For short cables with complex boundary conditions, the frequency-based method for cable tension identification relying on string/beam theoretical models yields significant errors. The introduction of the concept of Effective Vibration Length (EVL) allows the frequency method to circumvent the influence of boundary conditions. To address the limitations in EVL identification, this paper proposes a single-point measurement-based cable tension identification method for short cables under added mass conditions. Its core advantages are simplifying the acceleration sensor for vibration signal acquisition and eliminating the original method’s reliance on mode shape calculation to determine virtual hinges. During optimization, a length segment is selected and divided into multiple virtual hinge points; effective vibration lengths corresponding to these points are calculated under various mass conditions to generate a virtual hinge–effective vibration length diagram. Leveraging the invariant virtual hinge position and effective vibration length across different conditions, the true optimal effective vibration length is locked via curve intersections, enabling high-precision cable tension identification with a single sensor and without exact boundary conditions. Numerical simulations validate the robustness and accuracy of the method. Under various complex boundary conditions and mass block arrangements, the relative error in cable tension identification is generally below 3%, demonstrating good engineering adaptability. A full-scale indoor experiment further confirms that in a short cable with unknown boundaries, using only single-point accelerometer measurements and two added mass block conditions, the cable tension identification error is as low as 1.15%.
Accurate assessment of the three-dimensional (3D) nonlinear flutter response of full-bridge systems is regarded as a prerequisite for the future implementation of wind-resistant design standards that employ the amplitude threshold of the limit-cycle oscillations (LCOs) as the criterion for nonlinear flutter. To satisfy this requirement, a time-frequency hybrid model of three-degree-of-freedom coupled nonlinear self-excited forces was developed on the basis of time-varying flutter derivatives (FDs), and a 3D multimode coupled nonlinear flutter analysis method suitable for long-span bridges was proposed. Using two long-span bridges with markedly different natural mode shapes as case studies, the proposed method was systematically applied to examine the effects of multimode coupling on nonlinear flutter responses and static equilibrium positions of the main girders. Structural modes that exert a critical influence on nonlinear flutter were further identified, their contributions were quantified, and the underlying mechanisms were revealed. The results indicate that multimode coupling effects primarily reduce system stability through the enhancement of aerodynamic negative damping. Neglecting the effects of multimode coupling leads to substantial misestimation of the nonlinear flutter response, the critical flutter wind velocity, and the equilibrium position of the main girder. Moreover, the natural mode shapes of the bridge deck, particularly the purity of its first-order symmetric torsional mode, are demonstrated to be key factors governing multimode coupled flutter behavior.
The U-shaped stiffened plates are widely used in construction, machinery, ships and other fields. It will inevitably lead to structural vibration problems due to its various loads in engineering applications. The aim of this study is to establish a semi-analytical model for evaluating the vibration characteristics of U-shaped stiffened plates. To begin with, the energy expressions of the plate are derived by incorporating the domain decomposition approach, artificial spring method and shear deformation plate theory. It is assumed that the plate and stiffener are rigidly connected in this study. Kinematic admissible functions are constructed via superposition of characteristic orthogonal polynomials and trigonometric series. Subsequent implementation of the Rayleigh-Ritz variational principle enables systematic resolution of vibrational behaviors, while validation studies demonstrate exceptional consistency with benchmark solutions from FEM simulations. Ultimately, the influence of the characteristic parameters such as the number and size of the stiffeners, the structural parameters of the plate on the dynamic behavior is investigated.
