Equivalent Beam Model Research Articles

Bumper optimum design using the dynamically equivalent beam under various impact conditions

Nowadays it is required for the bumper system to meet the various impact conditions simultaneously; barrier impact, IIHS (Insurance Institute for Highway Safety) bumper impact and pedestrian impact. Firstly, dynamically equivalent bumper beam models were developed for each impact condition and its accuracy was verified by nonlinear finite element analysis result. Dynamically equivalent pedestrian impact beam model was developed by using the equivalent forces of bumper beam and stiffeners. Pedestrian bending angle was obtained by using this equivalent pedestrian beam model. By combining these equivalent beam models, bumper optimum design program was developed. In this optimum design program, direct search method was used for the optimization algorithm. To verify the accuracy of this optimum design program, a nonlinear finite element result was used. By using this optimum design program, it can be secured the bumper impact performances in an early design stage and it will be also contributed to reduce the design time and test costs.

A shear–shear torsional beam model for nonlinear aeroelastic analysis of tower buildings

In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.

Dynamic response of tall buildings to wind loads by reduced order equivalent shear-beam models

Two equivalent beam models are proposed in order to estimate the dynamic response of tall buildings affected by wind loads. The first model is based on the Timoshenko beam, which assumes bending and shear stiffness to be in series. The second model considers bending and shear stiffness to be in parallel. The parameters of the two equivalent beams are calibrated using the data of a complete structural system and imposing both the value of suitable displacements (static approach) and the value of the first natural frequencies (dynamic approach). Numerical analyses are performed using wind tunnel loads and FEM models. The accuracy of the dynamic response of the two equivalent beam models is assessed by comparison to a complete FEM model describing the structural system of a case study tall building. Furthermore, the ability of the equivalent shear-beam models to describe the random features of dynamic response is assessed using the first four statistical moments of the dynamic response.

Methodology for the accuracy improvement of FEM beam type T-junctions of buses and coaches structures

The analysis of structures with finite elements methods (FEM) represents a widely spread technique. For large tubular structures similar to the buses and coaches upper structures, beam type elements are utilized due to the fact that these elements provide satisfactory results at relatively reduced computational performances. However the beam type elements have a main disadvantage determined by the fact that the modeled joints have an infinite rigid behavior. This shortcoming determines a stiffer behavior of the modeled structures which translates into an error source for the structural simulations (up to 45%). To overcome this problem, a simple methodology was conceived and an alternative optimized equivalent beam model obtained. The methodology studies the behavioral characteristics of beam modeled T-junctions determining their limitations and comparing them to equivalent T-junctions modeled with shell and volume elements. This way an improved Tjunction has been obtained, in which the behavioral error was reduced to less than 5%. Furthermore the FEM obtained results were validated with real T-junctions.

A NUMERICAL INVESTIGATION ON THE FREE VIBRATION OF CARBON NANOPEAPODS AS VARIABLE FREQUENCY BEAM RESONATORS

This study aims at investigation of the resonance frequencies of carbon nanopeapods constructed by a single wall carbon nanotube and encapsulated buckyball molecules ( C 60). A nanopeapod can be used as a nanoscale variable frequency beam resonator according to the number and positions of the encapsulated fullerenes. Using the molecular structural mechanics method the covalence bonds are simulated by equivalent beam elements and the van der Waal interactions between the buckyballs and nanotube are modeled as linear springs. Also, an equivalent beam model is proposed for the nanopeapod with sectional properties which are obtained by the molecular structural mechanics model. The beam-like modes of free vibrations are obtained using both models and the effect of position and number of buckyballs on the resonance frequencies are investigated.

Effects on the various rubber fenders of a tripod offshore wind turbine substructure collision strength due to boat

An analysis is conducted to minimize the damage to tripod type offshore wind turbines substructure caused by collisions with boat. The impact of a wind turbine and a boat takes a complicated form. ANSYS LS-Dyna, a commercial FEM tool, is employed for the impact analysis. The FE model generated using equivalent beams for the blades which are verified the method through the results of static and dynamic analysis between full 3D blade model and equivalent beam model. The investigation is conducted in order to determine the influences of various boat speeds, which result in different loading conditions, and various rubber materials for the fender on strain energy, total deformation, plastic strain, internal energy, and permanent deformation. Natural rubber, composite rubber, and neoprene are modeled using Mooney–Rivlin constants, which are determined by material tests, and a time-marching analysis is conducted to account for their nonlinearity. Based on the analysis results, the minimum thickness of a rubber fender is suggested to decrease the effects of impact for the structures. This study provides relationship trends between the structure thickness and the rubber fender thickness, which may be useful in developing the structural design of a tripod type offshore structure.

