International Journal of Structural Stability and Dynamics

In this paper, the Ritz-based solutions are developed for the bending, buckling and vibration behaviors of laminated composite beams with arbitrary lay-ups. A quasi-3D theory, which accounts for a higher-order variation of both the axial and transverse displacements, is used to capture the effects of both shear and normal deformations on the behaviors of composite beams. Numerical results for various boundary conditions are presented and compared with existing ones available in the literature. Besides, the effects of fiber angle, span-to-height ratio, material anisotropy and Poisson’s ratio on the displacements, stresses, natural frequencies and buckling loads of the composite beams are investigated.

Presented herein is a novel computational approach using the moving element method (MEM) for simulating the dynamic response of Mindlin plate resting on a viscoelastic foundation and subjected to moving loads. The governing equations and the element mass, damping and stiffness matrices are formulated in a convected coordinate system in which the origin is attached to the point of the moving applied load. Thus, the method simply treats moving loads as ‘stationary’ at the nodes of the plate to avoid updating the locations of moving loads due to the change of the contact points on the plate. To verify the accuracy of the proposed computational approach, static and free vibration analyses of plates are investigated first. Next, the dynamic response of plate resting on a viscoelastic foundation subjected to a moving load is examined. A parametric study is performed to determine the effects of the load’s velocity, foundation damping and foundation stiffness on the dynamic response of a plate. Finally, the comparisons of the dynamic response of plates resting on viscoelastic foundation and subjected to moving vehicles with three models of load (single-wheel, single-axle and tandem-axle) are discussed.

This paper presents a numerical study on the out-of-plane responses of a high-speed train running on a curved railway track segment using the moving element method. The accuracy and efficiency of the proposed computation model presented herein are compared with available analytical results from the literature and a finite element solver based on a simplified moving load model. Thereafter, a half-railcar moving sprung-mass model and a double-rail track-foundation model are presented to investigate the behavior of a high-speed train traversing a curved track, particularly when the train speed is greater than the design speed of the curved track segment. The results show that the train speed and severity of track irregularity significantly affect the contact forces on the rails. This paper also presents a case of a railcar overturning when the train speed is greater than 2.5 times the design speed of a curved track segment.

Distributed strain measurement, such as long-gauge fiber bragger grating (FBG) techniques, has developed rapidly in the field of structural health monitoring. However, strategies of corresponding damage identification still need to be enhanced. The damage identification technique based on distributed strain measurement is proposed identifying the structural damage under ambient excitation. Damage indices, like the distributed strain energy difference (DSED) and the relative distributed strain energy (RDSE), are derived from the power spectral density of the frequency response function of distributed strain response and further employed by detecting damages in the structure. A numerical analysis is performed on a long-span cable-stayed bridge with several assumed damage scenarios at various degrees in the girder. Damage localization capability and robustness of the proposed damage indices are discussed. In addition, damage quantification utilizing the proposed indices is conducted. The results indicate that the proposed technique can accurately identify the locations and extent of the damage under ambient vibration excitation.

The vibration of a rotating sandwich beam with magnetorheological elastomer (MRE) as a core between two elastic layers is theoretically analyzed in this paper. This study is focused on the bending vibration along the edgewise direction of a sandwich beam of rectangular cross-section, which, to the best of our knowledge, has not been addressed yet. The classical Euler–Bernoulli beam theory is used to model the dynamic behavior of the elastic layers. In the modeling, the effect of the MRE layer is considered by incorporating its shear strains and the inertia due to shear deformation and bending motion. The governing equations of motion of the rotating sandwich beam are derived by using the Ritz method and the Lagrange’s equations. The effects of the applied magnetic field, core layer thickness, rotational speed, setting angle and hub radius on the natural frequencies and the corresponding loss factors are investigated parametrically. The results show the significant effect of the magnetic field intensity and the MRE layer thickness on the modal characteristics of the MRE sandwich beam.

In the present study, the thermoelastic vibration of shear deformable functionally graded material (FGM) curved beams with microstructural defects (porosity) has been analyzed by the finite element method. The formulation is based on the higher-order shear deformation theory. The material properties of FGM beams are allowed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Even and uneven distributions of porosities in the beam have been considered with temperature-dependent material properties. Comparison and convergence study has been performed to validate the present formulation. Parametric studies have been done to study the effect of different influencing parameters on the frequency of the FGM curved beam, i.e. porosity, temperature rise, volume fraction index and opening angle. Some new results are presented which can be used as benchmark solutions for future research.

