• Steel and Composite Structures
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• v.21 no.1
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• pp.195-216
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• 2016

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 partial-interaction 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.

• Steel and Composite Structures
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• v.37 no.3
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• pp.291-306
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• 2020

The noise from the elevated lines of rail transit has become a growing problem. This paper presents a new method for the rapid prediction of the structure-borne noise from steel or composite bridges, based on the receptance and Statistical Energy Analysis (SEA), which is essential to the study of the generation mechanism and the design of a low-noise bridge. First, the vertical track-bridge coupled vibration equations in the frequency domain are constructed by simplifying the rail and the bridge as an infinite Timoshenko beam and a finite Euler-Bernoulli beam respectively. Second, all wheel/rail forces acting upon the track are computed by taking a moving wheel-rail roughness spectrum as the excitation to the train-track-bridge system. The displacements of rail and bridge are obtained by substituting wheel/rail forces into the track-bridge coupled vibration equations, and all spring forces on the bridge are calculated by multiplying the stiffness by the deformation of each spring. Then, the input power to the bridge in the SEA model is derived from spring forces and the bridge receptance. The vibration response of the bridge is derived from the solution to the power balance equations of the bridge, and then the structure-borne noise from the bridge is obtained. Finally, a tri-span continuous steel-concrete composite bridge is taken as a numerical example, and the theoretical calculations in terms of the vibration and noise induced by a passing train agree well with the field measurements, verifying the method. The influence of various factors on wheel/rail and spring forces is investigated to simplify the train-track-bridge interaction calculation for predicting the vibration and noise from steel or composite bridges.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.4
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• pp.381-387
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• 2016

In this paper, the methodology applied to the improvement of stress analyses is extended to free vibration and buckling analyses. The essence of the methodology is the Saint-Venant's principle that is applicable to beam and plate models. The principle allows one to dimensionally reduce three-dimensional elasticity problems. Thus the methodology can be employed to vibration and buckling as well as stress analysis. First, the principle is briefly revisited, and then the formations of classical beam theories are presented. To improve the predictions, the perturbed terms (unknowns) are introduced together with the warping functions that are calculated by stress equilibrium equations. The unknowns are then calculated by applying the equivalence of stress resultants (i.e., Saint-Venant's principle). As numerical examples, cantilever and simply supported beams are analytically solved. The results obtained are compared with those of the classical beam theories. It is shown that the methodology can be used to improve the predictions without introducing shear correction factors.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.12
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• pp.866-873
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• 2015

The transverse vibration of the deploying beam from rigid hub was analyzed by simulation and experiment. The linear governing equation of the deploying beam was obtained using the Euler-Bernoulli beam theory. To discretize the governing equation, the Galerkin method was used. After transforming the governing equation into the weak form, the weak form was discretized. The discretized equation was expressed by the matrix-vector form, and then the Newmark method was applied to simulate. To consider the damping effect of the beam, we conducted the modal test with various beam length. The mass proportional damping was selected by the relation of the first and second damping ratio. The proportional damping coefficient was calculated using the acquired natural frequency and damping ratio through the modal test. The experiment was set up to measure the transverse vibration of the deploying beam. The fixed beam at the carriage of the linear actuator was moved by moving the carriage. The transverse vibration of the deploying beam was observed by the Eulerian description near the hub. The deploying or retraction motion of the beam had the constant velocity and the velocity profile with acceleration and deceleration. We compared the transverse vibration results by the simulation and experiment. The observed response by the Eulerian description were analyzed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.3
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• pp.235-240
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• 2011

A flexible hose attached to a mother ship experiences various motions that depend on the movement of the mother ship and that of underwater vehicle. Although the motion of the hose is a very important factor that determines how a mother ship should be steered in a real situation, it is difficult to experimentally obtain information about the hose motion. Therefore, we study the motion of the hose analytically. The ANCF(absolute nodal coordinate formulation) was used to model the hose, because this formulation can relax the Euler-Bernoulli theory and the Timoshenko beam theory and allow the deformation of the cross section. The mother ship is assumed to be a rigid body with 6 degrees of freedom. The motion of the hose is predominantly affected by the behavior of the mother ship and by the fluid flow.

• Steel and Composite Structures
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• v.36 no.2
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• pp.143-161
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• 2020