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions.

Assessment of vibrations induced in factories by automated guided vehicles

This study proposes a simplified sub-structural model to explore the floor micro-vibration induced by automated guided vehicles in thin-film transistor liquid crystal display factories. Time history analyses of a sequence of automated guided vehicles moving loads considering various car spacings on an equivalent three-span continuous beam model of a thin-film transitor liquid crystal display factory were simulated. The effectiveness of vibration control using viscoelastic dampers was also examined. Numerical simulations demonstrate that the simplified method can predict the measured floor vibration spectra with satisfactory accuracy and that the automated guided vehicles induced floor vibrations without control exceed the acceptable VC-B level required for the installation of specific precision process tools. The application of energy dissipation devices has shown to be effective in vibration mitigations as they enhance the damping characteristics of a multi-span floor system. The maximum response of the whole continuous beam induced by a group of automated guided vehicles can be effectively suppressed to a desired VC-B level if multiple viscoelastic dampers are implemented along the automated guided vehicles moving bay and the spacing between each automated guided vehicle is properly adjusted. The simplified analytical method can help engineers quickly assess the level of automated guided vehicles-induced floor vibration and assist in the design of low-vibration floor systems in high-technology factories.

1D system identification of buildings during earthquakes by seismic interferometry with waveform inversion of impulse responses—method and application to Millikan library

Two new algorithms have been introduced as a further development of a robust interferometric method for structural health monitoring (SHM) of buildings during earthquakes using data from seismic sensors. The SHM method is intended to be used in an automatic seismic alert system, to issue a warning of significant damage during or immediately after the earthquake, and facilitate decision making on evacuation, to avoid loss of life and injury from possible collapse of the weekend structure during aftershock shaking. The method identifies a wave velocity profile of the building by fitting an equivalent layered shear beam model in impulse response functions (virtual source at roof) of the recorded earthquake response. The structural health is monitored by detecting changes in the identified velocities in moving time windows, the initial window being used as reference. Because the fit involves essentially matching phase difference between motion at different floors, the identified velocity profile is not affected by rigid body rocking, and soil-structure interaction in general, as demonstrated in this paper. Consequently, detected changes in wave velocity during an earthquake are not affected by changes in the soil-foundation system, which is a major advantage over SHM by detecting changes in the observed modal frequencies. Further, the method is robust when applied to real buildings and large amplitude earthquake response, as demonstrated in previous work. The new fitting algorithms introduced are the nonlinear least squares (LSQ) fit and the time shift matching (TSM) algorithms. The former involves waveform inversion of the impulse responses, and the latter - iterative matching of the pulse time shifts, both markedly reducing the identification error as compared to the previously used direct ray algorithm, especially for more detailed models, i.e., with fewer floors per layer. Results are presented of identification of the NS, EW and torsional responses of the densely instrumented Millikan Library (9-story reinforced concrete building in Pasadena, California) during a small earthquake.

A non-parametric probabilistic model for soil-structure interaction

The paper investigates the effect of soil-structure interaction on the dynamic response of structures. A non-parametric probabilistic formulation for the modelling of an uncertain soil impedance is used to account for the usual lack of information on soil properties. Such a probabilistic model introduces the physical coupling stemming from the soil heterogeneity around the foundation. Considering this effect, even a symmetrical building displays a torsional motion when submitted to earthquake loading. The study focuses on a multi-story building modeled by using equivalent Timoshenko beam models which have different mass distributions. The probability density functions of the maximal internal forces and moments in a given building are estimated by Monte Carlo simulations. Some results on the stochastic modal analysis of the structure are also given.

Performance of an equivalent shear beam (ESB) model container for dynamic geotechnical centrifuge tests

In dynamic centrifuge tests, appropriate boundary conditions are required in order to simulate the seismic semi-infinite soil layer responses within the confines of a finite size model container. An ESB (equivalent shear beam) model container first designed at the University of Cambridge was built with a stack of light-weight aluminum frames separated by rubber to experimentally achieve this goal. In this paper, a significant number of dynamic centrifuge tests and the corresponding seismic response analyses were performed to evaluate the dynamic performance of a newly constructed ESB model container and to shed light on the range of testable soil conditions. In the set of conducted tests, it appears that the end walls of the ESB model container behave in accordance with the dynamic response of the soil deposit, despite a difference in the natural period depending on the relative density of the sand deposit. This is attributed to the differences in mass and stiffness of the end walls compared to those of the contained soil model. For partially filled model container, significant differences in seismic responses are observed in the end walls and in the soil deposit due to seismic interaction caused by the upper unfilled frames of the container. These findings suggest that dynamic model tests using this ESB model container should be conducted with the container completely filled. In addition, on the basis of a comparison with the seismic soil behavior inside a rigid-walled model container, it is clear that the ESB model container can provide a more representative lateral boundary configuration for dynamic site response studies.

