International Journal of Structural Stability and Dynamics

Piping systems are typical nonstructural components of a building. Previous investigations have reported many cases that earthquake causes damages or failures of piping system, resulting in secondary disasters. Therefore, this paper conducts a survey of the seismic damage of the piping systems of buildings and then reviews the state-of-the-art of the passive seismic protection methods. This paper proposes to classify the building piping system into rigid connected pipes, flexible connected pipes and semi-rigid connected pipes. Typical seismic damages of building pipes are presented following this classification. Then, several current seismic protection methods (including constructional measures, seismic braces, damping techniques and base isolation methods) are discussed regarding the theoretical mechanism and feasibility. Furthermore, the state-of-the-art of the building piping system and the passive protection methods with application prospects are evaluated. Based on the review, the flexible piping systems are most commonly used in existing old buildings and are more vulnerable in earthquakes due to their high flexibility. New buildings prefer the rigid connections which tend to restrain the motion of the pipe. However, the excessive stiffness of the rigid connection may cause overlarge internal stresses in both the connection and the pipe. Semi-rigid piping systems have sufficient overall stiffness and a degree of local deform ability and thus have the best seismic performance. In future studies, more research should be devoted to propose and develop new dampers suitable for piping systems, which will improve the seismic safety of building piping systems.

A simple solution method to identify buckling resistance of reinforced concrete (RC) columns during inelastic deformation is presented. Unlike conventional buckling solution methods, this proposed method predicts inelastic buckling loads of RC columns by directly solving the equilibrium differential equation under buckling. The method considers specific deflection configuration, end restraint conditions and inelastic material properties of the deformed column. In order to evaluate the reliability and accuracy of the proposed method, the results obtained from the purposed method are compared with the test results of eccentrically loaded RC columns. In addition, by using the proposed solution procedure, a parametric study is conducted to investigate the effects of critical RC column design parameters on column buckling behavior and resistance, including slenderness ratio, concrete strength, as well as longitudinal reinforcement and stirrup ratios. The results of the parametric study show that the proposed method is rational and can be adopted to effectively identify buckling resistance of RC columns subjected to inelastic damage, especially when load redistributions have occurred in the structure during progressive collapse.

Fluid sloshing in a rigid circular cylindrical tank is investigated; the tank is resting on soil foundation and is excited by horizontal seismic accelerations. A rigid annular baffle is connected to the inner wall of the storage tank to reduce liquid sloshing. By using the fluid subdomain method, the convective velocity potential is derived. An equivalent model with mass-spring oscillators is proposed to describe the sloshing motions of the contained liquid. Then, by means of the least square method, a complex polynomial fraction is employed to fit the dynamic impedance of the soil. A nested lumped parameter model is established to model the effect of the soil foundation. The substructure method allows to obtain the soil–tank–liquid coupled model. The equation of motion of the coupled system is solved by the Newmark-$\beta$ method. A comparison between the present sloshing results and those published in the literature shows an excellent agreement. The effects of the soil parameters, the baffle position and its size on the dynamic behavior of the soil–tank–liquid system are discussed in detail. The results demonstrate that the soil properties and the baffle parameters can have a remarkable influence on liquid sloshing. The novelty of this research is that an analytical model for the soil–tank–liquid–baffle coupled system is derived for the first time and it allows to study the dynamics and sloshing response of the system with accuracy and low computational cost.

The optimum design of distributed tuned mass dampers (DTMDs) is normally based on predefined restrictions, such as the location and/or mass ratio of the tuned mass dampers (TMDs). To further improve the control performance, a free parameter optimization method (FPOM) is proposed. This method only restricts the total mass of the DTMDs system and takes the installation position, mass ratio, stiffness and damping of each TMD as parameters to be optimized. An improved hybrid genetic-simulated annealing algorithm (IHGSA) is adopted to find the optimum values of the design parameters. This algorithm can solve the non-convexity and multimodality problems of the objective function and is quite effective in dealing with the large amount of computations in the free parameter optimization. A numerical benchmark model is adopted to compare the control efficiency of FPOM with conventional control scenarios, such as single TMD, multiple TMDs and DTMDs optimized through conventional methods. The results show that the DTMDs system optimized by using FPOM is superior to the other control scenarios for the same value of mass ratio.

