Beam Analysis Research Articles

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Effectiveness of shear key on torsional resistance of precast beam: An experimental and numerical investigations

The present study evaluates the behaviour of wet precast beam-to-beam connection under pure torsion through experimental and numerical studies. A wet connection is provided at the central region of the precast beam. Two precast beam elements are connected by welding the overlapped portion of reinforcement bars projecting from each beam element. Furthermore, inward and outward shear keys are provided within the connection region to examine the efficacy of shear keys on the torsional resistance of the precast beam. Also, the behaviour of precast beams with and without shear keys is compared with monolithic beams. Experiments are conducted using a loading frame, designed and fabricated to create a pure torsion effect on the beam specimen under the application of monotonic vertical load. The response of test specimens is evaluated through various parameters such as torque and corresponding twist at different phases of loading, torsional ductility index, crack formation and failure propagation. Experimental studies show that shear keys provided within the connection region effectively contribute to force transfer and enhance torsional resistance of the precast beam by 16 %−24 % as compared to monolithic beam and precast beam without the shear key. A numerical analysis of the precast beam is carried out, and the behaviour of test specimens obtained from experimental studies is compared. The damage pattern and torque-twist behaviour obtained from numerical studies adequately simulate the response of test specimens observed during the experimental study.

Forced vibration analysis of sandwich beam reinforced with graphene in piezoelectric medium on elastic substrate

In this study, using an analytical and precise solution, the dynamic transverse deflection of a five-layer beam with Prussian core with graphene platelet reinforced composite (GPLRC) under a moving harmonic load on a Pasternak elastic substrate is analyzed. First, the properties of the porous core materials and the piezoelectric layer and surface, which were graphene platelet reinforcements (GPLRs), were defined. The constitutive relations were extended using the Bonilla’s higher-order theory and Hamilton’s principle, relationships were extracted. Finally, using the Laplace method and analytical solution. A parametric analysis is provided to investigate impact of temperature distribution, porosity coefficient, thickness ratio, spring constant, voltage and excitation frequency on the responses.

A comprehensive study of beam modal functions in the free vibration analysis of cylindrical shells: Critical examination on the applicability to the clamped-free boundary condition

Over the past few decades, approximate methods that can provide solutions of sufficient accuracy have received considerable attention in the free vibration analysis of cylindrical shells, where a great deal of studies adopted the beam modal functions as the trial functions for the axial mode shapes of cylindrical shells. Nevertheless, most studies were restricted to the application of single term beam modal function and failed to simulate elastic boundary conditions of cylindrical shells, while the accuracy of the corresponding methods has recently sparked significant controversy, especially for cylindrical shells under the clamped-free boundary condition. This paper presents a comparative study of three forms of beam modal functions in the free vibration analysis of cylindrical shells, one of which is proposed for the first time to simulate elastic boundary conditions of cylindrical shells. A unified model is developed using the general Rayleigh–Ritz method, incorporating the breathing modes with circumferential orders being zero, and four types of commonly used thin shell theories, namely the Donnell, Reissner, Love, and Sanders theories. From both perspectives of natural frequencies and mode shapes, numerical results are validated by comparison with those existing in the literature and those calculated from the finite element method (FEM). The results not only clarify the distinction of different forms of beam modal functions used in the Rayleigh-Ritz method, but also provide explanations for the controversy raised in recent studies. Furthermore, the unified formulations can be extended to vibration analysis of various forms of shell structures, and can also be helpful to the vibration analysis of beams and plates with elastic boundary conditions.

Numerical analysis of fixed-end hollow rectangular beam under uniformly distributed load

The purpose of using opening in the reinforced concrete (RC) rectangular beam is the reduction of self-weight, cost, displacement, and strain. Therefore, this research performs linear elastic finite element analysis by using ETABS for fixed-ended RC hollow and solid rectangular beams under uniformly distributed loadings with variable beam lengths, compressive strengths, and opening sizes.The solid and hollow beams are considered to be a 2-nodded line element for the numerical analysis. The maximum range of validation result in case of hollow beam is found to be (3.9 to 7.9) %, which may indicate good accuracy of numerical analysis. The 50 × 50 mm opening size is suitable for 300 × 300 mm RC rectangular beam because of showing the positive normalized deflection of (0–1.45) % and lower strain rates (i.e. 0.13 % and 0.17 %) to compare the solid beam. This research may help professional engineers to use suitable opening size for design and construction works. Although, there is a scope to enhance this research in future by performing nonlinear analysis.

