International Journal of Structural Stability and Dynamics

In this paper, a simple formula is derived for the modal damping ratio of the bridge using the correlation between the instantaneous amplitudes of the related front and rear contact responses of a two-axle test vehicle by the Hilbert transform (HT). To start, closed-form solutions were derived for the dynamic response of the damped bridge and vehicle-bridge contact responses. Next, the HT was employed to generate the instantaneous amplitudes of the two contact points. Based on their correlation, a simple formula is derived for the bridge damping ratio. Finally, the reliability of the derived formula was verified in the numerical study. It was demonstrated that the proposed formula can be successfully used to determine the first bridge damping ratio, even in the presence of rough pavement, but with the aid of random traffic.

A meshless model is proposed to carry out the free and stationary stochastic vibration analysis of the functionally graded combined rectangular and cylindrical shells (FG-CRCS) structure under the aerodynamic and thermal environment. The FG-CRCS structure contains three combined structure types including rectangular–cylindrical shell (RC-type), cylindrical–rectangular–cylindrical shell (CRC-type), and closed rectangular–semicylindrical shell (CRS-type). The effects of aerodynamic and thermal loads on the dynamic behaviors of the FG-CRCS structure with temperature-dependency of material properties are investigated by introducing the supersonic piston theory and thermo-elastic theory. Furthermore, the pseudo-excitation method (PEM) is adopted to simulate the random loads applied to the FG-CRCS structure. The dynamic equations of the FG-CRCS structure are established in the theoretical frame of the first-order shear deformation theory (FSDT), whose general boundary conditions and coupling relationship are regulated by the artificial springs. Then, the reasonableness of this meshless model to predict free and random vibrations in aerodynamic and thermal environments is verified by comparing it with published literature and FEM results. On this basis, the contribution of essential parameters (including the aerodynamic load, thermal load, and boundary condition) on the free and random vibration behaviors of the FG-CRCS structure is presented, which may serve as guidance for the design of the plate–shell coupled structures in aerospace.

Fast-moving soft robotics usually suffer large-strain deformation with a relatively high velocity. To improve their performance, it is necessary to study the underly dynamical mechanism. However, the inherent strong material nonlinearity brings considerable difficulties in modeling and calculating the soft structure’s nonlinear dynamics. This work focuses on the large-strain vibrations of the hyperelastic rod under an axial tensile force. Several typical hyperelastic models, including the neo-Hookean, Mooney, and Yeoh models, are used to derive the equations governing the rod’s dynamics. The equations based on these models are relatively complex, and their corresponding numerical calculation diverges in some cases. Therefore, a reference stretch ratio(s) polynomial fitting (RSRPF) model is proposed to derive the concise governing equation. Such a governing equation is effectively solved by the combination of the Galerkin discretization and the fourth-order Runge–Kutta integration algorithm. The correctness of the developed model and the employed algorithm is verified by comparing with the previous data of a hyperelastic membrane. In most cases, the rod periodically vibrates under a periodic tensile force. However, when the structural damping is small and the load frequency approaches the resonant frequency, the hyperelastic rod may quasi-periodically vibrate. The revealed large-strain vibration mechanism is supposed to be useful for guiding the dynamical design of soft structures.

A series of bridge overturning accidents in recent years indicates that single-column pier bridges are susceptible to overturning failure. However, the traditional calculation method was incapable of ensuring an accurate prediction of the ultimate overturning capacity, which may lead to serious consequences in engineering practice. In this work, an analytical method was proposed based on the identified failure mechanisms. The forensic survey was first carried out on two typical overturning cases, and the findings of the surveys were summarized into three typical overturning failure modes and their corresponding criterion for failure evaluation. Further, the analytical method was proposed on the assumption that overturning of the girder consists of rigid and deformable body rotation and characters including radial bending and torsional deformation were considered. The method was later validated by the field data of the overturning cases. Besides, factors influencing the results were also compared and analyzed. The results demonstrate that, in comparison with the conventional calculation method, the proposed approach more effectively accounts for spatial parameter variations and nonlinear factors during girder rotation, thereby aligning better with the actual overturning process.