The presence of intermediate supports usually imposes difficulties in identifying the tension force of stayed cables in cable-stayed bridges or hanger cables in arch bridges. This paper establishes the partial differential equations of motion of the cable and derives two numerical models with (Model 1) and without (Model 2) considering the flexural rigidity. The effects of two intermediate supports on the identification accuracy of the cable tension force are further studied analytically and experimentally. The effects of several non-dimensional parameters (e.g. damper location, support stiffness, flexural rigidity, and mode order of the cable) on the identification accuracy of the models are also investigated. It is theoretically concluded that the simplified Model 2 provides acceptable accuracy on tension force identification when the non-dimensional parameter $\xi$ is greater than 90 (slender cables), whereas the accurate Model 1 can be applied for tension force identification at any scenarios. The feasibility of two models is further verified by three numerical examples and field tests on two real-world arch bridges.

The existing critical buckling load calculation methods of horizontal hydraulic cylinder failed to fully reflect the initial boundary conditions and some critical influence factors, resulting in an unjustified critical buckling load. A new method to analyze the buckling behavior of the horizontal hydraulic cylinder articulated at both supports is developed on basis of large deflection theory and Timoshenko beam theory. Friction at supports, self-weight and initial misalignment by clearances are taken into account. Friction moments of supports are built according to Hertz contact theory. Bending stiffness of cylinder-rod junction is figured out in terms of elastic deformation theory. Runge–Kutta and Newton–Raphson method are used in numerical calculation for the critical buckling load. Practical calculation and stability test are carried out to verify the necessity of considering large deflection and shear effect in the proposed method. Experimental work shows the critical buckling load by the proposed method can well match to that by stability test with 0.55% deviation. Moreover, the numerical calculation results demonstrate that the friction moment of the support at piston rod end is crucial for the buckling behavior. The critical buckling load rises increasingly as the friction coefficient ${\mu }_2$ rises. As the friction coefficients ${\mu }_2$ increases from 0 to 0.020, the rise rate of critical buckling load increases from 1.782% to 8.055% per 0.001. And the clearance at cylinder-rod junction is a minor factor on the critical buckling load. As the clearances increase by 10 times, the critical buckling load decreases by 3.542%.

This paper presents a unified framework for dynamic analysis of vehicle-bridge interaction (VBI) systems using a commercial finite element software suite (ABAQUS$\text{®}$). This framework can provide bridge designers and engineering practitioners with a general platform to analyze the coupled system with high modeling efficiency and accuracy in modeling and outputting. Moreover, it has readily available nonlinear material/element models and nonlinear dynamic analysis functions for complex structures. This analysis framework was first validated with a classical VBI problem involving a sprung mass moving on a simply supported beam, whose closed-form solution is readily available. Validation for the application on complex structure was then presented with a typical 16-car Japanese high-speed train (Shinkansen) and a three-block bridge. The cars comprised car bodies, bogies and wheelsets, which were all modeled as rigid bodies and which were connected with springs and dashpots. The bridge was modeled with typical three-dimensional solid elements. Interaction between wheelsets and tracks was realized using the penalty method. Rail irregularity was also considered in the analysis. The consistency between calculated dynamic responses and field experiment data of certain pre-specified observation points validated the proposed method. Furthermore, ease in analyzing VBI problems involving nonlinear material properties and with high spatial resolutions was demonstrated with a classical cracked beam problem: a point mass moving on a simply supported cracked beam. Both linear and nonlinear crack models were employed. The former model assigned crack surfaces with a mechanical contact property and showed its accuracy in comparison to the reference model. The latter assigned a nonlinear material model in crack-prone zones and illustrated the potential applicability to dynamic crack propagation simulation in VBI problems. The present framework was further applied to seismic response analysis of a train-bridge interaction system involving material nonlinearity and separation between track and wheel under a strong earthquake.

