International Journal of Structural Stability and Dynamics

Parameter uncertainty associated with concrete arch dams always arises from modeling assumptions and the lack of knowledge or information of the engineering geological situations, especially in the seismic stability analysis of arch dams. In this research, a high arch dam is selected as a case study for probabilistic analysis of the seismic stability performance. The arch dam abutment and the dam are coupled as a system. A comprehensive approach considering contraction joints, boundaries of the probable sliding rock mass and the dam-foundation interface is presented. The contact nonlinearity is solved by using the dynamic contact model with Lagrange multiplier method. The main parameters of the probable sliding block are considered as random variables containing the friction coefficients and cohesions. Both the slippage and sliding area ratio are chosen as the engineering demand parameters (EDP). The sensitivity analysis is performed to reveal the relative influence of each parameter separately by the approximate incremental dynamic analysis (IDA) method. The friction coefficients are shown to be more crucial than the cohesions on the dam’s resistance to seismic instability. The sliding area ratio can be better used for unveiling the sliding process of the arch dam of concern, while the slippage is useful for one to judging the stability of the arch dam under seismic hazards. The Latin hypercube sampling (LHS) with approximate moment estimation is used to investigate the parameter uncertainty to the seismic stability performance of the high arch dam. The results provide a useful reference for using the median/mean-parameter model to accurately estimate the median/mean response of the dam.

There have been numerous experimental studies on the seismic collapse of reinforced concrete (RC) buildings and RC girder bridges, but not on the seismic collapse of RC pedestrian cable-stayed bridges. Postearthquake field investigations revealed that if RC pedestrian cable-stayed bridges in seismic regions were not appropriately designed, they are likely to encounter severe damage or collapse. This paper thus presents an experimental investigation on a 1:12 scaled RC pedestrian cable-stayed bridge to explore the seismic behavior and collapse mechanism of the bridge under different levels of ground motion. The design, construction, and installation of the bridge, along with the shake table tests, were performed. The dynamic characteristic tests of the bridge were carried out, with the natural periods and mode shapes identified. The bridge was then tested by subjecting it to three levels of ground motion, i.e. small, moderate and large earthquakes. The seismic behavior and seismic-resistant capacity of the cable-stayed bridge were finally assessed at the component level and the failure mode of the bridge was identified based on the seismic responses recorded by the measurement system. The test results showed that the collapse of the RC pedestrian cable-stayed bridge was triggered from the flexure failure of its columns and ended with the flexure-shear failure of its tower.

As the surface roughness of a bridge has significant influence on the interaction between a moving vehicle and the bridge itself, it is one of the hurdles for the use of the drive-by technique in the assessment of bridges. Proper identification of the surface roughness of a bridge will help minimize the associated uncertainties and improve the accuracy of numerical simulation. This paper presents a method for estimating the surface roughness profile from the responses extracted from a vehicle instrumented with accelerometers passing on the bridge tested. By letting the vehicle run along the bridge multiple times with different added masses, an estimation of the roughness profile can be obtained based on the vehicle–bridge interaction theory. No baseline data is required. Three simplified vehicle models have been used in this study, i.e. spring–mass model, spring–damper–mass model and half-vehicle model. The feasibility and effectiveness of this method are evaluated by finite element simulation with a simply supported bridge and a continuous bridge. The performance of this method for different levels of road surface roughness is assessed by suitable error indicators. A parametric study about the influence of vehicle and bridge parameters, measurement noise and structural damage on the identified results have been carried out.

This paper proposes the radial point interpolation method (RPIM) for studying the dynamic behaviors of rotating Mindlin plates. By considering nonlinear coupling deformation, that is, the in-plane longitudinal shortening terms caused by transverse deformation, the first-order approximation coupled (FOAC) dynamic model is established using Lagrange’s equations of the second kind. The effectiveness of RPIM is first demonstrated in some static cases and then extended for dynamic analysis of a rectangular plate subjected to a large overall motion. The simulation results were compared with those obtained with zero-order approximation coupled (ZOAC) dynamic model, and it was observed that results obtained with FOAC dynamic model are more accurate, especially for cases involving high rotating speed. Furthermore, the influence of the radial basis shape parameters is discussed and the optimal parameters for plates are recommended. An approach to overcome the shear locking issue is also provided.

