a continuous partial-interaction composite beam, a type of composite beam which considers the interfacial slip. In contrast to the Euler–Bernoulli beam theory, the form of the general solution for the free-vibration governing equations of partial-interaction composite beams based on Timoshenko beam theory will change dramatically when the frequency is sufficiently high, indicating that shear deformation cannot be ignored at high-order frequencies. To tackle this difficulty, this paper presents a numerically stable and theoretically exact method to analyze the dynamic responses of continuous composite beams with partial-interaction. The new method can effectively overcome the problem of numerical instability encountered by traditional theoretical solutions such as the dynamic stiffness matrix method and transfer matrix method, particularly for high-order vibrations or long-span continuous beams. Some numerical examples are provided to demonstrate the performance of the proposed method.

Particle Swarm Optimization–Based Finite-Element Analyses and Designs of Shear Connector Distributions for Partial-Interaction Composite Beams

Particle Swarm Optimization–Based Finite-Element Analyses and Designs of Shear Connector Distributions for Partial-Interaction Composite Beams

Dynamic analysis of partial-interaction Kant composite beams by weak-form quadrature element method

In this paper, the Kant higher-order beam theory is applied to model each segment of the partial-interaction composite beams, aiming to capture as possible fidelity as the plane stress model. On this basis, the weak-form equation is obtained through the principle of virtual work. Besides, the weak-form quadrature element (WQE), as a counterpart of the conventional finite element (CFE), is derived and implemented to more efficiently solve problems, including free vibration eigenvalue analysis and dynamic responses prediction to moving loads. After the verification of all the programs developed, a series of numerical examples are given to investigate the WQE’s superiority on convergence rate and numerical smoothness over the CFE. At the end of the paper, the influences of structural damping and loads’ moving speed on impact factor of two-span continuous beams are analyzed. Numerical results show that the proposed WQE, due to the variable-order interpolation of the element, possesses overwhelmingly higher computational efficiency than the CFE, and the numerical smoothness problem in the internal force analysis is significantly alleviated by WQE method.

Static and dynamic analysis of two-layer Timoshenko composite beams by weak-form quadrature element method

• A variable-order quadrature element for Timoshenko composite beams is developed. • Static and free vibration analyses are conducted by FEM and weak-form QEM. • Convergence rate of conventional finite element analysis is significantly improved. • Numerical smoothness problem of stress and force analysis is greatly alleviated. To improve the efficiency in predicting the dynamic mode and static response of the two-layer partial interaction composite beams, this paper utilizes the differential quadrature technique to approximate derivatives of the primary unknowns with adaptive order of precision, rather than the low and constant order of interpolation used in the conventional finite element method (FEM). A degree-of-freedom-adaptive weak-form quadrature element (WQE) for dynamic analysis is formulated and implemented based on the principle of virtual work. For the purpose of comparison, a parabolic displacement-based finite element is also provided, thus (1) the predicted deflections and natural frequencies of the composite beams are verified; (2) the smoothness of the internal forces and stresses generated by WQE method and FEM are compared, and (3) the convergent rates of higher order free vibration modes are also examined. Numerical results show that the efficiency of the proposed WQE method has, on the one hand, significantly triumphed over that of FEM on analyses including static response, natural frequencies and higher order free vibration modes, on the other hand, the smoothness of results, including internal forces and stresses, is greatly refined.

Stiffness matrix for the analysis and design of partial-interaction composite beams

Compared to the classical Rayleigh-Ritz method and other analytical solutions, finite element (FE) method is more efficient and capable in calculating the deformations and stress states of partial-interaction composite beams, as well as manipulating the material and geometrical parameters for better engineering designs. Stiffness matrix of composite beams considering the interlayer slips is derived based on the kinematic assumptions of the Timoshenko’s beam theory by taking into account of the transverse shear deformations. A detailed derivation is elaborated to obtain the local stiffness matrix for a composite beam element, while the higher-order interpolation functions are adopted for the displacement fields (deflection, rotation, and interlayer slip). Then a finite element program is developed by assembling the local stiffness matrices and applying corresponding equivalent nodal stresses. Several numerical results are presented and compared against the analytical solutions available in the literature to demonstrate the accuracy of the proposed FE stiffness matrix. Finally, a design procedure by connecting particle swarm optimization technique with the present FE analysis is created to reduce the deformations of simply supported composite beams while the quantity of shear connectors remains the same, to prove the superior simulation capacity and efficiency of the derived FE stiffness matrix with other techniques. Compared to the analytical methods, the proposed finite element is more convenient and applicable in the analysis of partial-interaction composite beams under more complicated loading and boundary conditions. In the meantime, the explicitly expressed local stiffness matrix can be easily implemented into other commercial software packages asa subroutine for both professional and personal engineering designs and calculations.