Efficient layerwise multiphysics spectral element model for delaminated composite strips with PWAS transducers

Efficient structural element-based models are essential for fast simulations of wave propagation in composite structures for model-based and physics-informed data-driven structural health monitoring. This article introduces the first efficient multiphysics time-domain spectral structural element for wave propagation analysis of beam and panel-type composite structures with piezoelectric transducers (patch or full layers) containing delaminations. A general framework is presented to model multiple delaminations and transducer patches located arbitrarily. The intact host and patch transducer-bonded laminates and sub-laminates between delaminations are modelled separately using an electromechanically coupled efficient layerwise zigzag theory (ZIGT) for kinematics and a piecewise quadratic variation for the electric potential across piezoelectric layers. The high-order spectral element (SE) features a virtual electric node to model equipotential surfaces of piezoelectric transducers apart from the usual physical nodes having mechanical and internal electric degrees of freedom. A hybrid point-least squares continuity approach is employed to maintain continuity at the intersections of delaminated sub-laminates or the patch-bonded laminate with the host laminate. The model’s performance in capturing electroelastic waves’ interaction with delamination is examined with reference to the conventional finite element (FE) solution based on the ZIGT, continuum-based FE solutions, and the SE solution based on a non-layerwise version of the laminate theory. Finally, the model is used to examine the impact of interfacial location and size of delaminations on wave propagation behaviour.

The Flexural Behavior of Reinforced Ultra-High Performance Engineering Cementitious Composite (UHP-ECC) Beams Fabricated with Polyethylene Fiber (Numerical and Analytical Study)

Ultra-high performance engineered cementitious composite (UHP-ECC), which is a new and ductile version of concrete, has attracted researchers recently due to its exceptional mechanical properties: its very high compressive strength (from 100 to 200 MPa) and very high tensile strain capacity (not less than 3% and up to 8%). However, the available experimental literature is small due to its very high cost. To overcome the high cost of the experiments of UHP-ECC, the finite element modeling package ANSYS was used to create a new modeling technique using the Menetrey–Willam constitutive model, recently added to ANSYS. This technique was validated using previous experimental results for UHP-ECC beams and found to be accurate and effective. The previous FE model was used to conduct a parametric study and the variables—the compressive strength of the concrete, the percentage of the volume content of polyethylene fibers, the tensile reinforcement ratio, and the span-to-depth ratio—were found to be effective upon the flexure behavior of the reinforced UHP-ECC beams. As the analysis and design of UHP-ECC beams fabricated with polyethylene fiber are not available yet through design codes, an analytical model including some equations was deduced to calculate the flexure capacity of such beams. The results of the parametric study were used to investigate the validity and accuracy of the analytical model. The proposed equations demonstrated a good estimation compared with the numerical analysis results.

A high-order isogeometric vibrational method for adaptive analysis of athlete diving equipment using advanced kinematic and geometric modeling

Isogeometric high-order analysis of a sandwich beam is presented in this article. The kinematic and geometric modeling is applied using the higher order modeling based on the stretchable models. The suggested model in this article can be applied for the sport equipment specially for analysis of diving beams boards and beams. The Variational-based approach is extended to derive governing equations. The results are analytically obtained in order to seek impact of significant parameters of the problem on the responses. The results are confirmed through comparison with available ones in the literature.

Electro-magneto-elastic analysis of a sandwich composite beam as diving board in swimming with composed of graphene origami metamaterials

A novel composite structure composed of graphene origami reinforcement integrated with piezoelectric/piezomagnetic layers is defined in this paper. The Material composition is assumed as steel novel metamaterials. The proposed model can be used as a diving board in swimming. The vibrational-based formulation is extended using an advanced higher-order thickness-stretchable model. The governing motion equations are derived using Hamilton’s principle through the computation of strain and kinetic energies as well as external work. The constitutive relations are extended for the composite core in terms of volume fraction, folding degree, and thermal load using some modifier functions using Halpin-Tsai micromechanical models for modulus of elasticity, Poisson’s ratio, thermal expansion coefficient, and density. The natural frequency responses are derived using the analytical method in terms of characteristics of graphene origami such as thermal load, foldability parameter, and amount of reinforcement. Furthermore, an investigation on the impact of initial electro-magneto-mechanical loads is studied on the responses.