The presence of clearance in a spherical joint makes the ball of the joint easy to collide with the socket, which causes additional dynamic effects on the motion of spatial mechanisms. The complexity of interaction between different clearance joints and that between a clearance joint and connected component requires an effective analysis method. In this paper, a practical method is proposed for evaluating the dynamic effects of spatial flexible mechanisms with multiple spherical clearance joints using finite particle method (FPM) combined with a clearance contact model. First, the equations of motion of the particles and internal force formulas of spatial beam elements in the discretized FPM model are derived, and the explicit generalized-$\alpha$ method is adopted for time integration. Then, the contact state is detected based on the penetration depth, using the Lankanani–Nikravesh model to calculate the contact force and the Threlfall model to calculate the friction force during collision in the clearance joint. Specifically, a method considering the particle rotations is utilized to better evaluate the direction of the friction force. A spatial four-bar mechanism with spherical clearance joints is used to demonstrate the feasibilities of the proposed method. The effects of four parameters (i.e. clearance size, friction coefficient, multiple clearance joints, and bending stiffness) on the dynamic responses of the mechanism are fully investigated.

This paper deals with the stability and dynamic evolution of a sliding pipe conveying fluid in the three-dimensional sense. The pipe is assumed to slide out from a fixed channel so that its free end is moving at the same time, a problem often associated with instabilities in applications of aerial refueling operation. To tackle this problem, the nonlinear governing equations of motion are derived by using the Hamilton’s principle and then reduced to a set of ordinary differential equations by the Galerkin’s method. A parametric study is performed to explore the transient vibration responses of the pipe for different values of flow velocity and sliding rate. Various dynamic behaviors are detected for the pipe in sliding and conveying fluid. The results show that 3-D oscillations of the pipe occur when the flow velocity exceeds a certain value, which can be affected by the sliding rate. For various flow velocities, the evolution of the dynamic characteristics of the sliding pipe can be classified into three typical types of motion. When at low flow velocity, the pipe is mainly subjected to a single type of 3-D motion. When the flow speed increases to high values, multi-type of 3-D motion consisting of three typical types occurs on the pipe. In addition, the pipe can display planar motions, transferring from one plane to the other. The result presented herein is helpful to understand the stabilities and dynamic behaviors of sliding-pipe systems used in aerial refueling applications.

The stress distribution of a steel wall is important in the determination of its shear capacity, e.g. under a wind load or an earthquake load. Since the wall has also to simultaneously carry the gravity load, the influence of this uniform vertical load on the stress distribution is relevant. For a simple-supported thick and square wall, a stress distribution in a cosine form was adequate. However, for an extremely thin wall, a cosine distribution is no longer valid, especially in the post-buckling condition. In this work a three-segment distribution is proposed, i.e. at both edge segments a cosine distribution from edge stress to buckling stress and in the middle segment a constant distribution of buckling stress. To evaluate the proposed distribution, a finite element model using the software ANSYS/LS-DYNA is developed. This model has been verified using the results obtained from own experiments and works done by others. The results show that the proposed stress distribution is able to describe the behavior of thin walls for different aspect ratios and slendernesses. The cosine distribution and the effective width model are also discussed.

Minor structural damages like incipient cracks are difficult to detect as they alter the structural stiffness marginally. It is difficult to extract the features of minor damage, from the measured time history responses, which are usually contaminated by measurement noise. Also, the effect of environmental/operational variabilities often misleads the damage diagnostic process, especially for subtle damages. To tackle all the above challenges in detecting and locating the minor incipient damage, an automated multi-model based data-driven technique is proposed in this paper. It is based on the fact that a subtle damage alters only some structural modes, while the others remain unaltered. Hence, the proposal here is to decompose the measured time-history response into the modal components and then reconstruct the signal using only the modal components with the damage sensitive features. The reconstructed signal is used in damage diagnosis. As an improved version of the second-order blind identification, the blind source separation technique is proposed in this paper for signal decomposition and a crisp automated algorithm is presented for isolating the modal components with damage sensitive features. The autoregressive moving average with exogenous input model with the cepstral distance as the damage index is employed for localizing the damage. The proposed multi-model approach is completely automated. Numerical studies have been carried out to demonstrate the effectiveness of the proposed algorithm. Also, experimental studies have been conducted to ensure the practicality of the proposed technique.