In nanosized structures as the surface area to the bulk volume ratio increases the classical continuum mechanics approaches fails to investigate the mechanical behavior of such structures. In perforated nanobeam structures, more decrease in the bulk volume is obtained due to perforation process thus nonclassical continuum approaches should be employed for reliable investigation of the mechanical behavior these structures. This article introduces an analytical methodology to investigate the size dependent, surface energy, and perforation impacts on the nonclassical bending behavior of regularly squared cutout nanobeam structures for the first time. To do this, geometrical model for both bulk and surface characteristics is developed for regularly squared perforated nanobeams. Based on the proposed geometrical model, the nonclassical Gurtin-Murdoch surface elasticity model is adopted and modified to incorporate the surface energy effects in perforated nanobeams. To investigate the effect of shear deformation associated with cutout process, both Euler-Bernoulli and Timoshenko beams theories are developed. Mathematical model for perforated nanobeam structure including surface energy effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Closed forms for the nonclassical bending and rotational displacements are derived for both theories considering all classical and nonclassical kinematics and kinetics boundary conditions. Additionally, both uniformly distributed and concentrated loads are considered. The developed methodology is verified and compared with the available results and an excellent agreement is noticed. Both classical and nonclassical bending profiles for both thin and thick perforated nanobeams are investigated. Numerical results are obtained to illustrate effects of beam filling ratio, the number of hole rows through the cross section, surface material characteristics, beam slenderness ratio as well as the boundary and loading conditions on the non-classical bending behavior of perforated nanobeams in the presence of surface effects. It is found that, the surface residual stress has more significant effect on the bending deflection compared with the corresponding effect of the surface elasticity, Es. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams.

• Smart Structures and Systems
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• v.21 no.1
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• pp.53-64
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• 2018

Nondestructive testing methods are required to assess the condition of civil structures and formulate their maintenance programs. Axial force identification is required for several structural members of truss bridges, pipe racks, and space roof trusses. An accurate evaluation of in situ axial forces supports the safety assessment of the entire truss. A considerable redistribution of internal forces may indicate structural damage. In this paper, a novel compressive force identification method for prismatic members implemented using static deflections is applied to steel beams. The procedure uses the Euler-Bernoulli beam model and estimates the compressive load by using the measured displacement along the beam's length. Knowledge of flexural rigidity of the member under investigation is required. In this study, the deflected shape of a compressed steel beam is subjected to an additional vertical load that was short-term measured in several laboratory tests by using fiber Bragg grating-differential settlement measurement (FBG-DSM) sensors at specific cross sections along the beam's length. The accuracy of midspan deflections offered by the FBG-DSM sensors provided excellent force estimations. Compressive load detection accuracy can be improved if substantial second-order effects are induced in the tests. In conclusion, the proposed method can be successfully applied to steel beams with low slenderness under real conditions.

• Coupled systems mechanics
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• v.7 no.4
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• pp.485-507
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• 2018

The moving load causes the occurrence of vibrations in civil engineering structures such as bridges, railway lines, bridge cranes and others. A novel engineering method for separation of the variables in the differential equation of the elastic line of Bernoulli-Euler beam has been developed. The method can be utilized in engineering structures, leading to "a beam under moving load model" with generalized boundary conditions. This method has been implemented for analytical study of the dynamic response of the metal structure of a single girder bridge crane due to the telpher movement along the bridge girder. The modeled system includes: a crane bridge girder; a telpher, moving with a constant horizontal velocity; a load, elastically fixed to the telpher. The forced vibrations with their own frequencies and with a forced frequency, due to the telpher movement, have been analyzed. The loading resulting from the telpher uniform movement along the bridge girder is cyclical, which is a prerequisite for nucleation and propagation of fatigue cracks. The concept of "dynamic coefficient" has been introduced, which is defined as a ratio of the dynamic deflection of the bridge girder due to forced vibrations, to the static one. This ratio has been compared with the known from the literature empirical dynamic coefficient, which is due to the telpher track unevenness. The introduced dynamic coefficient shows larger values and has to be taken into account for engineering calculations of the bridge crane metal structure. In order to verify the degree of approximation, the obtained results have been compared with FEM outcomes. An additional comparison has been made with the exact solution, proposed by Timoshenko, for the case of simply supported beam subjected to a moving force. The comparisons show a good agreement.

• Geomechanics and Engineering
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• v.4 no.3
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• pp.173-190
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• 2012

With recent growing interests in the Performance-Based Seismic Design and Assessment Methodology, more realistic modeling of a structural system is deemed essential in analyzing, designing, and evaluating both newly constructed and existing buildings under seismic events. Consequently, a shallow foundation element becomes an essential constituent in the implementation of this seismic design and assessment methodology. In this paper, a contact interface fiber section element is presented for use in modeling soil-shallow foundation systems. The assumption of a rigid footing on a Winkler-based soil rests simply on the Euler-Bernoulli's hypothesis on sectional kinematics. Fiber section discretization is employed to represent the contact interface sectional response. The hyperbolic function provides an adequate means of representing the stress-deformation behavior of each soil fiber. The element is simple but efficient in representing salient features of the soil-shallow foundation system (sliding, settling, and rocking). Two experimental results from centrifuge-scale and full-scale cyclic loading tests on shallow foundations are used to illustrate the model characteristics and verify the accuracy of the model. Based on this comprehensive model validation, it is observed that the model performs quite satisfactorily. It resembles reasonably well the experimental results in terms of moment, shear, settlement, and rotation demands. The hysteretic behavior of moment-rotation responses and the rotation-settlement feature are also captured well by the model.

• Structural Engineering and Mechanics
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• v.61 no.5
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• pp.617-624
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• 2017

Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton's principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.