A simplified plane strain analysis of lateral wall deflection for excavations with cross walls

Previous studies have shown that installation of cross walls in deep excavations can reduce lateral wall deflection to a very small amount. To predict the lateral wall deflection for excavations with cross walls, it is necessary to perform a three-dimensional numerical analysis because the deflection behavior of the diaphragm wall with cross walls is by nature three dimensional. However for the analysis and design of excavations, two-dimensional plane strain analysis is mostly used in practice . For this reason, based on the deflection behavior of continuous beams and the superimposition principle, an equivalent beam model suitable for two-dimensional plane strain analysis was derived to predict lateral wall deflection for excavations with cross walls. Three excavation cases were employed to verify the proposed model. Case studies confirm the proposed equivalent beam model for excavations with cross walls installed from near the ground surface down to at least more than half the embedded depth of the diaphragm wall. For the case with a limited cross-wall depth, the proposed model yields a conservative predicted lateral wall deflection.

Transverse impact characteristics of a rubber pipe expansion joint

The transverse impact characteristics of a rubber pipe expansion joint are studied. A pair of joints assembled end to end with an inserted middle mass is tested on a drop shock testing machine. Based on the test results, an equivalent fixed-fixed beam model with polynomial stiffness and damping is applied to predict the transverse impact response and identify the nonlinear impact parameters. The least square residual between the computed and test results is defined to drive the identification optimization. The response surface methodology in combination with the generalized reduced gradient method is used to search the best matching coefficients. Final results show that the equivalent bending stiffness of the tested rubber expansion joint gradually decreases with the transverse deformation and is greatly influenced by its internal working pressure.

A method for predicting the vibrations of underwater cylindrical shells by using the equivalent beam model

The vibrations of cylindrical shells with large length-to-radius radio are similar to those of beams in very low frequency band. One-dimensional beam theoretical model is only considered about the transverse displacement, neglecting the coupling effects of displacements in other directions. Only the first order beam-type modal frequency, not the other higher orders, of cylindrical shells can be predicted precisely by one-dimensional beam theoretical model. To solve this problem, an equivalent beam theoretical model is established, based on Euler-Bernoulli beam theory, in this paper. In this model, a cylindrical shell model is considered as a beam model with the same structural parameters and boundary conditions, the interaction between the structures and water is approximated to added mass. Different Young's modulus values have been searched to make the calculated results identical to those obtained by cylindrical shell theoretical model. The results show that the beam-type modal frequencies are mainly dominated by the length-to-radius radio for shells with length-to-radius radio L/a>10 and radius-to-thickness radio a/h>20, and the effect of the shell thickness to the modal frequencies can be neglected in such conditions. The equivalent Young's modulus curves for the first five order beam-type modal frequencies of cylindrical shells with different length-to-radius radio have been calculated.

Diversity between shell-like and beam-like regions for a cantilever cylindrical shell under follower forces

The effect of length and thickness on dynamic stability analysis of cantilever cylindrical shells under follower forces is addressed. Beck's, Leipholz's, and Hauger's problems were solved for cylindrical shells with different length-to-radius and thicknesses-to-radius ratios using the Galerkin method. First-order shear theory was used, and rotary inertias were considered in deriving the differential equations. Critical circumferential and longitudinal mode numbers and loads were evaluated for each case. Diagrams containing nondimensional load parameters vs. length and thickness parameters were plotted for each problem. For some shells with small length-to-radius ratios, flutter occurred in high longitudinal mode numbers where the first-order shear theory may not suffice to accurately evaluate the deformations. However, for long and moderately thick shells, there are ranges in which the shell can be analyzed using the simplified equivalent beam model.

Seismic design and hybrid tests of a full‐scale three‐story buckling‐restrained braced frame using welded end connections and thin profile

