International Journal of Structural Stability and Dynamics

This research is designed to investigate the vibrational characteristics of a sandwich cylindrical shell structure with an elastic-porous metal–rubber core in the thermal environment by the power flow method. The finite element models of the homogeneous and sandwich cylindrical shell structures are established for harmonic response analysis completed by the mode superposition method. Further, the structural power flow is calculated and visualized based on the results of the finite element analysis. A comparison is made with the results for a plate available in the literature validating the effectiveness of the power flow visualization method. The effects of some key factors, such as the frequency, the metal–rubber core, the length-to-radius ratio, and the temperature on the power flow of the sandwich cylindrical shell structure, are analyzed using power flow cloud pictures and vector diagrams. The results reveal that the frequency affects the distribution of power flow, and the metal–rubber core can dissipate energy, whereas the length-to-radius ratio and temperature do not have a significant influence on the power flow of the sandwich cylindrical shell structure with a metal–rubber core (SCSMR). This work should be valuable for the noise and vibration control application of the SCS-MR.

A thermoelastic coupling model of axially moving beam based on Timoshenko beam model is established, which comprehensively takes into account the length–diameter ratio, axial load and moving speed, and unify the axial tension and compression load into one governing equation, and study the influence of the length–diameter ratio, axial load, motion speed and thermal load of the beam model. The differential governing equations of transverse vibration of axially moving beam with considering the axial tensile and compressive loads are established based on the Timoshenko beam theory and Hamilton’s principle. The dynamic characteristics of different slender beams with axial load and pinned–pinned, clamped–clamped and clamped-free boundary conditions are investigated, respectively. The dimensionless frequencies of beam calculated numerically with the differential quadrature method (DQM) are compared with analytical solutions for some special cases. For axially moving beams working in the thermal environment, the temperature field inside the beam is simulated by the heat conduction equations, and the thermal effect on dynamic characteristics of beam is studied under different thermal heating cases.

The suspension system of the maglev train will inevitably be disturbed by random factors such as track irregularities, which will cause random vibration of the train and even affect the safety of the train. Therefore, the research on the response and reliability of suspension system under random disturbance is crucial to its safe operation. In this paper, the response and the reliability of a suspension system are investigated using the theory and methods of stochastic dynamics. First, the magnetic gap and vertical velocity of the suspension system are random due to the random disturbance. Thus, the stochastic response is investigated through the probability density function (PDF), which is governed by the Fokker–Planck–Kolmogorov (FPK) equation corresponding to suspension system. And the response statistics of the suspension system under different system parameters and disturbance intensities are analyzed by solving the corresponding FPK equation using the finite difference (FD) method. Second, random disturbance may lead to the vibration amplitude of the suspension system exceeding the safety domain and causing safety incident, which is a reliability problem in stochastic dynamical systems. The probability that response is still in the safety domain at a given time is the reliability function of the suspension system, which is governed by the backward Kolmogorov equation. The time that the response first passes through the safety domain is the first-passage time, and its n-order moment satisfies the generalized Pontryagin equation. Reliability of the suspension system is analyzed by solving these governing equations using the FD method. In addition, the results of the FD method in this paper are verified with those of Monte Carlo (MC) simulation, which shows the correctness of FD method.

The operator-splitting (OS) method for real-time substructure testing (RTST) provides explicit and unconditionally stable solutions for structures with softening type stiffness and damping has been widely used for precisely disclosing the seismic performance of structures with velocity-dependent specimens. However, the OS method for RTST provides only explicit target displacement and velocity but not an explicit target acceleration, so that it is essentially an implicit method for Dynamic real-time substructure testing (DRTST) with dynamic system specimens. For precisely disclosing the seismic performance of multiple-degree-of-freedom structures with dynamic system specimens, one improved OS method is proposed for DRTST in this paper. The methodology and stability of the proposed OS method are investigated, and the effectiveness of the proposed OS method is validated by numerical simulations and experimental tests. By using the predictor displacement, velocity, and acceleration approximations, the OS method is an explicit algorithm for DRTST. The stability analysis shows that the proposed OS method is conditionally stable for DRTST, and its stability limit decreases with the increase of the mass ratio and the stiffness ratio, while it increases first and then decreases with the increase of the damping ratio. The numerical and experimental results confirm the stability and accuracy of the OS method. The OS method for DRTST provides a practical and precise investigation strategy for structures with dynamic system specimens and may have broad application prospects in civil engineering.

