International Journal of Structural Stability and Dynamics

The complex damping model can only be used to calculate the steady-state responses, while the transient responses are divergent. Based on the complex damping model, the Hilbert transform is introduced to establish a hysteretic damping model, eliminating the divergence phenomenon. However, with the increase of the loss factor, the damped natural frequency also increases. To overcome this shortcoming, a frequency-independent damping model is proposed based on the hysteretic damping model. However, traditional time-domain methods are no longer applicable to frequency-independent damping models. Therefore, the transient response and steady-state response are separated, and the assumption of external excitation acceleration is introduced. Time-domain methods-based linear polynomial assumption, quadratic polynomial assumption and trigonometric function assumption are proposed, respectively. Numerical examples show that the time-domain methods based on linear polynomial assumption and quadratic polynomial assumption have high computational efficiency. But these two methods cannot take into account the vibration frequency of external excitation acceleration. Hence, the computational accuracy is low. Compared with them, the time-domain method based on trigonometric function assumption has the lowest computational efficiency and the highest computational accuracy.

This study explores the nonlinear free vibrations of anisogrid lattice cylindrical panels under clamped circumstances for the first time. The lattice panel is made of repeating circumferential hexagonal unit cells with helical and circumferential isotropic ribs. The panel’s stiffness and mass are calculated using a continuous model based on orthotropic deep panel theory. The strain–displacement relationships are based on von-Kármán’s geometrically nonlinear theory. Using the Hamilton principle, nonlinear two-dimensional (2D) motion equations are extracted in their strong form. A 2D collocation approach based on the Sinc functions with double exponential (DE) transformation with a high convergence rate is used to solve the governing motion equations. The time variable is then eliminated from the equations using the weighted residual Galerkin procedure. Finally, the system’s nonlinear natural frequencies are computed using an iterative algorithm based on the bilateral displacement control. The influence of unit cell features, such as the angle of helical ribs, the number and thickness of ribs, and the panel dimensions, is examined in detail on the panel’s linear and nonlinear vibration behavior.

Polyvinyl butyral (PVB) laminated glass is widely used in architectural structures and automotive glass due to its remarkable cushioning and cohesive properties, and its lamination thickness has a significant effect on the overall impact resistance of the glass. In this paper, two conventional laminated glass thicknesses of 0.76 mm and 1.52 mm were selected to study the dynamic performance and damage morphology of laminated glass under three different impact velocities using light gas gun impact tests combined with industrial CT scanning-3D reconstruction techniques. The results showed that the PVB sandwich thickness had a significant positive correlation with the energy absorption effect, but under different impact velocities and glass thickness, the sandwich thickness and impact resistance showed a differentiated “marginal effect”. At moderate impact velocities, the impact resistance was most sensitive to the change in sandwich thickness. With the increase in glass thickness, the sensitivity of impact resistance to the change of sandwich thickness decreased. According to the characterization of full-dimensional cracks under medium-velocity impact conditions, it could be seen that the sandwich had the function of buffering dissipation and gathering recovery in different stress directions, and the thickness of the sandwich was a key functional parameter to reduce the flying of glass fragments. Therefore, the results of this study can provide a reference for the analysis and design of the impact resistance of PVB laminated glass.

Structural health monitoring (SHM) of cable-stayed bridges requires periodic assessment for the deteriorating stay cables to ensure a long-term service life of the bridge. However, conducting the non-destructive SHM for operating cable-stayed bridges and analyzing the safety statuses of all the working cables are still challenging, due to the lack of in situ cable data for previously constructed bridges. This study developed an innovative framework of health condition assessment for stay cables based on cable vibration frequencies from an interferometric radar (IBIS-FS) using engineering reliability analysis (ERA). Taking a cable-stayed bridge in Victoria, Australia as a target structure for the case study, it shows that the presented framework can remotely monitor the accurate real-time load bearing conditions of stay cables by calculating tension forces, and effectively assess their health conditions. The results show that the natural frequency (up to the fifth mode) of a healthy cable remains constant under different external loadings but varies for damaged cables. The measured reliability index of all the stay cables is higher than the safety threshold factor at ultimate limit states, while one carries tension force higher than the maximum design load (lower than the minimum breaking load) and other three cables need to be monitored regularly due to their low reliability indices. This is attributed to an integrated effect of applied tension force, cable diameters, and minimum breaking loads.