Haunch cracking in Prestressed Concrete (PC) box girders is a practical damage problem that may facilitate moisture ingress and accelerate durability deterioration. However, the cracking mechanism in the haunch zone remains insufficiently understood, particularly when prestressing tendons are anchored along the girder–width and the associated bursting stress cannot be accurately quantified. In the haunch zone, anchorage-induced bursting stress is an important source of local tensile stress. To solve this problem, this study establishes a Three-Dimensional (3D) bursting–stress model and applies it to identify the governing mechanical contributor of construction-stage haunch cracking in PC box girders. First, the analytical solution for 3D bursting stress is derived, and the relationship between tendon anchorage orientation and the direction of the maximum bursting stress is clarified with the aid of finite element analysis. On this basis, the governing cracking mechanism is identified by correlating crack morphology in the haunch zone with the 3D bursting–stress field under different tendon anchorage orientations. The proposed method is then validated through actual bridge cases of haunch cracking. The results show that the theoretical calculations of the maximum bursting stress agree well with the finite element results, with a maximum error of less than 8%. For height-anchored tendons, the maximum bursting stress is mainly distributed along the girder–width direction, whereas for width–anchored tendons, it is mainly distributed along the girder–height direction. The agreement among the theoretical calculations, finite element results, and field-observed crack morphology indicates that excessive bursting stress is the governing mechanical contributor of haunch cracking in PC box girders during construction.
The shear-thickening fluid (STF) damper is a passive vibration-mitigation device. The damping force is passively regulated by shear-rate-dependent changes in STF viscosity during external excitation. The hysteretic behavior of the STF damper was examined using mechanical tests. The vibration-mitigation characteristics under different loading conditions were then analyzed. The viscosity distribution in the fluid domain at different shear rates was characterized through simulations. The effect of variations in STF viscosity on the hysteretic response was analyzed. A theoretical model was derived from the shear-rate distribution within the gap. These results show that the STF damper exhibits a passive, nonlinear rate-dependent response. The damping index [Formula: see text] decreases with increasing velocity. Efficient energy dissipation over a broad frequency range can therefore be achieved. Finite element analysis further showed that the nonlinear damping-force response arises from shear-thickening and shear-thinning responses of the STF induced by the local shear-rate field in the gap. This study identifies a key finding: The peak damping force and hysteretic energy dissipation capacity are governed mainly by the viscosity of the STF in the shear-thinning regime, whereas viscosity changes in the shear-thickening regime mainly affect the initial damping-force growth rate.
Beams, as essential supporting and load-bearing structures in fields such as aerospace and defense, are frequently subjected to complex and variable loads. This often leads to nonlinear vibrations induced by large structural deformations and excessive noise, whereas dynamic vibration absorption provides a viable solution for the safety and comfort design of structures. Aiming to establish an efficient semi-analytical framework for the nonlinear vibration control of advanced composite structures, this study couples a Dynamic Vibration Absorber (DVA) to a Functionally Graded Carbon Nanotube Composite (FG-CNTC) beam. Within the framework of the First-order Shear Deformation Theory (FSDT) and incorporating geometric nonlinearity, the displacement field is formulated using a spectral-geometric series expansion. Subsequently, the Incremental Harmonic Balance (IHB) method is employed to solve the free and forced vibration responses of the coupled system, yielding the beam’s nonlinear frequency parameters and frequency-domain response curves. Comparisons of the present results with existing literature and finite element simulations validate the convergence and accuracy of the proposed coupled system model. Through comprehensive numerical examples, the influences of material properties, geometric parameters, and DVA characteristics on the nonlinear dynamic response of the beam are extensively investigated. This work expands the nonlinear dynamic analysis methodology for DVA-coupled FG-CNTC beams and provides fundamental support for the vibration attenuation design of FG-CNTC beam structures.
This study examines the mass-loading sensitivity (MLS) of Love-type wave (LTW) propagation in a rotating structure composed of a pre-stressed functionally graded piezoelectric-viscoelastic (FGPV) substrate underlying a dissimilar pre-stressed FGPV layer, by introducing a thin sensitive layer at the surface. The analysis also accounts for interfacial imperfections between the layer and the substrate by incorporating springmembrane (SM) interface model. Employing an appropriate analytical approach, the frequency relations governing wave propagation in the considered structure are derived under both electrically open (EO) and electrically short (ES) surface conditions. Special cases of the obtained relations concur well with the reported results in the literature. A comprehensive numerical simulation is carried out to graphically investigate the influences of rotation, gradient parameters, spring interface parameters, pre-stresses, membrane parameters, piezoelectric constants and piezoelectric loss moduli on the MLS. A comparative analysis is also conducted to highlight the impact of mass-loading on the phase velocity (PhV) of LTW in the considered structure. The reported consequences offer a deeper understanding of MLS in pre-stressed FGPV rotating structure with interface effects, and may be applied in the design of advanced acoustic wave sensors and biosensors.
