International Journal of Structural Stability and Dynamics

The nonlinear characteristic of vibration control systems has attracted increasing attention for its advantage in improving structural performance. In this paper, a new type of viscoelastic damping limb-like-structure (VE-LLS) device is proposed by combing the viscoelastic (VE) damper and limb-like-structure (LLS) together, which possesses coupling nonlinearity characteristic caused by geometric and material factors, as well as a remarkable advantage in improving the control performance. First, to explore the nonlinear geometrical effects on the static stiffness of the VE-LLS device, a formula is derived from static stiffness, and the results are discussed. Second, dynamic analysis is performed of the proposed device considering the coupling geometrical and material nonlinearities in frequency domain, with the real-time effect of frequency and temperature on the mechanical properties of the viscoelastic damper considered in solving the nonlinear vibration equation. The harmonic balance method (HBM) is used to solve the nonlinear dynamic equation. Then, the displacement transmissibility of the VE-LLS device is calculated and assessed. The results indicate that the proposed device possesses excellent vibration isolation performance, and the geometric parameters of the viscoelastic damper have significant nonlinear effect on the performance. Finally, an experiment is carried out of the VE-LLS device to verify the accuracy of the static stiffness analysis. The results show that the theoretical results agree well the experimental ones, and that the theoretical results have high accuracy and reliability.

Transmission towers with steel tubes or so-called tubular towers are widely used for ultra-high voltage (UHV) transmission because of their overall higher strength and stability, and better wind resistant capability. However, within a specific wind velocity range, tubular members with a high slenderness ratio are susceptible to joint fatigue failure under the vortex-induced vibration (VIV). To thoroughly unveil the mechanism of VIV of tubular members in UHV transmission towers, this paper first measures the acceleration and corresponding wind velocity of a tubular member under the VIV, followed by an identification of the first-order frequency. Then, a simulation framework for the tubular members subjected to the VIV is proposed. The system considered is simplified as a mass–spring–damping system with the non-linear coupling effect between the tubular member and wind field taken into account. Based on the analysis, the lock-in region and maximum displacement amplitudes in the cross-wind direction are calculated, while the simulation accuracy is verified via comparison with the on-site measured data. Meanwhile, the influence of damping ratio on the VIV is studied. Finally, a new type of radial spoiler is proposed to suppress the VIV of the tubular members. The results of the 3D simulation show that the proposed radial spoiler can effectively suppress the vortex generation, and there is no noticeable vibration after the installation of the countermeasure. In effect, it was demonstrated that the proposed countermeasure can effectively suppress the VIV of the tubular tower. The parametric analysis reveals that the distance between two adjacent spoilers has a significant impact on the control efficiency and should be carefully designed for each project.

The prime objective of this research work is to develop an efficient small scale-dependent computational framework incorporating microstructural tensors of dilatation gradient, rotation gradient, and deviatoric stretch gradient to analyze nonlinear lateral stability of cylindrical microshells. The numerical strategy is established based upon a mixed formation of the third-order shear deformable shell model and modified strain gradient continuum mechanics. The graphene nanoplatelet reinforcements are assumed to be randomly dispersed in a checkerboard scheme within the resin matrix. Accordingly, to extract the effective material properties, the Monte Carlo simulation together with a probabilistic technique are employed. The numerical solution for the microstructural-dependent nonlinear problem is carried out via the moving Kriging meshfree method having the capability to accommodate accurately the essential boundary conditions using proper moving Kriging shape function. It is represented that the role of the stiffening characters related to the effect of microstructural dilatation gradient, rotation gradient, and deviatoric stretch reduces continuously by going to deeper territory of the load-deflection stability path. Moreover, it is indicated that among various microstructural gradient tensors, the stiffening character of the rotation gradient is higher than deviatoric stretch gradient, and the stiffening character of the latter is more considerable than the dilatation gradient tensor.

Buckling design of axially compressed cylindrical shells is still a challenging subject considering the high imperfection-sensitive characteristic in this kind of structure. With the development of various design methods, the energy barrier concept dealing with buckling of imperfection-sensitive cylindrical shells exhibits a promising prospect in recent years. In this study, buckling design of imperfection-sensitive cylindrical shells under axial compression based on the energy barrier approach is systematically investigated. The methodology about buckling design based on the energy barrier approach is described in detail first taking advantage of the cylindrical shells whose buckling loads have been extensively tested. Then, validation and discussion about this buckling design method have been carried out by the numerical and experimental analyses on the cylindrical shells with different geometrical and boundary imperfections. Results in this study together with the available experimental data have verified the reliability and advantage of the buckling design method based on energy barrier approach. A design criterion based on the energy barrier approach is therefore established and compared with the other criteria. Results indicate that buckling design based on energy barrier approach can be used as an efficient way in the lightweight design of thin-shell structures.