In this paper, structural columns with cross-section sizes of 100 mm × 100 mm, 75mm × 150 mm, and 85 mm × 121 mm are designed based on the same notional size of member. The acceleration signals of each column at axial compression ratio of 0.1, 0.2 and 0.3 were obtained by impact hammering. The corresponding frequency and damping ratio are obtained by half power wideband method. Based on the statistical method, the variation rules of acceleration signal characteristics, frequency characteristics and damping characteristics in different thickness directions under different axial compression ratios were analyzed. The correlation between frequency and damping ratio in different thickness directions with different axial compression ratios is discussed. The results show that under the same axial compression ratio, the damping ratio and frequency tend to decrease with the increase of the thickness in the tapping direction. Under the same thickness, the frequency decreases with the increase of the axial compression ratio. The damping ratio of the column decreases with increasing stress ratio when the thickness in the knocking direction is less than 100 mm. The damping ratio of the column increases with the increasing stress ratio when the thickness in the knocking direction is equal to 100 mm. The damping ratio of the column increases slightly with the increasing stress ratio when the thickness in the knocking direction is greater than 100 mm. By fitting the discrete data, the frequency variation range is 229.65–511.07 Hz, and the range of the damping ratio variation is 0.1–0.5%.

This study focuses on solving the geometric nonlinear dynamic equations of structures using the multi-point iterative methods within the optimal three-step composite time integration method (OTCTIM). The OTCTIM, initially devised for linear dynamic systems, is now proposed to encompass nonlinear dynamic systems in such a way that the semi-static nonlinear equations in time sub-steps can be solved using multi-point methods. The Weerakoon–Fernando method (WFM), Homeier method (HM), Jarrat method (JM), and Darvishi–Barati method (DBM) have been extended as multi-point solvers for nonlinear equations in OTCTIM, which exhibit a higher convergence order than the Newton–Raphson method (NRM), without requiring the calculation of second and higher derivatives. Several structural examples were solved to examine the performance of these methods in the OTCTIM approach. The results demonstrated that the multi-point iterative methods outperform NRM (in terms of the number of iterations) within the OTCTIM for geometric nonlinear structural dynamics and, among the multi-point methods, the JM and DBM converged with fewer number of iterations and lower error levels. Furthermore, it has been observed that when solving nonlinear dynamic equations for structures with a high number of degrees of freedom, the incorporation of the DBM into the OTCTIM mitigates the convergence iterations and the average elapsed time for iterative sub-steps.

In this paper, to investigate the dynamic responses of underground circular shells subjected to subsurface denotations and provide a feasible engineering design method, a simplified mathematical modelling was proposed. The dynamic medium–structure interaction (MSI) was introduced into the equations of motions through an interfacial damping between the structure element and the surrounding geomaterial, in which the effects of the shear and the rotary inertia were neglected. By means of modal superposition, the analytical solutions of the dynamic responses were deduced. The effects of geometric parameters and acoustic impedances on the dynamic responses were discussed. It is suggested that protective structures are better to be constructed in geomaterial with small impedance to attenuate the intense shock wave effects.

In this paper, the vibration and stability of spinning viscoelastic tapered shafts with axial motion are investigated. The model of the shaft system is developed by incorporating the spinning motion, axial motion, axial load, viscoelasticity, and geometric properties. The coupled governing equations of motion of the spinning shaft system are obtained by applying Hamilton’s principle. By employing the Laplace transform and Galerkin discretization method, the natural frequency and modal damping are computed. Also, the critical divergence axial and spinning velocities, as well as the flutter axial velocity, are determined. As a result, the divergence and flutter instability conditions of the system are examined. The effects of the main parameters, such as taper ratio, axial load, and viscoelasticity of material, on the vibration behavior of the shaft system are evaluated. The results show that compared to the homogeneous spinning shaft system with uniform cross-section, the vibration and stability of the viscoelastic tapered shaft system undergo an essential evolution. It is further demonstrated that the axial load and viscoelasticity are also the key parameters governing the stability of the system.