Offshore Triceratops are classified as form-dominant structures possessing the novelty of counteracting the lateral loads with material strength and geometric form. The deck is supported by the buoyant legs, which are positioned on the seabed using taut-moored tethers. Ball joints connect the legs with the deck and help partially isolate the deck to remain horizontal under waves and wind. While offshore structures commonly have tubular legs, the current study investigates Triceratops with elliptical legs under the postulated failure of tethers. Detailed dynamic analysis under postulated failure conditions is carried out using ANSYS AQWA, while the LIBRIUM analysis is used to obtain the equilibrium position of the platform under intact and postulated failure conditions. Results show that under postulated failure conditions, the peaks of the power spectral density function of the pitch response are seen closer to its natural frequency and the input wave frequency. Ball joints restrain this rotation from transferring to the deck, conforming to one of the advantages of its existence. The fatigue life of tethers calculated for different load cases under intact and postulated failure conditions helps understand the stability conditions of the platform.

The active angular absorber for angular vibration control is proposed. Characteristics of the angular absorber are analyzed and an experiment is performed. The active angular absorber consists of a base and two identical voice coil actuators. The actuators have central symmetry and the coils are series connected to get the same current so that they output inertia forces with the same amplitude in opposite directions. There is a certain distance between the axes of the two actuators to produce a moment from the inertia forces, which can be employed to actively control the angular vibration. First, the mechanics of the angular absorber are presented. Then, the dynamic model of an angular vibration system with the absorber is demonstrated and the control law is proposed. Parameters of the absorber are discussed, showing that the absorber has the advantages of reliable structure and flexibility for installation. Next, numerical simulation is performed and the results show that the control method is effective and the simplification of the dynamic model is reasonable. Finally, a prototype of the absorber is produced and the angular vibration control experiment is conducted. Test results show that angular vibration with the amplitude of 1” level and at a frequency of 6 Hz can be attenuated by 93% to the level of the noise, while vibration at 0.1” level and 46 Hz can be attenuated by 80.7% to 0.01”. The control process is rapid and convergence is stable.

The present study examines a microplate with a porous structure and two nanocomposite piezoelectric layers. All the layers’ properties are graded functionally, bonded to each other, and supported by an elastic foundation that can withstand both normal and shear loads. Additionally, carbon nanotubes are used to increase the electro-mechanical performance of the piezoelectric patches, which are exposed to an externally applied electric voltage. Using a higher-order trigonometric shear deformation theory and von Karman’s assumptions, the kinematic relations are demonstrated. The governing motion equations are derived using Hamilton’s principle and variational technique, and the modified couple stress theory is employed to take the scale effect into account. An analytical method based on Fourier series functions is used to solve the differential motion equations, and the impact of diverse factors such as porosity percentage, pore distribution patterns, carbon nanotubes distribution patterns, and other key parameters on the normalized frequencies of the model is analyzed after verifying the accuracy of the results. The findings of this research may aid in the development and production of smart structures and devices with increased efficiency.

A novel wave energy harvester (WEH) that can recover energy in the direction of heave, sway, and surge is designed under the background of low recovery efficiency and complex installation of the existing wave energy harvester. The harvester consisted of four main components: energy input module, energy transfer module, energy conversion module, and energy store module. In the paper, to convert more wave energy into electrical energy and improve the energy conversion efficiency of WEH, the motion transfer module is divided into vertical and horizontal motion transfer modules, which are used to harvest vertical and horizontal wave energy, respectively. The vertical motion transfer module combined with the ball screw structure, planetary gear structure, and one-way gear units ensure the generator has high speed. The horizontal motion transfer module is mainly composed of three uniformly distributed one-way gear units, ensuring collect the wave energy in all horizontal directions. The dynamic model of the harvester is established, and the simulation experiment is carried out under wave conditions with periods of 2 s, 2.5 s, and 3 s, respectively. The simulation results show that when the wave period is 2s, 2.5 s, and 3 s, the corresponding energy conversion efficiency of the WEH is 66.7%, 60.9%, and 57.1%, respectively. The proposed study provides a theoretical reference for modeling similar WEHs and can effectively balance energy supply and demand and further support the global agenda of UN-2030 for sustainable development, especially SDG-7.