This paper developed a numerical model for predicting the seismic responses of vehicle–guideway bridge systems for low–medium-speed (LMS) maglev trains. Each vehicle was characterized as a multi-rigid-body with 50 degree of freedoms (DOFs), and the guideway bridge was modeled by the finite element method. The actively controlled electromagnetic forces were considered in simulating the vehicle–guideway interaction relationship. Subsequently, the equations of motion for the vehicle–guideway coupled system under earthquake were, respectively, established in relative and absolute coordinate systems to quantify the effect of structural pseudo-static components, so that the seismic effect can be taken into account. Case study was then conducted to thoroughly discuss the seismic responses of the vehicle–guideway coupled system in both time and frequency domains. Furthermore, parametric study was carried out to determine the effect of key parameters (i.e. vehicle speed, stiffness of guideway) on the system’s responses. The results show that the conventional seismic analysis method relative motion method (RMM) (ignoring the structural pseudo-static component) will considerably underestimate the seismic responses of the coupled system, especially of the vehicle. It is suggested that the formulation be established in the absolute coordinate system (i.e. using direct solution method, DSM) for more actual prediction. The frequency responses indicate that the vibrations of vehicle–guideway coupled system under earthquake relate significantly to the natural frequencies of vehicle and bridge, while the same is not true for the vehicle-induced excitation.

Sloshing may induce adverse loads to cause structural instability and damage. A vertical elastic baffle mounted at the inside bottom of a rectangular container is used as an anti-slosh device to attenuate the liquid oscillation. A semi-analytical model is presented to analyze the hydroelastic problem. The liquid is partitioned into four simple sub-domains with three hypothetical interfaces. The velocity potential of each sub-domain is analytically deduced by the separation of variables. The baffle deflection is expanded into the Fourier series by its dry modals. The eigenvalue equation is formulated by plugging the velocity potentials into the sloshing conditions, interface continuity conditions, as well as the dominant equation and compatibility conditions of the baffle. Then, the velocity potential is expressed by a complete basis of the coupled mode shapes for the system considered under lateral excitation. The system response equation is constituted by inserting the velocity potential into wave equations and baffle equation. The proposed method is verified by comparing the present results with the available data. In addition, numerical analyses are performed to examine the effects of baffle parameters on the natural frequencies, mode shapes and dynamic responses of the container. The sloshing frequency may be altered to a higher value due to the installation of the elastic baffle.

This paper investigates the vibrational behavior of sandwich conical shells with geodesic lattice core and variable skin thicknesses using analytical and numerical approaches. The filament wound conical shell has been considered to have varying skin thickness along the longitudinal direction. The smeared stiffener approach has been used to obtain the equivalent stiffness parameters due to the geodesic lattice core via the force and moment analyses of a unit cell. Superimposing the stiffness contribution of the stiffeners with those due to the inner and outer skins, one can calculate the equivalent stiffness of the whole structure. The equations of motion have been formulated based on the first-order shear deformation theory. The power series method has been implemented for extracting the natural frequencies of vibration. To validate the analytical results, a 3-D finite element model has been provided which is then used to conduct an extensive parametric study. The comparisons indicate an acceptable agreement between the two approaches. Moreover, the effect of variable skin thickness on the natural frequency has been examined. Furthermore, the influences of skin lamination angle, semi-vertex angle of the cone and stiffeners orientation angle have been discussed. The obtained results can be used for future relevant researches.

A novel two-stage method is proposed to properly identify the location and severity of damage in plate structures. In the first stage, a superposition of modal flexibility curvature (SMFC) is adopted to locate the damage accurately, and the identification index of modal flexibility matrix is improved. The low-order modal parameters are used and a new column matrix is formed based on the modal flexibility matrix before and after the structure is damaged. The difference of modal flexibility matrix is obtained, which is used as a damage identification index. Meanwhile, based on SMFC, a method of weakening the “vicinity effect” is proposed to eliminate the impact of the surrounding elements to the damaged elements when damage identification is carried out for the plate-type structure. In the second stage, the objective function based on the flexibility matrix is constructed, and according to the damage location identified in the first stage, the actual damage severity is determined by the enhanced whale optimization algorithm (EWOA). In addition, the effects of 3% and 10% noise on damage location and severity estimation are also studied. By taking a simply supported beam and a four-side simply supported plate as examples, the results show that the method can accurately estimate the damage location and quantify the damage severity without noise. When considering noise, the increase of noise level will not affect the assessment of damage location, but the error of quantifying damage severity will increase. In addition, damage identification of a steel-concrete composite bridge (I-40 Bridge) under four damage cases is carried out, and the results show that the modified method can evaluate the damage location and quantify 5%–92% of the damage severity.