Evaluation of the flexural stiffness of a lattice girder composite slab at the construction stage according to the lattice girder shape

Lattice girder composite slabs (LGCS) for use in construction stages are structures in which part of the lattice girder is embedded in precast concrete panels with a thickness of less than 100 mm. they serve as a permanent formwork supporting the casting loads of on-site concrete while constituting a portion of the RC slab. In this study, analytical research was conducted to evaluate the flexural stiffness of LGCS effectively and simply considering a range of variables. Based on the results, an Euler-Bernoulli beam-theory-based equivalent sectional analysis method is proposed. To achieve this, the study extracted the second moments of area (Iexp) from the experimental results of previous researchers and compared them with the second moments of area (Ibeam) calculated using the Euler-Bernoulli beam-theory-based sectional analysis, analyzing how the ratio (Ibeam/Iexp) varies according to the design parameters. Variable analyses over a wide range were conducted by expanding the types and ranges of variables, and the effects of different variables and ranges were analyzed by comparing the second moments of area based on an FE analysis of LGCS (IFEM) with those based on a beam analysis (Ibeam). Furthermore, to apply the equivalent sectional analysis method to LGCS, equivalent second-moment-of-area formulas were proposed through the equivalent neutral axis and equivalent arm length for each sectional element.

Drop Tests and Numerical Analyses of Composite Beams with Corrugated Web

To evaluate the energy absorption ability of composite beams with corrugated web under impact, the drop tests were conducted to demonstrate the fracture modes and obtain the load and energy history curves. Based on the drop tests, a finite element (FE) model was proposed with a weak link designed to trigger crushing, developed using Abaqus/Explicit, which integrates cohesive elements and employs the improved Hashin criterion along with the Choi–Chang criterion to accurately predict the onset and progression of delamination. The model accounts for the anisotropy and progressive damage in composite laminates. The periodic boundary conditions (PBCs) were integrated into the single-wave corrugated web beam model, the inherent limitations of which were corrected, enabling it to simulate the crushing process with the same effectiveness as the multi-wave model. As a result, the proposed model can accurately depict the progressive crushing behavior of corrugated web beams under impact loads while maintaining high computational efficiency.

Nonlinear buckling and free vibration analysis of auxetic graphene origami composite beams under nonuniform thermal environment

This study examines the thermo-mechanical behavior of auxetic metamaterial beams enhanced by graphene origami (GOri) under spatially varying nonuniform temperature distributions (SVTD). Utilizing Timoshenko beam theory considering von-Kármánn type nonlinear strain–displacement relationship, GOri beams are modeled as layered structures. The Ritz method is employed to solve equilibrium equations, analyzing the impact of GOri distribution patterns, content, and folding degree on post-buckling and vibration paths. The effects of five SVTDs, three end conditions, and three GOri distribution patterns on buckling, post-buckling behavior, and nonlinear free vibration characteristics are explored. Findings reveal that the parabolic temperature distribution with peak temperatures at beam ends (P-MAE) results in higher critical temperatures and nonlinear free vibration frequencies. This research provides crucial insights into the design and optimization of GOri-enabled metamaterial structures in complex thermal environments, highlighting the significant influence of nonuniform temperature distributions along the beam’s length.

Critical buckling load analysis of Euler-Bernoulli beam on two-parameter foundations using Galerkin method

The critical buckling load determination of Euler-Bernoulli beams on two-parameter elastic foundations (EBBo2PFs) is important to avert buckling failures. The governing equation for buckling of thin beam on two-parameter elastic foundation is a homogeneous ordinary differential equation (HODE) of fourth order and constant parameters when the beam is prismatic and homogeneous. The HODE has been solved in this work by Galerkin method for simply supported, clamped and clamped-simply supported ends. One-parameter algebraic shape function formulation was used to reduce the problem to an algebraic eigenvalue problem, which is solved to find the critical buckling load for each studied case. The critical buckling load for EBBo2PF for simply supported boundary conditions was found to be closely identical to the exact solutions. The solutions for clamped-clamped edges and clamped-simple supports were found to be accurate. The merit of the Galerkin method is the simplicity and the accuracy even when one-parameter shape function has been used.