Closely spaced modes commonly observed in long-span suspension bridges can greatly increase the difficulty of identifying and tracking modal parameters. Most existing studies generally focus on identifying the closely spaced modes and quantifying the uncertainties based on numerical and experimental models. Further research focusing on full-scale long-span bridges is still required. A case study on identifying the closely spaced modes of the Qixiashan Yangtze River Bridge, a long-span suspension bridge with a main span of 1 418 m, is conducted in this paper. The effectiveness of the generalized fast Bayesian fast Fourier transform (GFBFFT) method is verified by both the simulated and monitoring data. The results show that a larger coefficient of variation (COV) and higher uncertainty is typically contained in the closely spaced modes than the separated modes. Compared with the FDD and SSI methods, the GFBFFT method guarantees higher identification accuracy of modal parameters and can serve as a reliable tool to identify the closely spaced modes.

To better suppress low-frequency vibrations of flexible manipulators induced by the rotation of motors and eccentricity, a novel type of tuned particle damper (TPD) is designed by combining the advantages of classical dynamic vibration absorber (DVA) and particle dampers (PD). Compared to traditional DVAs, this TPD can reduce additional mass and effectively broaden the frequency band of the DVA. Firstly, an equivalent theoretical model is established to describe the frequency tuning principle of the designed TPD. Based on the theory of a single particle damper, the equivalent damping and stiffness of the particles are calculated through an approximate approach. Then, a three-degree-of-freedom vibration model of the manipulator system with the TPD is built, and the dynamical characteristic of the primary resonance for the coupled system are analyzed by the perturbation method. Finally, the experimental platform is set up to verify the theoretical results. A manipulator is applied to test the low-frequency vibration absorption of the designed TPD, and the vibration suppression effect is discussed both in theoretical analysis and experiments.

Incremental dynamic analysis (IDA) is one of the widely used methods for structural assessment analysis and fragility curve development, given its unique capabilities in taking into account the aleatory uncertainties of earthquake records and its ability to provide a desirable statistical population of the system response. However, the strong dependence of the results on the number of selected records, the record selection process and scaling procedure, as well as the associated high computational costs are some of the obstacles, which limit the practicality of the IDA method especially in the case of large-scale structures. In the present study, an alternative approach called “Response Bounds” is proposed to estimate the expected range of structural responses under earthquakes with different intensity levels and to develop seismic fragility curves. To reduce computational costs and address the challenges associated with the record selection, a novel scenario-based Endurance Time (ET) analysis method is adopted. The good agreement between the fragility results of 5-, 10-, and 15-storey steel moment-resisting frames obtained by the proposed method and the IDA (less than 9% error) demonstrated the accuracy and reliability of the predicted results. The method could also estimate the mean loss ratio from fragility curves with less than 5% error in all cases. The proposed response-bound method can significantly reduce the computational costs of conventional seismic fragility assessment methods, and therefore can be used as an efficient tool for seismic reliability analysis in practical applications.

In practical engineering, a thin-walled cylindrical shell structure is more easily subjected to localized axial compression loads caused by external adjacent structures or devices. However, until now there are few studies to reveal the buckling behavior of cylindrical shells under such nonuniform loading conditions based on initial imperfection sensitivity. Therefore, buckling analysis of cylindrical shell under localized axial compression loads is investigated in this paper. Based on the buckling test, the influence of the morphology and amplitude of measured initial geometric imperfection are studied using the finite element method. Meanwhile, the inherent reason for initial geometric imperfection affecting the buckling load is elaborated. The influence of amplitude, distribution range, and different combinations of local dent imperfections are also elucidated. In addition, the effects of inclined loading imperfection and uneven shell thickness distribution imperfection are analyzed in the form of deterministic numerical simulation. Finally, a new buckling load knockdown factor that can reasonably consider the influence of loading imperfection and shell thickness variation imperfection is proposed. This work elucidates the initial imperfection sensitivity of the thin-walled cylindrical shell structures under localized axial compression load and can provide useful guidance for the buckling design and preventing buckling failure of these structures.