Since the bridge is often treated as the uniform beam for simplicity in most numerical studies of vehicle-bridge interaction, this study proposes a non-uniform vehicle-bridge interaction system by incorporating a three-mass vehicle model in a non-uniform bridge for wider applications, in which non-uniform beam elements of constant width and varying depth are considered. For clarity, the inclined ratios of the entire bridge and one beam element are separately defined in order to describe the non-conformity in computation while both mass and stiffness matrices are re-formulated to comply with the finite element sign convention. As the natural frequencies of a non-uniform bridge cannot be accessed directly, the vehicle scanning method is first adopted to obtain the bridge frequencies. Then, the parametric study is conducted by considering vehicle damping, bridge damping, and pavement irregularity. In addition to the vehicle frequency, the numerical results show that the proposed vehicle-bridge interaction system is able to scan the first four bridge frequencies with desired accuracy subject to pavement irregularity. Concerning the pitching effect of the vehicle, it is shown that the locations for installing sensors are actually affected by both the geometry and the cross-sectional geometry of the bridge in the concern of achieving high resolution of frequency identification.

Model updating of large-scale structures is difficult to carry out when using a frequency response function (FRF) for damage identification, as the solutions for the global system matrices with too many degrees of freedom are required in each iteration. In this paper, a substructure damage identification method is proposed based on the model updating of the acceleration FRF. The original finite element model is divided into several substructures using the improved reduced system (IRS) by the dynamic condensation method, resulting in the simplified substructure model. The final simplified model is composed of the simplified mass matrix and stiffness matrix of the substructure considered. The damage acceleration FRF to be identified is used to iteratively update the simplified model. The locations and extents of the damage elements are obtained by updating the results, which reduces the number of uncertain parameters to be updated and leads to the rapid convergence of the optimization process. In the iteration, L1 norm regularization is introduced to solve the ill-posed problem, which improves the stability of the identification results. A numerical simulation of a six-story steel frame structure under various working conditions was carried out to verify the effectiveness of the proposed method, which was also validated by the experiments. The robustness and performance of the proposed damage identification method based on substructures have been demonstrated.

This paper presents a new formulation combining the nonlinear theory of Novozhilov with the classical finite element method for the purpose of evaluating the vibratory characteristics of thin, closed and isotropic cylindrical shells. The theory developed in this paper is able to include the shell curvature effect in the circumferential direction of the orthogonal displacements and considers the impact of initial geometric imperfections on the dynamic response of the system. The formulation first takes a general form by expressing the shell displacements as an alliance between the generalized coordinates and spatial functions. Nonlinear kinematic relationships are inferred from Novozhilov’s theory. The equations of motion as well as the expressions of the mass, linear and nonlinear stiffness matrices are derived through the Lagrange method by considering the coupling between the different modes. An application of this model is illustrated in a further step, by adopting the displacement functions derived from exact solutions of linear Sanders’ theory equilibrium equations for thin cylindrical shells. The governing equations of motion are solved with the help of a direct iterative method. Linear and nonlinear frequencies are validated by comparison with the results in the literature. The relative nonlinear frequencies are determined as a function of vibration amplitudes and then compared with published results for several cases of shells. Excellent agreement is observed between the results derived from this theory and those found in the literature. The effect of different parameters including axial and circumferential wave number, length-to-radius ratio, thickness-to-radius ratio and various boundary conditions, on the nonlinear frequencies of cylindrical shells is investigated.

The variation principle widely used in structural dynamics analysis allows us to transform the differential equation of the boundary value problem into a functional with extreme value. In recent years, it has been applied to the band-gap analysis of periodic structures. However, for periodic beam-plate composite structures with periodic and ordinary boundaries, it is relatively difficult for the traditional energy methods, such as the Rayleigh–Ritz method, to construct the displacement functions that satisfy boundary conditions. Hence, a hybrid solution is proposed in this paper to account for various boundary conditions of the periodic beam-plate composite structure. Specifically, the displacement functions constructed by the plane wave series can automatically satisfy the periodic boundary conditions. With the ordinary boundaries modeled by artificial springs, the spectral functions conforming to arbitrary boundary conditions are used to represent the displacement functions. The proposed solution is used to solve the band-gap problems of CRTS-III and CRTS-II slab ballastless tracks in China, and the accuracy of the solution is verified by comparing the calculated results with numerical simulations. In addition, through band-gap formation mechanism analysis, the frequency range of propagating flexural waves in each track component is accurately evaluated, which provides a theoretical basis for refined structural vibration reduction in the future. The solution proposed in this paper is flexible and convenient, which can be extended to a more complex band-gap analysis of periodic structures.