Deep learning techniques have gradually attracted considerable research interest in numerous application scenarios because of their capacity to simplify and accelerate calculations. Several researchers have adopted deep learning models, primarily end-to-end long short-term memory networks, to predict structural seismic responses in a data-driven manner and have achieved remarkable improvements. However, further research is required to reduce the training cost and complexity while maintaining the prediction accuracy of end-to-end models. In this study, a pre-training strategy was developed to meet these requirements. In brief, a generic base model was pre-trained by embedding the knowledge of calculating the response of single-degree-of-freedom systems, which was used as the basis for building tailored top models for the online prediction of seismic responses of different structures. This strategy modularized and simplified deep-learning-based seismic response prediction for training while maintaining the advantages of the end-to-end method. Proposed method was verified by using both simulation and actual datasets. The results demonstrated that a significantly lower training cost and complexity were required to achieve a prediction accuracy similar to that of the classic end-to-end method. Specifically, there was a reduction in FLOPs ranging from 20% to 80%, and a decrease in training time ranging from 44% to 82%. Moreover, the performance of deep learning with limited actual data was discussed.

To solve the mutual constraint between the large load capacity and low stiffness of large-scale air-floating micro-vibration isolation (LAMI), a spatial magnetic ring array stiffness regulation method (SMRASRM) is proposed, in which multi-layer magnetic rings are axially arranged, and the adjacent layers are magnetized perpendicularly to each other to form a spatial magnetic ring array with high magnetic density, thus realizing low stiffness under large load capacity. The analytical magnetic force and stiffness model of SMRASRM is established to analyze its effect on the dynamics of LAMI, and the design constraints, characteristics, and laws for reducing the stiffness of LAMI and achieving low-frequency isolation under large load capacity are also investigated. An experimental setup is built, and experimental results show that the stiffness of LAMI decreases by 28.40%, and the peak transmissibility decreases from 15.61 dB to 3.94 dB, which combines low stiffness and low transmissibility under large load capacity.

When the drilling and blasting method is used to excavate urban subway tunnels, the blasting seismic waves will inevitably produce vibration effects on the pile foundations under the surface buildings, which will seriously threaten the safety of surrounding buildings and the environment. Based on the transmission and reflection laws of stress waves at the interface between soil medium and pile medium and the displacement–stress continuous assumption, the wave function expansion method is used to analyze the whole process mechanism of vibration effect of hollow pipe piles under the action of incident $P$ waves. In addition, the theoretical model of safety criterion for hollow pipe piles under blasting vibration is proposed and the reliability of the model is verified. Furthermore, the impacts of the elastic modulus, density, and pile section parameters of soil and piles on the safety criterion for the blasting vibration effect of hollow pipe piles are analyzed. The results show that as the elastic modulus and density of the soil increase, the critical peak particle velocity (PPV) curves of hollow pipe piles move to the high-frequency and low-frequency bands, respectively, resulting in a decrease in the overall safety of piles. This indicates that hollow pipe piles should not be buried in soil layers with high elastic modulus and density. It is also shown that the larger the hollow area of hollow pipe piles, the lower their safety. Compared to solid circular piles, hollow pipe piles have a higher overall seismic safety reserve. The study results have guidance and reference value for effectively evaluating and controlling the harm of blasting vibration effects of hollow pipe piles.

Accurate identification of moving vehicle loads on bridges is one of the challenging tasks in bridge structural health monitoring, but lacks of intensive investigations to merge the heterogeneous data of vision-based vehicle spatiotemporal information (VVSI) and vehicle-induced bridge responses for moving force identification (MFI) in the existing time domain methods (TDM). In this study, a novel MFI method is proposed by integrating instantaneous VVSI and an improved TDM (iTDM). At first, a novel VVSI method combining background subtraction with template matching is presented to accurately track moving vehicles on bridges. With the calibration technique and camera perspective transformation model, the distribution of vehicles (DOV) on bridges is obtained and used as a priori information in the subsequent MFI. Then, the iTDM is developed based on the MFI equation re-formed in the form of instantaneous VVSI instead of the constant speed vehicle crossing bridges assumed in the traditional TDM. Finally, based on the redundant dictionary matrix composed of Haar functions for a moving load, the MFI problem is converted to explore a solution to the atom vectors and then solved by the Tikhonov regularization method. Experimental verifications in laboratory and a comparative study with the existing three methods are conducted to assess the feasibility of the proposed method. The results show that the proposed MFI method outperforms the existing methods and can effectively identify the moving vehicle loads with a higher and acceptable accuracy. It is successful for the proposed method to replace the assumption of constant speed vehicle crossing bridge in the traditional TDM with the instantaneous VVSI in the MFI problem.