In this paper, the approximate analytical solutions obtained by using the constrained parameter-splitting-multiple-scales (C-PSMS) method to the primary and $1/3$ sub-harmonic resonances responses of a cantilever-type energy harvester are presented. The C-PSMS method combines the multiple-scales (MS) method with the harmonic balance (HB) method. Different from the erroneous stability results obtained by using the Floquet theory and the classical HB method, accurate stability results are obtained by using the C-PSMS method. It is found that the correction to the erroneous solution when the HB method and Floquet theory are adopted in the stability analysis of the primary and $1/3$ sub-harmonic resonances of a largely deflected cantilever-type energy harvester is necessary. On the contrary, the C-PSMS method gives much improved results compared to those obtained by using Floquet theory and HB method when the numbers of terms in each response expression are the same. The frequency response curves of the primary resonance and the $1/3$ sub-harmonic resonance of the harvester obtained by the C-PSMS method are compared to those obtained by the HB method and verified by those obtained by the fourth-order Runge–Kutta method. Moreover, the basin of attraction based on the fourth-order Runge–Kutta method is presented to confirm the inaccurate stability results obtained by using the HB method and Floquet theory. The convergence examinations on the stability analysis carried out by the HB method and Floquet theory show that enough terms in the response assumption are needed to achieve relatively accurate stability results when studying the stability of the primary and sub-harmonic resonances of a cantilever by using the HB method and the Floquet theory. However, the low-order C-PSMS method is able to give an accurate frequency-amplitude response and accurate stability results of the primary and sub-harmonic resonances of a largely deflected cantilever-type energy harvester.

In the complex mountain wind environment, especially in the strong wind, fluctuating wind speed is a non-stationary and non-Gaussian random process. With the increase of suspension bridges’ span, they are more sensitive to wind-induced vibration response. In this paper, a non-stationary and non-Gaussian buffeting reliability analysis method for long-span bridges is presented. Firstly, the non-stationary wind speed is simulated by the modulation function based on the stationary wind speed model. Secondly, the load is obtained by simulated wind speed, the obtained loads are loaded on the finite element model by ANSYS and the whole bridge time-domain analysis is performed, the time history of displacement response is obtained. Thirdly, based on the first excursion failure criterion of random vibration, the samples of the non-stationary and non-Gaussian displacement time history are transformed into a standard Gaussian process through a modified Fleishman approximation method, and then the non-stationary Poisson distribution method is used for structural reliability analysis. Finally, a mountainous long-span suspension bridge is used as the engineering background, and the proposed reliability analysis method is applied to analyze the reliability of the bridge. The influence of different wind attack angles and modulation functions on the dynamic reliability of the bridge is further studied. The results indicate that the displacement response obtained by the transformation of non-stationary and non-Gaussian random process is less reliable than that obtained by traditional analysis method. Its dynamic reliability is maximum at 1${}^{\circ }$ wind attack angle, the reliability of negative wind attack angle is lower than that of positive wind attack angle, and decreases with the increase of wind attack angle. The reliability obtained by using different modulation functions is lower than that of traditional method. If the traditional analysis method is still used for reliability analysis, it will produce unsafe consequences and reduce the engineering safety reserve.

The complexity in nonlinear behavior of torsional-irregular buildings in combination with uncertainty due to the natural randomness of earthquake records has been always a main challenge for buildings’ seismic design. To find a solution to this challenge, three reinforced concrete (RC) building archetypes were designed and next developed into their nonlinear models. Nonlinear static (pushover) analyses were performed to calculate the capacity of the archetype models in all principal and non-principal directions while incremental dynamic analyses (IDAs) were conducted by applying 30 accelerograms from both near-field and far-field earthquakes. The IDA capacity curves, collapse fragility curves and log-normal cumulative distribution functions (CDFs) were established by including both the aleatory randomness and epistemic uncertainty. Despite previous studies wherein fragility curves were given by evaluating structures’ collapse along structural reference axes or simply on $x$, $y$-axes, in this paper, possible building collapse on a critical non-principal direction (where maximum seismic response was observed) was simulated and its probability was accounted for developing IDA curves and log-normal CDFs. Accordingly, this issue was mirrored in computing available/acceptable collapse margin ratios (CMRs). In addition to the well-known outline used for calculating CMRs in the literature (that is based on estimation of collapse capacity in terms of earthquake intensity measure (IM)), the framework proposed here includes a new method for calculating the CMRs in terms of displacement-based drift, ductility, and damage. The superiority of the proposed method over the former is consistent with the buildings’ design procedure that is governed by storey drift control rather than base-shear strength. Refined statistics of CMRs given by taking into account displacement-based responses illustrate the available CMRs exceed the acceptable CMRs, meaning that a satisfactory safety margin against collapse will be anticipated in the targeted building class if a suitable yielding mechanism with sufficient ductility is provided for seismic force-resisting system by applying seismic design provisions of the current codes.