Reconstruction of data loss in structural seismic responses is important for structural health monitoring to evaluate the safety of structures. A physics-guided neural network that leverages the prior knowledge was proposed for reconstructing structural seismic responses that were inaccessible to measure or missing during earthquakes. The presented methodology consisted of convolutional neural networks with dilated kernel and fully connected neural networks, which were developed to achieve a multitask learning that involved the regression task with measured labeled displacement data and the reconstruction task of seismic response without any labels. To better balance the loss gradient across different tasks, a probabilistic model was introduced to optimize the weight coefficient for each task by quantifying the task-dependent uncertainty based on Bayesian statistics. The weight coefficient for each task can be dynamically updated during the training process, thereby improving the learning efficacy and performance accuracy of the neural networks. The probabilistic model with task-dependent uncertainty was validated to outperform the equal-weighted model (i.e. equal weight for each task) in reconstructing the structural seismic responses based on numerical data, even when the relevant physical information (i.e. Bouc–Wen model) was not complete.

Lunar-based equipment undertakes the task of movement and transportation in the construction of unmanned lunar base. In the process of moving, the mechanical legs of the equipment are influenced by the lunar soil with special mechanical properties. In order to avoid these uncertainties caused by the lunar soil and other lunar environmental conditions affecting the safety during the mission, a new robust control method with the form of sectionalized expression is proposed based on the dynamic model of the leg-soil system. Lyapunov second method is introduced to demonstrate that the proposed control method can maintain the stability of the leg-soil system successfully. In order to clarify the contact force in the dynamics model, CAS-1 lunar soil simulant that can accurately simulate real lunar soil is used in the calibration test to obtain the precise mechanical parameters. Simulation and experiment are also carried out to verify the proposed control method and the traditional control methods are introduced to make a comparison. Both the simulation and experiment results show that the proposed control method has a better control effect than traditional methods. The proposed method improves the accuracy by an average of 75.7% and 55.9% compared to the traditional methods and the error is limited to 0.2%. By maintaining the stability and accuracy of the leg-soil system, the stability of the lunar-based equipment is improved when performing construction tasks. This study lays the foundation for the construction of unmanned lunar base in advance.

The current work deals with the mechanical buckling behavior of saturated porous toroidal shell segments sandwiched by piezoelectric actuator layers. Material properties of the porous shells with nonuniform distributed porosities are assumed to vary as a specific function of the thickness and porosity parameters. The nonlinear equations of the sandwich toroidal shell having either positive or negative Gaussian curvature are obtained on the basis of Biot’s poroelasticity theory. The energy method as the minimum potential energy principle is applied to derive the governing equations of the sandwich shells. The buckling equations of the piezo-porous sandwich shells under various types of mechanical loading are established by employing the adjacent equilibrium criterion. The governing equations as a set of the coupled partial differential equations are solved using an analytical method including the Airy stress function. Closed-form solutions are derived for shallow segments of the sandwich toroidal shell with positive/negative Gaussian curvature under lateral pressure, axial compression, and hydrostatic pressure loadings. Novel numerical results are presented in this work to show the effects of important factors such as the piezoelectric layer thickness, applied voltage, shell geometrical ratio, and variation of the porosity coefficient on the buckling behavior of these structures.

The Tibet Plateau is an area with abundant solar energy resources. However, it is also a location where severe thunderstorm disasters, for instance hail, frequently occur. In this paper, the dynamic response of the heliostat under impact by continuous hails was investigated. The effects of time interval of hail impact, hail diameter, impact position, as well as random multi-hail impact and random multi-hail distribution density were studied on the dynamic failure assessment of heliostat under continuous hail impacts. Results indicate that the continuous impact of hail on the same position of the heliostat causes a superposition effect on the heliostat. In case where larger-diameter hail initially impacts the heliostat, followed by smaller-diameter hail impact, the maximum principal stress in heliostat reaches its peak after the first hail impact and then steadily declines. When the heliostat is hit first by small-diameter hail followed by larger-diameter hail, it causes more damage to the heliostat compared to the case when the impact sequence is switched. The distance between continuous hail impacts reduces the increase of the maximum principal stress of the heliostat while increases the displacement value at the impact point of the heliostat. When the hail density increases by twice, the maximum principal stress increases significantly. The larger the hail distribution density, the smaller the stress concentration area, and then it gradually expands to both ends over time.