This paper presents a fluid–structure coupling model to investigate the vortex-induced vibration of a circular cylinder subjected to a uniform cross-flow. A modified van der Pol nonlinear equation is employed to represent the fluctuating nature of vortex shedding. The wake oscillator is coupled with the motion equation of the cylinder by applying coupling terms in modeling the fluid–structure interaction. The transient responses of the fluid–structure coupled model are presented and discussed by numerical simulations. The results demonstrate the main features of the vortex-induced vibration, such as lock-in phenomenon, i.e. resonant oscillation of the cylinder occurs when the vortex shedding frequency is near to the natural frequency of the cylinder. The resonant responses of the fluid–structure coupled model in the lock-in region are determined by the multiple scales method. The accuracy of the asymptotic solution by the multiple scales method is verified by comparing with the numerical solution from the motion equation. The effects of different parameters on the steady state amplitude of oscillation are investigated for a given set of parameters. Frequency–response curves obtained from the modulation equation demonstrate the existence of jump phenomena.

This work aims to construct accurate and simple lower-order analytical approximation solutions for the free and forced vibration of electrostatically actuated micro-electro-mechanical system (MEMS) resonators, in which geometrical and material nonlinearities are induced by the mid-plane stretching, dynamic pull-in characteristics, electrostatic forces and other intrinsic properties. Due to the complexity of nonlinear MEMS systems, the quest of exact closed-form solutions for these problems is hardly obtained for system design and analysis, in particular for harmonically forced nonlinear systems. To examine the simplicity and effectiveness of the present analytical solutions, two illustrative cases are taken into consideration. First, the free vibration of a doubly clamped microbeam suspended on an electrode due to a suddenly applied DC voltage is considered. Based on the Euler–Bernoulli beam theory and the von Karman type nonlinear kinematics, the dynamic motion of the microbeam is further discretized by the Galerkin method to an autonomous system with general nonlinearity, which can be solved analytically by using the Newton harmonic balance method. In addition to large-amplitude free vibration, the primary resonance response of a doubly clamped microbeam driven by two symmetric electrodes is also investigated, in which the microbeam is actuated by a bias DC voltage and a harmonic AC voltage. Following the same decomposition approach, the governing equation of a harmonically forced beam model can be transformed to a nonautonomous system with odd nonlinearity only. Then, lower-order analytical approximation solutions are derived to analyze the steady-state resonance response of such a problem under a combination of various DC and AC voltage effects. Finally, the analytical approximation results of both cases are validated, and they are in good agreement with those obtained by the standard Runge–Kutta method.

The geometrically nonlinear response of sandwich functionally graded cylindrical shells reinforced by orthogonal and/or spiral stiffeners and subjected to axial compressive loads is investigated in this paper. Two types of sandwich functionally graded material models are considered. The formulations are based on the Donnell shell theory considering geometrical nonlinearity and Pasternak’s elastic foundation. The improved Lekhnitskii’s smeared stiffener technique is used to account for the stiffener effects with both mechanical and thermal stresses. The results obtained indicate that the spiral stiffeners have significantly beneficial influences in comparison with orthogonal stiffeners on the nonlinear buckling behavior of shells. The relatively large effects of temperature change, geometrical and material parameters are also demonstrated in the numerical investigations.

Shape Memory Alloys (SMAs) are now widely used as a damping element into the isolation systems. The pre-stressed SMAs exhibit hysteretic damping through a nonlinear flag-shaped hysteresis loop. Many nonlinear models of the SMA are available to depict such behavior. The nonlinear models require a lot of effort and computational time for the analysis of base-isolated structures. Therefore, the codes recommend that a nonlinear model can be replaced by an equivalent linear model in the analysis. Linearization is a method to convert the nonlinearity of a system into a system with analogues linear parameters. This paper proposes an empirical equation for a damping ratio to get a linear damping coefficient of the SMAs which can be used in the seismic analysis of base-isolated structures.