Large-displacement corner deformation often occurs at the joints of towering structures and long-span space structures subjected to strong earthquake. In order to improve the energy dissipation capacity of structural joints, the Nitrile Butadiene Rubber/High Abrasion Furnace Black (NBR/HAF) high damping composite was fabricated by formulation optimization in this paper, where a nonlinear large-deformation viscoelastic joint damper was proposed. The damper consists of five layers of restrained steel plates and four layers of shear energy dissipating material, which can reach 60mm shear displacement. In this paper, dynamic mechanical performance tests and static mechanical tests were firstly conducted on the core energy dissipating media of the damper. The loss factor of NBR/HAF composite reached a peak of 1.51 at about 8.2°C, while its wide damping temperature range was 27°C. Second, the accuracy of the simulation method was verified by comparing the simulated and experimental hysteresis curves. Then, the refined numerical simulation of this damper was carried out using ABAQUS finite element software with the high damping material as its core energy dissipating media. Finally, the magnitude and type of energy dissipation of each part of the viscoelastic joint damper under different loads were investigated. It was found that the large-deformation viscoelastic joint damper based on the composite had good damping capacity. Its dynamic characteristics were affected by the displacement amplitude and excitation frequency, which exhibited hardening nonlinear characteristics. As the frequency and load amplitude increased, the peak displacement in the loading direction gradually decreased, whereas the total energy input to the damper and the energy dissipated by the viscoelastic material increased monotonically. The input energy was only dissipated by the viscoelastic material, and no plastic loss occurred in the steel plate during the entire loading stage. Under high frequency and large loads, the damper can also have good energy dissipation characteristics. Because of the negative strain energy caused by plastic dilatancy, the energy dissipated by the material was gradually greater than the input energy with the load increasing.

This paper presents a dynamic analysis of trusses with an initial length imperfection of the elements, considering geometrical nonlinearity. In the nonlinear analysis of trusses, the hybrid finite-element formulation considers the initial length imperfection of the elements as a dependent boundary constraint in the master equation of stiffness. Moreover, it was incorporated into the establishment of a modified system of equations. To overcome the mathematical complexity of dealing with initial length imperfections, this study proposes a novel approach for solving nonlinear dynamic problems based on a hybrid finite-element formulation. In this study, the unknowns of the dynamic equilibrium equations were displacements and forces, which were obtained using virtual work. The hybrid matrix of elements of the truss is established based on the hybrid variation formulation with length imperfections of elements, considering large displacements. The authors applied Newmark integration and Newton–Raphson iteration methods to solve the dynamic equations with geometrical nonlinearity. An incremental iterative algorithm and calculation programming routine were developed to illustrate the dynamic responses of trusses with initial-length imperfections. The results verified the accuracy and effectiveness of the proposed approach. The uniqueness of the proposed method is that the length imperfection of the truss element is included in the stiffness matrix and is considered a parameter that affects the dynamic response of the system. This helps to solve the problem of the dynamic response of trusses with length imperfections becoming simpler. The numerical results show that the effect of length imperfection on the dynamic response of the trusses is significant, particularly on the dynamic limit load. In addition, to completely evaluate the behavior of the trusses, this study also developed formulas and analyses to consider the inelastic and local buckling of the truss structures, named ‘Inelastic post-buckling analysis (IPB).’

An aluminum foam/polyurethane interpenetrating phase composite damper (AF/ PUCD) can perform multi-functional energy dissipation to address different seismic hazards due to its multiphase hysteretic behavior. To improve the design of AF/PUCDs in engineering structures, a highly effective model based on the real deformation of an AF/PUCD is needed to describe its multiphase hysteretic behavior. In this paper, a novel viscoelastic-friction model composed of a viscoelastic component and a friction component is constructed. The hysteretic responses in each phase under various external excitations are described through the different combinations of the viscoelastic component and friction component. The unknown model parameters are identified through the Universal Global Algorithm (UGO). The model results are compared with the experimental results and the results from the Modified Bouc–Wen model and Optimum model. The comparative results show that the viscoelastic-friction model has a higher accuracy in capturing the multiphase hysteresis of AF/PUCD and predicting the boundary of each phase when the AF/PUCD is subjected to various cyclic excitations. Therefore, the viscoelastic-friction model is a good candidate for the design of AF/PUCDs applied in vibration control structures.