International Journal of Structural Stability and Dynamics

In recent years, with the development of urban rail transit, more and more attention has been paid to the vibration problems caused by its operation. As the main form of urban rail transit’s underground construction, the shield tunnel is the first to bear the brunt. However, the existing researches on the vibration of shield tunnel usually take it as a homogeneous barrel and do not consider the impact of its assembly joints on the vibration propagation. In this paper, to study the influence of the joints caused by the shield tunnel’s assembly forms on the propagation of vibration, two finite element models of shield tunnels with different assembly forms are established. The analysis and comparing results of these models show that the joints caused by segment assembly of shield tunnel have obvious hysteresis and reduction effect on the vibration waves and this ability is obviously related to its location. In addition, the ability to weaken the vibration wave is also related to the frequency of the vibration wave.

Undesirable vibration of aircraft panel structures has a significant impact on the safety of their occupants and the operational reliability of various systems. The traditional time-domain controller based on the parallel multi-frequency filtered-x least mean square (FxLMS) control algorithm is simple and effective. However, the mutual influence of convergence steps and the induced harmonic components will limit its performance. An improved parallel multi-input multi-output multi-frequency FxLMS (MIMOMF-FxLMS) algorithm is proposed, considering the multi-input multi-output (MIMO) control requirement of the aircraft panel structure active vibration control (AVC) system and its inevitable channel coupling phenomenon. The feedback error signal and the control channel model are processed by frequency division in the MIMOMF-FxLMS algorithm, so that the FxLMS algorithm of each control channel runs independently, effectively avoiding mutual interference between convergence steps and the generation of induced harmonic components. Simulation and experimental research on multi-frequency AVC of the panel structure model is performed using a new type of piezoelectric stack actuator. The test results show that the proposed controller reduces the vibration level of each observation point by more than 98%, and the vibration responses of the first two-order frequency component are significantly suppressed, which also has strong adaptability and anti-noise ability.

This study proposes integrating the particle damping technology into multiple tuned mass damper (MTMD) to form a multiple tuned impact damper (MTID) system for suppressing the vibrations of nonlinear high-rise buildings under earthquakes. A systematic performance comparison comprising vibration damping effects and working strokes between the optimal MTMD and optimally designed MTID with a distinct multi-objective optimization strategy is addressed. The energy-based analysis is also conducted to essentially reveal the difference in damping mechanisms of the two dampers. Furthermore, due to the parameter deviations of engineering structures in practice, the robustness of MTID and MTMD is evaluated involving structural mass, damping and stiffness. The results show that MTID is capable of transferring more energy to the damper and reducing structural energy to a greater extent, thus presenting superiority in controlling structural root mean square (RMS) responses and nonlinear indicators comprising joint curvature and the number of plastic hinges compared with MTMD. Through parametric evaluation, greater robustness is validated in MTID under deviations of various structural parameters with downgraded performance fluctuation in both range and degree, and the efficient operating range of MTID under the deviation of structural parameters is given. Furthermore, a smaller working stroke of the optimal MTID system is required compared with MTMD, permitting the improved applicability of the MTID system and better space utilization in the practical building.

In seismically active regions, high-filled embankment slopes on liquefiable soils tend to damage after strong earthquakes. Therefore, post-seismic damages should be estimated as soon as possible to mitigate potential losses. Fragility function is an efficient tool for assessing the seismic vulnerability conditions of structures, which links the probability of exceeding different limit states to seismic intensity. An embankment slope on liquefiable soils at Yading Airport in China was selected as the study object, and a series of numerical analyses of the embankment-foundation system utilizing the finite element method were conducted. Advanced dynamic constitutive models considering liquefaction and hysteresis characteristics were also adopted to simulate the nonlinear stress–strain behavior of soils under cyclic loadings. The post-seismic stability of embankment slopes was assessed using the strength reduction method (SRM) based on the stress–strain analysis. On this basis, the permanent ground deformation (PGD) at the ground-free field conditions was selected as the intensity measure (IM), while the factor of safety (FoS) of the slopes was selected as the damage measure (DM). Then, a procedure was presented for deriving seismic fragility functions with different damage states in light of incremental dynamic analysis (IDA). This paper aims to investigate the effects of different embankment typologies, such as the thickness of liquefiable soils and slope inclination, on the post-seismic vulnerability of embankment slopes. The fragility curves constructed in this study may soon be helpful for predicting the post-seismic damage of similar high-filled embankment slopes on liquefiable soils, which enables efficient traffic control and rapid disaster response.