The evaluation of any damping ratio using the traditional system identification method does not give precise solutions due to variation in hysteretic parameters and the unpredictable nature of an earthquake. The empirical equation is proposed using a set of optimal statistical data obtained from the seismic analysis of a base isolated structure. Moreover, analysis of the base isolated structure using the newly modified equivalent elastic-viscous SMA model gives comparable and conservative results with a nonlinear SMA model as compared to the existing elastic-viscous SMA model. Since the hysteresis parameters are used to derive the empirical equation for the damping ratio, this equation is also applicable for any type of structure.

This paper describes an analytical and numerical continuous wave-based approach for the forced vibration analysis of large waveguide systems. With Timoshenko beam theory as the basis for modeling wave propagation in the waveguides, the refraction of waves at discontinuities is studied analytically. Within this context, the refraction of waves at multi-member joints is formulated. In addition, a joint-based procedure is introduced to assemble analytical joint equations in the global system matrix. The joint-based approach is mathematically equivalent with the existing element-based approaches but has the advantage of accounting for the effects of a rigid joint region explicitly. The method is used to find the response of a large frame subjected to steady-state dynamic loadings with a wide range of frequency excitations. The fidelity of the methodology is verified using finite element simulations. The main advantage of the new approach is that it can analyze arbitrary waveguide systems for a wide range of frequencies, which makes it suited for studying the behavior of complex large systems using a single global matrix with a very low computational cost.

The rail–wheel interaction can induce train and track vibrations and consequently lead to noise impact, passengers’ discomfort, high maintenance cost, etc. Due to the complexity of the rail–wheel interaction and the high cost of field tests, as well as the difficulties in data collection, numerical analyses have been widely resorted to for predicting the train and track vibrations, for which numerous numerical models have been developed. According to track modeling approaches, numerical models can be generally divided into two categories, i.e. beam models and continuum finite element (FE) models. In this paper, these two models are systematically compared and discussed. First, a typical beam model of Wu and Thompson [T. X. Wu and D. Thompson, On the parametric excitation of the wheel/track system, J. Sound Vib. 278(4) (2004) 725–747.] is introduced, based on which a modified model is then established. Secondly, a plane continuum FE model with high mesh quality is established, in which the transition mesh generation, contact treatment and element size determination are presented. Numerical tests are conducted to validate the proposed plane FE model. Finally, both the beam and the plane continuum FE models are examined through typical rail–wheel interaction examples, in which the linear response of the track as well as the rail–wheel vibrations under both a single rolling wheel and two rolling wheels are analyzed. The results show that most of the vibration trends obtained from the two models agree well with each other. Nevertheless, it is noteworthy that the continuum FE model has superiorities, especially for analyzing vibrations at higher frequencies. The present study can be of considerable help for designers and engineers in the railway industry to achieve the trade-off between the simulation demands and the computational cost.

This paper presents an accurate analysis of the natural frequency and mode shape of carbon fiber-reinforced steel–concrete composite beam with double-slip surfaces. To study the flexural vibration of the composite beam, a governing differential equation considering the shear-slip effects of two interfaces is formulated. Based on this formulation, the natural frequency and mode shape of carbon fiber-reinforced composite beams are calculated. For comparison purpose, numerical simulations of the composite beams are conducted using the ANSYS in order to verify the present results. High consistency in the two calculation values is revealed. In addition, carbon fiber-reinforced composite beams are fabricated and tested. It is found that the experimental values agreed well with the theoretical results. The findings from this study may provide the benchmark reference for engineering analysis and design of carbon fiber-reinforced steel–concrete composite beams.

In this study, the effects of micro-structural parameters such as particle volume fraction, size and random distribution of Al 6061/SiC particulate metal-matrix composite (MMC) beams on free vibration response and the active vibration control are investigated. For this purpose, numerical particle-reinforced MMC (PRMMC) beam specimens were modeled with 3D finite elements, and the cubic-shaped reinforcing SiC particles were randomly distributed in Al 6061 metal matrix similar to an actual micro-structure. The particle size and especially volume fraction play an important role on the natural frequencies of the smart PRMMCs although they have no effect on the mode shapes. The random particle distribution has minor effect on the natural frequencies of the smart PRMMCs. With the increase of the feedback control gain, both the vibration amplitude and the suppression time are reduced reasonably. Increasing the particle volume fraction induces an important reduction in the damping time and the vibration amplitude for both the controlled and uncontrolled damped vibrations. Finally, increasing the particle size decreases the vibration suppression capacity and increases the vibration amplitude and time slightly. Random particle distribution had no obvious effect on the uncontrolled and controlled vibrations.