Critical lateral‐torsional buckling loads of porous orthotropic rectangular beams containing warping effects

AbstractDue to their elemental porosity, porous materials display individual mechanical properties, rendering them essential components in various engineering applications. So, this study investigates the lateral‐torsional buckling (LTB) sensitivity of porous orthotropic rectangular beams subjected to a concentrated load, including the warping effects. Porosity‐dependent material properties vary along the beam's height via four different porosity distribution patterns. The constitutive equations are obtained using the principle of virtual work based on the classical beam theory containing the warping effect, and the governing equations are solved by performing the Ritz method to obtain the critical LTB load. The porous orthotropic beams and the warping effects add complexity to the analysis. So, the influence of some parameters, such as porosity coefficients, porosity distribution patterns, orthotropy, height‐to‐width ratio, slenderness ratio, and warping coefficients, on the LTB characteristics of porous orthotropic rectangular beams are investigated in detail. The novelty of this study lies in its comprehensive LTB analysis of orthotropic rectangular beams under specific effects, such as porosity and warping factors. The findings offer valuable insights into the LTB characteristics of orthotropic porous beams, contributing to an improved comprehension of their structural behavior and facilitating the design of engineering structures. This study contributes to the composite materials and structural stability analysis, offering potential applications in many engineering domains.

On the bending, buckling and free vibration analysis of bio-inspired helicoidal laminated composite shear and normal deformable beams

The mechanical behaviours of bio-inspired helicoidal symmetric laminated composite (BIHLC) beams are investigated via the Ritz method. By exploiting the variational formulation, equations of motion along with element stiffness, geometrical stiffness, and mass matrices are derived. The study conducts a thorough examination, covering bending, buckling stability, and free vibration analyses of BIHLC beams with various lamination schemes. The developed model is verified against existing literature on conventional composite laminated and BIHLC beams. The study also examines the mechanical response of BIHLCs, considering boundary conditions, lamination schemes, orthotropy ratios, and aspect ratios. Notably, deflections, critical buckling loads, and fundamental frequencies demonstrate variations dependent on the specific lamination scheme, boundary condition, and aspect ratio. Novel findings, presented for the first time, offer valuable insights for future studies in this area.

Dynamic Modeling and Analysis of Multi-Span Timoshenko Beams Under Moving Loads

Dynamic response analysis of multi-span beams is one of the important topics in the field of highway and railway engineering, which provides valuable guidance for the design, operation and maintenance of multi-span bridges. It is worth considering how to calculate the dynamic characteristics of multi-span beams quickly and conveniently. In this study, an effective analytical method is developed for the dynamic modeling and investigations of multi-span Timoshenko beams under moving loads by employing the assumed mode method (AMM). Based on Hamilton’s principle, the equation of motion of the Timoshenko multi-span beam subjected to moving loads is formulated and the natural frequencies are calculated. A comprehensive investigation is conducted on the dynamic responses of the multi-span Timoshenko beam considering different factors, including the length-to-thickness ratio, disorder degree, arrangement order, number of spans and related parameters of moving loads. In addition, the influence of the interval and velocity of the moving load series on the dynamic responses, including displacement, velocity and acceleration of the multi-span beam, are analyzed in detail. The theoretical calculation results of multi-span Timoshenko beams under moving loads are compared with numerical results obtained from ANSYS software, and the results are in good agreement. This demonstrates that the developed method, which utilizes the AMM to analyze the dynamic characteristics of multi-span beams subjected to moving loads, significantly simplifies the calculations and is well-suited for practical engineering applications.

Extending the Natural Neighbour Radial Point Interpolation Meshless Method to the Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core