In this paper, an analytical solution is proposed for longitudinal dynamic responses of long tunnels under arbitrary excitations. For the derivation, the tunnel is assumed as a Timoshenko beam resting on a visco-Pasternak foundation. The Timoshenko beam theory is employed to consider both effects of the shear distortion as well as the rotary inertia of the tunnel, which are neglected by the Euler–Bernoulli beam. The visco-Pasternak foundation is applied to represent the viscoelastic compressive and shear resistance of soil. The governing equations of motion are transformed from partial differential forms into algebraic forms through integral transformations, and thus the solutions are conveniently obtained. The analytical solutions of the tunnel under several specific dynamic loads, including impulsive loads, moving line loads as well as traveling loads, are presented in detail and verified by comparing to the known degraded solution in literature and finite element results. Several examples are also conducted to investigate the influence of the relative stiffness ratio between the soil and the tunnel structure on the tunnel responses.

Suspended monorail transportation (SMT) plays an important role in alleviating the urban traffic pressure, and its vehicle–bridge dynamic features are significantly different from those of the traditional railway. To grasp the coupled vibration features of suspended monorail train–bridge system (SMTBS), this paper presents a comprehensive experimental investigation on the vehicle–bridge vibrational responses under different operating conditions. First, based on the Chengdu SMT test line in China, a full-scale field measurement of the coupled vibration responses of the SMTBS is elaborately conducted under constant speed conditions. Then, the vibrational responses of the SMTBS are analyzed in the time and frequency domains to reveal its coupled vibration features and vibration transmission characteristics. Further, considering an extreme train operating condition, the vibrational responses of the SMTBS are tested and analyzed under train emergency braking; and the vibration features of the vehicle and bridge are examined for emergency braking, along with several key indexes evaluated for the train braking performance. Results show that the vibrational accelerations transmitted from the frame to the center pin and then to the carbody will be significantly decreased in turn, and the vibrational dominant frequencies of the bogie, center pin, and carbody mainly fall with 0–100Hz, 0–50Hz, and 0–20Hz, respectively. Under moving train loads, the box beam produces plentiful high-frequency vibrations and the vibrations transmitted from the driving track to the top plate are drastically reduced. The train braking significantly intensifies the car-body longitudinal vibration; however, it has small influences on the car-body vertical and lateral vibrations.

Medium-low speed maglev trains (MSMTs) with a levitation gap of only 8–10mm need an adequate decoupling capability on the levitation frames to ensure stability control in levitation, while preventing the train from rolling sideways when in landing. Based on the geometric and kinematic relationships, two types of levitation frames are studied, i.e. levitation frame with end-set air spring (LFEAS) and levitation frame with mid-set air spring (LFMAS). For each levitation frame, the decoupling process and mechanism are analyzed, the analytical equations for the kinematic attitude are derived, the decoupling capability under different excitations is calculated, along with the effect of various structural parameters assessed. In addition, a test method is designed for the rolling of the levitation frame, particularly with the anti-rolling capability of the LFMAS measured. The results indicate that oscillation of the hanger rods and anti-rolling beams can compensate for displacement when the motion of the levitation frame is decoupled, which is the key to the decoupling capability. Also, the position of the anti-rolling devices and the length of hanger rods do not affect significantly the decoupling capability. However, a longer anti-rolling beam is more conducive to decoupling, but it does not affect the anti-rolling capacity of the levitation frame. The maximum roll computed of the LFMAS is 2.84mm, which meets the anti-rolling requirement.

In this work, a systematic vehicle–curved track dynamic model is presented, in which the vehicle is modeled as a multi-rigid-body system. The track structure is modeled by finite element method with curved rail beam element considered in geometry. To obtain accurate dynamic behavior of railway ballasted track, the resistance characteristics of ballast bed are revealed by introducing the discrete element method. Besides, a two-step iterative-update method is improved to solve the multi-nonlinearity of the vehicle–curved track dynamic interaction. To improve the computational efficiency, and the improved infinite cyclic calculation method is introduced. Apart from the model validations, the application of this model in engineering practices, such as the vehicle-induced vibration of the continuously welded rail (CWR), has been revealed, and some conclusions are drawn from the numerical studies.