Due to the lack of analytic technique for simulating the vortex-induced vibration (VIV) of long-span bridges, a combination of the VIV semi-empirical model with the structural equation of motion is widely employed to calculate the responses of bridge structures. However, the applicability of this method has seldom been investigated before. In this study, the theoretical defects of the conventional combination strategy (i.e. the finite element procedure or the linear normal mode procedure, LNM) are first discussed, a more theoretically reliable approach (the nonlinear norm mode approach, NNM) is then proposed, and the closed-form expression for the NNM of the VIV system is derived. The accuracy of the proposed method is further illustrated by two case studies. This new approach offers a theoretically reliable tool for analyzing the VIV of long-span bridges. It can also be applied to the process of VIV fatigue analysis or control strategy optimization.

The instantaneous amplitude squared (IAS) of the driving component of the contact-point response of a moving test vehicle was proposed for the damage detection of the sustaining bridge. As a supplement to the properties previously presented for the IAS, this paper is aimed at unveiling the key feature of the discontinuity amplification inherent in the IAS through the double guarantee of a “square operation” in the definition and a “second derivative” in computing the contact-point response. The capability of the IAS was demonstrated with regard to the effects of the environmental noise, vehicle damping and bridge damping in the numerical simulation. It is confirmed that the IAS can be reliably used in the damage detection of bridges by a moving test vehicle.

An analytical approach for predicting the free vibration and elastic critical load of functionally graded material (FGM) thin cylindrical shells filled with internal pressured fluid is presented in this study. The vibration of the FGM cylindrical shell is described by the Flügge shell theory, where the internal static pressure is considered as the prestress term in the shell equations. The motion of the internal fluid is described by the acoustic wave equation. The natural frequencies of the FGM cylindrical shell under different internal pressures are obtained with the wave propagation method. The relationship between the internal pressure and the natural frequency of the cylindrical shell is analyzed. Then the linear extrapolation method is employed to obtain the elastic critical load of the FGM cylindrical shell from the condition that the increasing pressure has resulted in zero natural frequency. The accuracy of the present method is verified by comparison with the published results. The effects of gradient index, boundary conditions and structural parameters on the elastic critical load of the FGM cylindrical shell are discussed. Compared with the experimental and numerical analyses based on the external pressure, the present method is simple and easy to carry out.

This paper presents a novel closed-form analytical approximate solution for the local buckling behavior of composite laminated beams under uniform axial compression. The laminates that constitute the segments of the beam cross-sections (i.e. webs and flanges) are assumed to be moderately thick so that the current analysis approach is based on Reddy’s third-order shear deformation theory? (TSDT). The idealization relies on the discrete plate approach, meaning that the individual segments are separated from the beam cross-section, and the local buckling behavior is analyzed by performing a TSDT-based plate buckling analysis by assuming adequate boundary conditions for webs and flanges. At those edges where the segment under consideration has been separated from the cross-section, elastic restraints are applied to the stiffness values of which depend on the geometric and material properties of the adjacent segments. The analysis approach uses the principle of minimum elastic potential of the considered discrete plate in the buckled state and relies on rather simple shape functions for the buckling modes, thus eventually enabling a closed-form analytical approximate solution that does not necessitate any numerical means of evaluation. Results are generated for a number of I-beam configurations and are compared to results generated in the framework of classical laminated plate theory (CLPT) and first-order shear deformation theory (FSDT). It is shown that the present new approach delivers reliable results without any significant computational effort and thus can be recommended for all engineering analysis tasks where computational time and effort are deciding factors in day-to-day engineering work, such as systematic optimizations or extensive parametric studies.

High-rise television towers are prone to external wind and earthquake-induced oscillations in severe environments. To avoid excessive vibration under strong earthquakes, a large television tower requires certain measures to abate its dynamic responses. Friction dampers are simple and low-cost solutions for realizing the response control of television towers. In this study, response mitigation and performance assessment are conducted on a large-scale television tower with friction dampers under strong earthquakes. A 3D finite element static model of the high-rise television tower is first established, and then a 2D lumped mass dynamic model is developed. The mechanical model for the friction dampers is presented with the axial stiffness considered. The equations of motion of the damper–tower system under seismic excitations are then determined. The control force transformation, displacement increment transformation, and numerical integration of the coupled damper–tower system’s equations of motion are defined on the basis of the two aforementioned models. Finally, the seismic responses of a high-rise television tower system constructed in China are taken as an example to investigate the validity of the proposed control approach using the friction dampers. The results demonstrate that the implementation of friction dampers with optimal parameters in a large truss tower can substantially suppress the structural seismic responses in terms of peak responses and vibrant energy.