SUMMARYA series of hybrid and cyclic loading tests were conducted on a three‐story single‐bay full‐scale buckling‐restrained braced frame (BRBF) at the Taiwan National Center for Research on Earthquake Engineering in 2010. Six buckling‐restrained braces (BRBs) including two thin BRBs and four end‐slotted BRBs, all using welded end connection details, were installed in the frame specimen. The BRBF was designed to sustain a design basis earthquake in Los Angeles. In the first hybrid test, the maximum inter‐story drift reached nearly 0.030 rad in the second story and one of the thin BRBs in the first story locally bulged and fractured subsequently before the test ended. After replacing the BRBs in the first story with a new pair, a second hybrid test with the same but reversed direction ground motion was applied. The maximum inter‐story drifts reached more than 0.030 rad and some cracks were found on the gusset welds in the second story. The frame responses were satisfactorily predicted by both OpenSees and PISA3D analytical models. The cyclic loading test with triangular lateral force distribution was conducted right after the second hybrid test. The maximum inter‐story drift reached 0.032, 0.031, and 0.008 rad for the first to the third story, respectively. This paper then presents the findings on the local bulging failure of the steel casing by using cyclic test results of two thin BRB specimens. It is found that the steel casing bulging resistance can be computed from an equivalent beam model constructed from the steel core plate width and restraining concrete thickness. This paper concludes with the recommendations on the seismic design of thin BRB steel casings against local bulging failure. Copyright © 2011 John Wiley & Sons, Ltd.

A modified beam modeling method considering dynamic characteristics for curved flexible pipes

When a curved or flexible pipe is modeled with straight beam elements, its flexibility, especially in bending behavior, is underestimated compared to its actual value. In this study, we present an equivalent beam modeling method for predicting the dynamic characteristics of curved flexible pipes, which can be applied similarly to curved pipes. To reflect rationally the increased flexibility of curved flexible pipes due to curvature, we introduce a strain energy concept into the proposed beam model. The validity of the proposed beam modeling method is verified through comparison with results by shell modeling and dynamic experiments.

An equivalent beam model for the analysis of tunnel-building interaction

The aim of this work is to study the effect of structural characteristics, including stiffness, geometry and weight on tunnel–adjacent structure interaction. Ground materials, tunnel geometry and excavator device are related to a part of metro tunnel of Tehran. To describe the ground behavior due to tunneling, a 3D FE code with an elastoplastic soil model was used. The adjacent building was modeled in two ways: one as an equivalent beam or shell and the other as a real geometry (3D frames). The obtained results from this theoretical work indicate particularly that the stiffness of adjacent structure controls the ground movement distribution induced by tunnel excavation which in agree with other researchers. As it was predicatively, increasing in structure weight leads to create the large displacement components in the ground. The structure width plays also a significant role in displacement distribution of ground. The comparison of the obtained results using two methods of structure modeling shows a very good conformity between them.

A study on AGV-induced floor micro-vibration in TFT-LCD high-technology fabs

SUMMARY This study explores vertical floor micro-vibration induced by the automated guided vehicles (AGVs) in thin-film-transistor liquid-crystal-display (TFT-LCD) fabs. The state-space procedure is adopted to compute the AGV-induced floor vibration as it preserves the desired numerical stability and accuracy in high-frequency responses. The dynamic analysis of an AGV moving on an equivalent three-span beam model of a TFT-LCD building is simulated by taking into account various AGV speeds and engine forces. Numerical simulations demonstrate that if proper engine forces and excitation frequency contents of the AGV moving loads are used, the peak AGV-induced floor micro-vibration level can be predicted by the proposed method. Moreover, the effectiveness of vibration control by span-reduction as well as energy-dissipation by viscoelastic dampers is also examined. In comparison with span-reduction, application of energy-dissipation devices is more effective in vibration suppression as they enhance the damping characteristics of the multi-span floor system whose natural frequencies are potentially in resonance with the excitation frequencies of the AGV moving loads ranging in a broad bandwidth. Copyright © 2011 John Wiley & Sons, Ltd.

Receptance Coupling for Tool Point Dynamics Prediction on Machine Tools

Chatter has been a primary obstacle to the successful implementation of high speed machining. The frequency response function(FRF) of the tool point is crucial for identification of chatter free cutting conditions. In order to quickly acquire the FRF of the different components combinations of machine tool, the assembly of machine tool was always decomposed into several parts, where the fluted portion of tool, however, was always treated as a uniform beam, and the associated discrepancy was ignored. This paper presents a new method to predict the dynamic response of the machine-spindle-holder-tool assembly using the receptance coupling substructure analysis technique, where the assembly is divided into three parts: machine-spindle, holder and tool shank, and tool's fluted portion. Impact testing is used to measure the receptance of machine-spindle, the Timoshenko beam model is employed to analyze the dynamics of holder and tool shank, and the finite element method(FEM) is used to calculate the receptance of the tool's fluted portion. The approximation of the fluted portion cross section using an equivalent diameter is also addressed. All the individual receptances are coupled by using substructure method. The predicted assembly receptance is experimentally verified for three different tool overhang lengths. The results also show that the equivalent diameter beam model reaches an acceptable accuracy. The proposed approach is helpful to predict the tool point dynamics rapidly in industry.