Thermoelastic dissipation or thermoelastic damping (TED) can restrict the quality factor of micro/nanoring resonators seriously. This paper employs the non-Fourier model of Guyer–Krumhansl (GK model) to render a size-dependent formulation and analytical solution for approximating the amount of TED in micro/nanorings with circular cross-section by inclusion of nonlocal and single-phase-lagging effects. To fulfill this objective, the equation of heat conduction in the ring is first established according to GK model. Then, by placing the temperature distribution obtained from the heat conduction equation in the TED relation defined on the basis of thermal energy approach, an expression in the form of infinite series is given for TED, which includes non-classical parameters of GK model. Finally, after checking the validity of the model through a comparative study, several simulation results are prepared to emphasize on the influence of different factors such as non-classical parameters of GK model, geometry of ring, vibrational mode and ambient temperature on TED value. Numerical examples reveal that the mentioned factors along with the two- or three-dimensional heat transfer (2D or 3D) model have major influences on TED variations.

By introducing the concept of a graded structure to seismic metamaterials, a new type of graded seismic metamaterial assembled using four steel sections with different graded levels is proposed to investigate its attenuation performance for surface waves. The dispersion curves and vibration modes are obtained using the finite element method and the sound cone method. A comparative analysis of the band gap characteristics of the four graded seismic metamaterials shows that an increase of the graded level is beneficial for widening the total band gap to a much larger relative bandwidth in the range of 0.1–13.07 Hz. In addition, a detailed analysis of the vibration modes reveals that local resonance is the main mechanism for the generation and change of the three band gaps. Moreover, the filling materials in the cavities, material and geometric parameters of the structure play important roles in the distribution and relative bandwidth of the band gaps. Finally, frequency–domain analysis is carried out on a finite system, and the agreement with the bandgaps is verified. This study paves the way for the design of graded seismic metamaterials. This concept allows flexible manipulation of the surface wave propagation by adjusting the graded level, fillers, geometric parameters of the steel sections, and soil materials to achieve seismic wave attenuation in low-frequency broadband.

Track irregularity is the main factor that affects the safety and comfort of high-speed railway. It is important to study the influence of the track irregularity on the safety service of high speed train–track coupling system. In this paper, a vehicle–track spatial nonlinear coupled system dynamics model is developed with FEM. The model includes vehicle subsystem and track subsystem, which are coupled by wheel–rail interface. The vehicle subsystem is a 31-DOF spatial vehicle model, and the track subsystem is a three-dimensional slab track model composed of the rail, rail pad and track slab. Considering wheel tread profile and rail head profile, the wheel–rail spatial contact geometry relationship is established, and the “Trace method” and the “Minimum distance method” are used to search for wheel–rail contact points. Considering the nonlinear contact between the wheel and the rail, a numerical approach is presented, where the “Trace method” is embedded into the algorithm for solving the vehicle–track nonlinear coupling dynamics equation by cross iteration, realizing searching the wheel–rail contact points and solving the vehicle–track nonlinear coupling equation simultaneously, which greatly improves the efficiency of numerical analysis. As application examples, the dynamic responses of a high speed train–track spatial nonlinear coupled system excited by the track V-shaped local profile irregularity and the track torsional irregularity are analyzed. The results show that the algorithm is effective in solving the vehicle–track spatial nonlinear coupled system dynamics problem, and the track irregularity has significant influence on the dynamic response of vehicle and track structure.

Simply supported bridges are the main bridge types in many transportation systems, and their damage can significantly reduce their load-carrying capacity. To detect possible damage, the time history and spatial distribution of the static responses of bridges (deflection, rotation, and strain influence lines/deformation curves) have recently been proposed as important indicators due to their good local damage detection ability and low testing cost. This paper attempts to establish connections between different static curve-based damage indicators through the various forms of Maxwell-Betti’s law. Damage indicators related to seven static curves are then rewritten as a unified framework. The framework states that all these static curves are directly related to the flexural stiffness distribution of the main girder for the simply supported bridge. Then, the theoretical formulations for the difference between the static curves of bridges in intact and damaged states are derived, and the response difference surfaces (RDSs) are plotted to visualize the sensitivity of different static curves to damage. Sensor placement suggestions for stiffness degradation evaluation are presented based on the damage sensitivity analysis at the end of this paper. The results of this study provide comprehensive theoretical support for static response-based damage identification of simply supported bridges.