This work investigates the mechanical behaviour of sandwich beams with cellular cores using a multiscale approach combined with a meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The analysis is divided into two steps, aiming to analyse the efficiency of NNRPIM formulation when combined with homogenisation techniques for a multiscale computational framework of large-scale sandwich beam problems. In the first step, the cellular core material undergoes a controlled modification process in which circular holes are introduced into bulk polyurethane foam (PUF) to create materials with varying volume fractions. Subsequently, a homogenisation technique is combined with NNRPIM to determine the homogenised mechanical properties of these PUF materials with different porosities. In this step, NNRPIM solutions are compared with high-order FEM simulations. While the results demonstrate that RPIM can approximate high-order FEM solutions, it is observed that the computational cost increases significantly when aiming for comparable smoothness in the approximations. The second step applies the homogenised mechanical properties obtained in the first step to analyse large-scale sandwich beam problems with both homogeneous and functionally graded cores. The results reveal the capability of NNRPIM to closely replicate the solutions obtained from FEM analyses. Furthermore, an analysis of stress distributions along the beam thickness highlights a tendency for some NNRPIM formulations to yield slightly lower stress values near the domain boundaries. However, convergence towards agreement among different formulations is observed with mesh refinement. The findings of this study show that NNRPIM can be used as an alternative numerical method to FEM for analysing sandwich structures.

Manufacturing and aging behavior of CuCr1Zr powder: Analysis and modelling of close-coupled gas atomization of CuCr1Zr and its impact on the melt beam disintegration and analysis powder oxidation kinetics

Powder bed-based additive manufacturing methods represent an increasingly vital role in industrial applications. Specifically, there has been considerable focus on highly reflective metals, such as CuCr1Zr, in recent years. However, current research primarily revolves around developing appropriate manufacturing parameters e.g. laser powder bed fusion (PBF/LB-M) and assessing the corresponding mechanical and electrical properties of CuCr1Zr. The impact of manufacturing routines and oxidation behavior of CuCr1Zr powder are seldom discussed in additive manufacturing. Therefore, the present study addresses the analysis of powder production and the oxidation behavior of CuCr1Zr powder via close-coupled gas atomization to analyze the disintegration of a CuCr1Zr melting jet during gas atomization of CuCr1Zr by using a high-speed camera. Critical conditions for secondary disintegration were calculated as a function of the initial gas pressure. Additionally, calorimetric measurements and isothermal oxidation experiments were conducted to quantify oxide formation and growth. According to the results, initial oxide formation occurs after 42 days with CuCr1Zr powder at room temperature in a nitrogen atmosphere. Subsequently, oxide growth follows a logarithmic law, associated with the formation and conversion of Cu2O to CuO.

Effects of chromatic dispersion on single-photon temporal wave functions in quantum communications

In this study, we investigate the effects of chromatic dispersion on single-photon temporal wave functions (TWFs) in the context of quantum communications. Departing from classical beam analysis, we focus on the temporal shape of single photons, specifically exploring generalized Gaussian modes. From this foundation, we introduce chirped and unchirped Gaussian TWFs, demonstrating the impact of the chirp parameter in mitigating chromatic dispersion effects. Furthermore, we extend our investigation to time-bin qubits, a topic of ongoing research relevance. By exploring the interplay of dispersion effects on qubit interference patterns, we contribute essential insights to quantum information processing. This comprehensive analysis considers various parameters, introducing a level of complexity not previously explored in the context of dispersion management. We demonstrate the relationships between different quantities and their impact on the spreading of TWFs. Our results not only deepen the theoretical understanding of single-photon TWFs but also offer practical guidelines for system designers to optimize symbol rates in quantum communications.

A Novel Approach of the Viscoelasticity of Axially Functional Graded Bar and Application of Harmonic Vibration Analysis of an Isotropic Beam as Support

The use of smart materials and passive controllers in modern technologies has stimulated the study of vibration in elastic systems with viscoelastic damping. It is also possible to create components with precise material distribution coefficients and distinct properties, such as Functionally Graded Materials. This work investigates the resonant frequency characteristics of a beam supported at its ends by Axially Functionally Graded (AFG) viscoelastic bars using the finite element method. The set of equations governing motion is obtained by assuming Euler–Bernoulli beam theory for the beam and bar theory for the bars using Lagrange’s equations. The material properties of the functionally graded bar is assumed to vary through the length according to the power law distribution. The longitudinal loss factor values are used to define the internal damping coefficient, which is also dependent on the Young’s modulus value varying along the bar. The effects of the length-varying material properties and internal damping of the FG support bars on the force transmission TR and frequency parameters λ are examined in detail. No study has been found in the literature on the vibration of viscoelastic FG bar-supported beams subjected to a harmonic force at the centre point. It is shown that using bars formed with combinations of different materials considering material damping will be useful to keep the vibration level and force transmission at a certain value and control the frequency parameters.