An approach to predicting the vibration responses of a bridge and analyzing the wave propagation characteristics along the bridge is proposed based on the waveguide finite element (WFE) method. For verification, a field vibration test was performed on a 30m-long simply supported box-girder on the fourth line of Guangzhou Metro in China. The numerical results were shown to agree well with the test results, demonstrating the accuracy of the proposed approach. The advantages of the WFE approach are discussed by comparing the WFE with finite element (FE) analyses. The dispersion characteristics and mode shapes of waves propagating in the box-girder are calculated by using the WFE method, from which the dominant wave modes corresponding to the peaks of the medium- and high-frequency train-induced vibrations are identified. A vibration reduction measure is considered. Both the test and numerical results show that the medium- and high-frequency vibrations of the box-girder are predominately in the 1/3 octave center frequency range of 63–100Hz with maximum occurring at the center frequency of 80Hz. The WFE method has higher computational efficiency and requires smaller storage space than the FE counterpart, but provides similar predictions as the latter. In total, there are 14 wave modes propagating in the box-girder below 200Hz. The G1, A1 and D2 wave modes are the dominant wave modes generating vibration velocity peaks on the top, bottom and flange slabs, respectively. Adding a middle web slab to the center of the cross-section is an effective way to mitigate the vibration of the box-girder bridge.

This paper proposes a novel functionally graded (FG) concrete slab and investigates its thermal buckling and postbuckling performance using the finite-element (FE) method. The concrete slab consists of three homogeneous thick layers — a fiber-reinforced concrete layer, a geopolymer concrete layer, and a plain Portland cement (PPC) layer — with a thin FG layer between the thick layers. The mechanical properties of the thin FG layers are exponentially graded across the thickness direction. The effects of initial imperfection, the self-weight of the slab, and the friction between the slab and rigid foundation are considered in the analysis. The FE model is validated against the results reported in the literature. A comprehensive parametric study is conducted to examine the effects of the thickness and volume fraction index of the FG layer, initial imperfection, self-weight, friction, and slab slenderness ratio on the thermal buckling and postbuckling behaviors of the concrete slab. The numerical results demonstrate that the proposed FG slab exhibits remarkably better buckling and postbuckling resistance than a conventional PPC concrete slab and that the influences of both self-weight and friction are important and cannot be neglected.

This study presents a framework for dynamic analysis of a coupled system of high-speed maglev train and curved viaduct. A series of trajectory coordinates are used to define the motion of maglev vehicles moving over a horizontally curved track, the stiffness and damping matrices of the equations can be thus reduced into those of the straight track. The curved viaduct system is modeled in the global coordinate system using the finite element method, in which the inner and outer rails in the different horizontal planes are duly included. The electromagnet force-air gap model is adopted for the maglev vehicle via its electromagnets and rails on the viaduct, by appropriate transformation of coordinates. By applying the proposed framework to the Shanghai maglev line, curved path-induced dynamic responses and characteristics of the vehicle are explored, which agree well with the measurement ones. The dynamic responses of the curved viaduct are also examined in the vertical, lateral and rotational directions by comparison with the straight viaduct. Moreover, the effect of various curve radii and cant deficiencies on the coupled system are investigated. The results show that for a maglev vehicle moving with an initial equilibrium state, its lateral and rotational response are mainly excited by track roughness. In addition to the track radius, cant deficiencies significantly affect the operational safety of the viaduct.

The present study deals with numerical and experimental investigations on the vibration behavior of fiber-metal-laminated (FML) plates, a new aircraft material. A finite element (FE)-based formulation is established for the plate using the first-order Reissner–Mindlin theory, including both fibers and metals of different material properties in alternate layers. A four-node isoparametric quadratic element with five degrees of freedom per node is adopted in the analysis. Convergence studies and comparison with previous studies are made to validate the present FE formulation. A set of experiments was conducted to get natural frequencies of vibration for glass FML (GFML) plates using Bruel and Kjaer (B&K) Fast Fourier Transform (FFT) analyzer with PULSE platform. The effects of different parameters such as aspect ratio, side-to-thickness ratio, ply orientation, and boundary conditions on the dynamic behavior of the FMLs are studied. Good agreement is achieved between the numerical and experimental results. Both results indicate that increasing the aspect ratio can increase the natural frequency of the FML plate, while the increase in the side-to-thickness ratio decreases the natural frequency of vibration. The boundary conditions can significantly affect the natural frequency of the FML plates due to the restraint effect at the edges.

In this paper, the inverted pendulum model is proposed to describe a pedestrian’s walking motion by considering that the pivot point vibrates periodically up and down. The stability, periodic solutions and oscillations of the inverted pendulum are theoretically investigated, the correctness of which is illustrated by numerical simulations. According to frequency spectrum analysis, the inverted pendulum can exhibit periodically or quasi-periodically stable oscillations. However, we demonstrate that the inverted pendulum will maintain the ratio between the lateral and vertical vibration frequencies near $1∕2$ as an optimizing selection of stability. The theoretical result agrees with the measurement result for a normal pedestrian such that the lateral step frequency is always half the vertical step frequency, which means that it is feasible and reasonable to describe a pedestrian’s walking motion using the inverted pendulum with the pivot vibrating harmonically in the vertical direction. The inverted pendulum model suggested in this paper could contribute to the study of pedestrian–footbridge interaction, which overcomes the difficulty of directly determining the expression of the lateral force induced by pedestrians.