Dynamic characteristics analysis of partial-interaction composite continuous beams

The dynamic characteristics of continuous steel-concrete composite beams considering the effect of interlayer slip were investigated based on Euler Bernoulli\'s beam theory. A simplified calculation model was presented, in which the Mode Stiffness Matrix (MSM) was developed. The natural frequencies and modes of partialinteraction composite continuous beams can be calculated accurately and easily by the use of MSM. Proceeding from the present method, the natural frequencies of two-span steel-concrete composite continuous beams with different span-ratios (0.53, 0.73, 0.85, 1) and different shear connection stiffnesses on the interface are calculated. The influence pattern of interfacial stiffness on bending vibration frequency was found. With the decrease of shear connection stiffness on the interface, the flexural vibration frequencies decrease obviously. And the influence on low order modes is more obvious while the reduction degree of high order is more sizeable. The real natural frequencies of partial-interaction continuous beams commonly used could have a 20% to 40% reduction compared with the fully-interaction ones. Furthermore, the reduction-ratios of natural frequencies for different span-ratios two-span composite beams with uniform shear connection stiffnesses are totally the same. The span-ratio mainly impacts on the mode shape. Four kinds of shear connection stiffnesses of steel-concrete composite continuous beams are calculated and compared with the experimental data and the FEM results. The calculated results using the proposed method agree well with the experimental and FEM ones on the low order modes which mainly determine the vibration properties.

Dynamic stiffness matrix of partial-interaction composite beams

Composite beams have a wide application in building and bridge engineering because of their advantages of mechanical properties, constructability and economic performance. Unlike static characteristics, the methods of studying the dynamic characteristics of partial-interaction composite beams were limited, especially dynamic stiffness matrix method. In this article, the dynamic stiffness matrix of partial-interaction composite beams was derived based on the assumption of the Euler–Bernoulli beam theory, and then it was used to predict the frequencies of the free vibration of the single-span composite beams with various boundary conditions or different axial forces. The corresponding vibration modes and buckling loads were also obtained. From the comparison with the existing results, the numerical results obtained by the proposed method agreed reasonably with those in the literatures. The dynamic stiffness matrix method is an accurate method which can determine natural vibration frequencies and vibration mode shapes in any precision theoretically. As a result, when the higher precision or natural frequencies of higher order are required, the dynamic stiffness matrix method is superior when compared to other approximate and numerical methods. The dynamic stiffness matrix method can also be combined with the finite-element method to calculate the free vibration frequencies and natural mode shapes of composite beams in complex conditions.

Analysis of higher order composite beams by exact and finite element methods

In this paper, a two-layer partial interaction composite beams model considering the higher order shear deformation of sub-elements is built. Then, the governing differential equations and boundary conditions for static analysis of linear elastic higher order composite beams are formulated by means of principle of minimum potential energy. Subsequently, analytical solutions for cantilever composite beams subjected to uniform load are presented by Laplace transform technique. As a comparison, FEM for this problem is also developed, and the results of the proposed FE program are in good agreement with the analytical ones which demonstrates the reliability of the presented exact and finite element methods. Finally, parametric studies are performed to investigate the influences of parameters including rigidity of shear connectors, ratio of shear modulus and slenderness ratio, on deflections of cantilever composite beams, internal forces and stresses. It is revealed that the interfacial slip has a major effect on the deflection, the distribution of internal forces and the stresses.

Dynamic analysis of two-layer composite beams with partial interaction using a higher order beam theory

Kant׳s higher order beam kinematics, which takes into account both the longitudinal and transverse higher order deformation of beam, is applied to the dynamic model of two-layer partial interaction composite beams. To establish and solve the mathematical problem, the finite element for the composites is then formulated using the principle of virtual work. Furthermore, the finite element of Timoshenko composite beam model, for the purpose of comparison, is also given in this paper. The numerical performance and reliability of the proposed finite elements are verified through the comparison with the results of ABAQUS using the plane stress model and those based on Reddy׳s higher beam theory and classical beam theories from the literature. Besides, the responses to the seismic and moving load of the proposed composite beam model are also presented, and subsequently the influences of parameters including damping ratio, velocity of moving load, slenderness ratio and interfacial stiffness on the mechanical behavior are studied. Numerical results show that the present higher order composite beam model can achieve higher accuracy on the dynamic analyses than the classical and Reddy׳s models, and the impact effects of moving load together with the partial interaction between sub-layers should be considered.

Bending Solutions of the Timoshenko Partial-Interaction Composite Beams Using Euler-Bernoulli Solutions

For partial-interaction composite beams, two beam theories (i.e., the Euler-Bernoulli and Timoshenko beam theories) are usually used to investigate their deflections, slips, and stress resultants. However, the relationships between the solutions of partial-interaction composite beams based on the two beam theories have not been discussed while the corresponding relationships for homogeneous beams have been investigated in detail for several years. By analyzing the constitutive relationships and equations of equilibrium, the authors derived the relationships of the solutions between single-span Euler-Bernoulli and Timoshenko partial-interaction composite beams. The integral constants are also presented for various boundary conditions. Through the presented relationships, the solutions of the Timoshenko partial-interaction composite beams could be readily obtained from the solutions of the corresponding Euler-Bernoulli counterparts. As a result, the more complicated flexural-slip-shear deformation analysis based on Timoshenko beam theory may be avoided for engineering designers.