As cracks are unavoidable and always reduce structural local stiffness and strength, this paper pays attention to the effect of cracks on the stability of the cracked functionally graded (FG) graphene-nanoplates reinforced composite (GRC) beam covered with piezoelectric layers. Both the critical buckling loads and postbuckling paths of the novel structures with cracks are considered. The massless rotational spring model is employed to calculate the bending stiffness of the cracked section. Three different graphene platelets (GPLs) distribution patterns along the thickness direction of the FG-GRC core beam are studied. The effective material properties of the FG-GRC core beam are calculated by Halpin–Tsai model and the rule of mixture. The governing equations of stability of the cracked FG-GRC piezoelectric beam are established within the framework of the first-order shear deformation beam theory, von Kármán geometric nonlinearity and Ritz method. The direct iteration method is used to examine the effects of boundary conditions, crack parameters, piezoelectric layers and GPL parameters on the critical buckling loads and postbuckling responses of the cracked FG-GRC piezoelectric beams. Results clearly illustrate that GPLs can significantly improve the stability of the cracked FG-GRC piezoelectric beams, while the increasing crack depth has the opposite effect.

Wave impeding block (WIB) barriers are often used to reduce vibration from different sources, but traditional vibration isolation of WIB has been limited to homogeneous materials and single-phase elastic or two-phase saturated foundations by many researchers. In fact, soils in nature are usually tri-phase unsaturated materials, and the propagation characteristics of elastic waves in unsaturated medium are completely different from those in single-phase elastic medium or two-phase saturated porous medium. In addition, the conventional WIB barrier has better vibration isolation only at low frequencies. Therefore, this paper improves the vibration isolation of the WIB by double-layer WIB with the same thickness on the basis of traditional WIB. Based on the wave theory of unsaturated porous media and elastic media, and according to the Helmholtz principle, we can obtain the solution of surface vertical displacement after setting double-layer WIB in unsaturated foundation, and then the isolation effect of double-layer WIB in unsaturated foundation under $P$-wave incidence is investigated. The wave impedance ratio at the interface between WIB and unsaturated soil and wave impedance ratio at the interfaces among the layers of WIB is first analyzed on the vibration isolation effect of double-layer WIB, and the wave impedance ratio corresponding to the optimal vibration isolation effect of WIB barrier is achieved. Then the key factors such as incidence angle, incidence frequency, saturation, thickness, and burial depth of the double-layer WIB are evaluated on its vibration isolation properties. Finally, the isolation effects of single-layer homogeneous WIB and double-layer non-homogeneous WIB with the same thickness are compared. For the same thickness isolation barrier, the vibration isolation efficiency of double-layer WIB is 42.73% higher than single-layer at the incidence angle of $16^{\circ }$–$90^{\circ }$. The double-layer WIB has better isolation effect at low, medium and high frequencies than single-layer WIB.

In this paper, a novel family of fourth-order accurate explicit time integration schemes is developed by combining the new time approximations and the explicit fourth-order Runge–Kutta (RK4) method. Inaccurate predictions due to the presence of excessive numerical dissipation are often observed in practical analyses of structural dynamics when the RK4 is employed for both displacement and velocity approximations. To remedy this, novel time approximations with adjustable algorithmic parameters are employed for the displacement vectors while the velocity vectors are approximated by using the RK4. For the complete elimination of numerical dissipation, algorithmic parameters are unconventionally determined by taking the determinant of the amplification matrix as unity. A set of algorithmic parameters obtained from this process makes the new schemes completely non-dissipative while keeping the computational cost the same as the RK4. Due to this improvement, the new schemes have enhanced total energy-conserving capabilities for nonlinear systems and give noticeably more accurate predictions in practical analyses. Until now, controllable numerical dissipation and fourth-order accuracy are not attained simultaneously in a unified set of time schemes. In the new schemes, however, a systematic way to adjust the level of numerical dissipation is also presented while attaining fourth-order accuracy. The numerical results of various test problems show that the new time schemes can provide more accurate predictions for nonlinear conservative dynamic problems than the existing time schemes.

Reliable connections are crucial for a bridge anti-collision protective system. Thus, this study proposes an innovative butterfly-like connection to tightly connect all segments of the pier composite protective system. The composite protective system is composed of four large segments, made of glass fiber-reinforced polymer (GFRP) panels, GFRP lattice plates, GFRP octagonal honeycomb tubes, round steel tubes, and polyurethane (PU) foam cores. The segments are jointed as a whole protective system by using eight proposed butterfly-like connections. First, the quasi-static tensile test is carried out to study the tensile strength and failure mechanism of the proposed connection. Then, a numerical model of the connection is established to determine the optimization parameter, and the numerical results are verified by experimental data. The optimal structural parameters for the connection are determined by parameter analysis using numerical results. Finally, a case study of a cable-supported bridge under vessel collision is numerically analyzed to comprehensively evaluate the overall protective performance and the dynamic reliability of the connection. It was found that the dynamic performance of the proposed connection is so reliable that it can ensure the protection system’s excellent performance. Also, the composite protective system can effectively reduce the collision force and the damage to both bridge and vessel.