This research presents a numerical approach to address the moving load problem of functionally graded (FG) beams with rotational elastic edge constraints, in which the regularized Dirac-delta function is used to describe a time-dependent moving load source. The governing partial differential equations of the system, derived in accordance with the classical Euler–Bernoulli beam theory, are approximated by the discrete singular convolution (DSC) method. The resulting set of algebraic equations can then be solved by the Newmark-β integration scheme. Such a singular Dirac-delta formulation is also employed as the kernel function of the DSC method. In this work, the material properties of FG beams are assumed to be changed in the thickness direction. A convergence study is performed to validate the accuracy and reliability of the numerical results. In addition, the effects of moving load velocity and material distribution on the dynamic behavior of elastically restrained FG beams are also studied to serve as new benchmark solutions. By comparing with the available results in the existing literature, the present results show good agreement. More importantly, the major finding of this work indicates that the DSC regularized Dirac-delta approach is a good candidate for moving load problems, since the equally spaced grid system adopted in the DSC scheme can achieve a preferable representation of moving load sources.

Previous studies have shown that Eringen’s differential nonlocal model leads to some inconsistencies for both the Euler–Bernoulli and Timoshenko beams subjected to different boundary conditions. In this paper, the free vibration analysis of the Euler–Bernoulli and Timoshenko beams is performed theoretically using the stress-driven nonlocal integral model. The Fredholm-type integral constitutive equations of the first kind are transformed to Volterra integral equations of the first kind by simply adjusting the limit of integrals. Also, the general solutions to the deflection, bending moment and so on are derived by solving the integro-differential governing equations by the Laplace transformation, of which the unknown constants are determined by the boundary conditions and extra constraint equations related to the constitutive relationship. Then the characteristic equations for free vibration of the Euler–Bernoulli and Timoshenko beams are derived, from which the vibration frequency for different boundary conditions can be determined. The effects of nonlocal parameter and vibration order on the natural frequency of the Euler–Bernoulli and Timoshenko beams are investigated numerically. The results from the present model are validated against those existing in the literature, and demonstrated to be theoretically consistent.

In this paper, hydroelastic behavior of a pontoon-type very large floating structure (VLFS) subjected to a moving single axle vehicle is computed using a novel numerical approach, in which the boundary element method (BEM) is firstly extended to cooperate with the moving element method (MEM), named the BEM–MEM. By utilizing this paradigm, the plate and fluid are discretized into “moving structural element” and “moving boundary element”, respectively, which are conceptual elements and “travel” with the moving vehicle. Thus, the proposed method can absolutely eliminate the need of keeping track the location of the moving load with respect to the floating structure. Particularly, the surrounding fluid is defined based on the potential flow theory and the motion of a floating plate is governed by the vibration equation of a thin plate. The governing equations of motion, moving element and fluid matrices of boundary element are formulated in a relative coordinate system traveling with the moving vehicle. Several examples are numerically conducted to illustrate the performance and ability of the BEM–MEM. Its obtained results are compared with those of the traditional finite element method for validation. The outcomes reveal that the proposed method is effective for the large-time behavior owing to the fact that it does not require a domain with the length greater than the horizontal displacement of the vehicle. The paper also discusses the effect of the liquid and structural parameters on responses of the vehicle and floating structure.

This paper aims to study the effects of fish nets on the nonlinear dynamic performance of a floating offshore wind turbine integrated with a steel fish farming cage (FOWT-SFFC). Fully coupled aero-hydro-servo-elastic numerical models of FOWT-SFFC, with and without nets, are constructed to probe the nonlinear time-domain stochastic response. The first-order potential flow model with quadratic drag forces is employed to calculate the hydrodynamic loading on the foundation. The effects of nets on the damping ratios of 6 degree-of-freedom motions and on their displacement response amplitude operators (RAOs) are respectively investigated in numerical decay tests and monochromatic regular waves. The results show that the nets help to increase the damping level for the whole system and reduce motion RAOs when wave periods are around the natural periods of motions, while nets play insignificant role in motions when wave periods are far away from motion natural periods. The dynamic performances of FOWT-SFFC with and without nets under random ocean waves, the combined random wind and random waves as well as current are comprehensively compared and discussed. The simulation results indicate that in wind-sea dominated conditions, the nets tend to slightly increase the dynamic responses of FOWT-SFFC, especially the components corresponding to natural periods. Nonetheless, under sea states that comprise both wind-sea waves and swell, nets help to reduce the dynamic responses of FOWT-SFFC by introducing additional damping.