Great attention has been given in the last few years to steel–concrete composite beams due to the gains in strength that can be obtained with the small cost of installing a shear connection between the steel profile and the concrete slab. In continuous and semicontinuous composite beams close to the internal supports, hogging bending moments are developed and the compressed bottom flange may buckle laterally in an unstable way known as the lateral-distortional buckling, characterized by a horizontal displacement and twist of the bottom flange with an out-of-plane distortion of the web. In the literature, several formulations were proposed to determine the critical moment for this type of buckling. Among them, some of the most relevant are presented by [K. Roik, G. Hanswille and J. Kina, Solution for the lateral torsional buckling problem of composite beams (in German), Stahlbau 59 (1990)] and [G. Hanswille, J. Lindner and D. Munich, Lateral torsional buckling of composite beams (in German), Stahlbau 67 (1998)]. In the present work, a new procedure is developed to determine the elastic critical moment of lateral–distortional buckling of composite beams under uniform hogging moment. To assess and calibrate this procedure, 7772 numerical models were analyzed by the finite element code ANSYS and the results were compared with the ones obtained from the new proposed formulas. The procedure presented excellent agreement with the numerical results, with an average deviation of 2.33% from the computational simulations. The formulations of [K. Roik, G. Hanswille and J. Kina, Solution for the lateral torsional buckling problem of composite beams (in German), Stahlbau 59 (1990)] and [G. Hanswille, J. Lindner and D. Munich, Lateral torsional buckling of composite beams (in German), Stahlbau 67 (1998)] did not lead to such satisfactory results, presenting an average deviation of 12.41% and 16.51%, respectively.

This paper presents a sensitivity analysis on the performance of optimal proportional–integral–derivative (PID) controller for use in nonlinear smart base-isolated structures with uncertainties. A set of nine performance indices is defined to evaluate the performance of the controller in the presence of uncertainties in the superstructure, lead rubber bearing (LRB) seismic isolation system, and applied loads. The time delay effect on the stability and performance of the PID controller is also examined. The results show that the PID controller is robust against the uncertainties up to $\pm 15$% in the damping and stiffness coefficients of the superstructure, the yield force of the LRB and the artificial earthquake. In the case with $\pm 15$% of uncertainty, the input energy entering into the structure is increased with respect to the nominal model. However, the changes of the performance indices related to the damage energies are negligible. An uncertainty of $-$20% in the stiffness coefficient and stiffness ratio of the LRB gives an increase of 15% in the maximum and root mean square (RMS) of the structural responses. In the case with $-$20% of uncertainty, the damage and damping energies do not change in comparison with the case of the nominal model, but a significant decay in the performance index related to the input energy response is obtained in this case. Not all performance indices are sensitive to time delay. For large time delays, the performance index for the seismic input energy increases significantly, while the maximum damage and damping energies increase up to 5% and 10%, respectively.

A novel size-dependent coupled symplectic and finite element method (FEM) is proposed to study the steady-state forced vibration of built-up nanobeam system resting on elastic foundations. The overall system is modeled as a combination of nonlocal Timoshenko beams. A new analytical subsystem modeling with formulation and another numerical subsystem modeling are developed and discussed. In the analytical subsystem model, the uniform nanobeams are modeled and solved by a new approach based on a series of analytical symplectic eigensolutions. The numerical subsystem model applies a nonlocal FEM to solve nonuniform nanobeams. Analytical and numerical solutions are presented, and a proper comparison between the two approaches is established. Comprehensive and accurate numerical result is subsequently presented to illustrate the accuracy and reliability of the coupled method. The new results established are expected to have reference values for future studies.