Based on unsaturated poroelastic media theory, this study establishes an analytical model for the scattering of plane SV waves by an underground tunnel in an unsaturated half-space using the Fourier-Bessel series expansion of wave functions. Numerical analyses are performed to investigate the effects of saturation, incident frequency, incident angle, and burial depth ratio on surface displacement and the dynamic stress concentration factor (DSCF) around the tunnel. The results show that saturation and incident frequency exhibit a pronounced coupling effect. Surface displacement and DSCF exhibit asynchronous evolution under different parameter combinations. The incident angle significantly modulates the spatial distribution of the wave field. Near the critical angle, the coupled interaction between the incident SV wave and the converted P wave, together with multi-wave interference, is markedly enhanced. Increasing burial depth attenuates the surface response, whereas its effect on the tunnel DSCF exhibits a non-monotonic oscillatory pattern rather than a simple amplitude decay trend.
Although buckling-restrained braces (BRBs) have been widely investigated for regular multi-span frame systems, their application to irregular three-dimensional frame structures composed predominantly of single-bay frame lines remains insufficiently understood. This study systematically evaluates the seismic performance of BRBs in an irregular three-dimensional frame structure composed predominantly of single-bay frame lines. A typical school building in Bao'an District, Shenzhen, characterized by plan and vertical irregularities, discontinuous floor slabs, and pronounced translation-torsion coupling, is selected as a case study. A refined finite element model is developed and subjected to multiple representative ground motions with distinct characteristics. The structural responses, including story shear, story displacement, interstory drift ratio, damage distribution, and energy dissipation, are comparatively examined to clarify the seismic mitigation mechanism of BRBs in irregular three-dimensional frame systems dominated by single-bay frame lines. In addition, several BRB layout schemes are evaluated. The results show that BRB installation markedly reduces the overall interstory drift ratios, with maximum mitigation rates of 12.59% in the X-direction and 11.67% in the Y-direction under maximum considered earthquake (MCE) excitation. A supplementary elastic torsional assessment shows that the torsional-to-translational period ratio decreases from 0.863 to 0.782, while the maximum floor and interstory torsional displacement ratios decrease modestly, by up to 0.7% and 3.1%, respectively. Under increasing seismic intensity, the BRBs exhibit a staged response mechanism, transitioning from stiffness contribution to limited energy dissipation and finally to pronounced energy dissipation, thereby improving the global energy-dissipation capacity of the structure. Damage analysis further indicates that BRBs reduce the spatial extent of concrete compression damage and limit high reinforcement strain demands, particularly under DBE and MCE excitation. The comparative assessment of the examined layout schemes shows that lower-capacity BRBs activate earlier and provide greater drift reduction within the investigated, non-normalized parameter range; this result is interpreted as case-specific rather than as evidence of universal superiority. These findings elucidate the seismic mitigation mechanism and comparative layout behavior of BRBs in irregular three-dimensional frame structures with predominantly single-bay frame lines, providing a theoretical basis and practical guidance for the seismic design and retrofit of complex irregular structures.
In this paper, a new method for predicting hemispherical shell buckling under external pressure is presented. Due to the suddenness of collapse under external pressure and uncertainty in buckling calculation in the shells with non-zero Gaussian curvature, this method can be used for health monitoring of deep submarines. In this paper, the effect of external pressure on the natural frequency of the system was initially investigated, and it was shown that the natural frequency decreases under the impact of external pressure. In various examples, it has been shown that the value of the natural frequency under the effect of external pressure reaches zero between 60% and 80% of the value of the linear buckling pressure. Due to the error in linear buckling analysis of the hemispherical shell, explicit dynamic analysis has also been used. Eventually, it is shown that the buckling pressure can be predicted when the external pressure is about 90% of the collapse pressure. The findings of this paper show that by evaluating hull vibrations, it is possible to practically predict the buckling of deep-sea submarines before the submarine collapses.
The torsional vibration phenomenon is a common issue in various transmission systems, such as vehicles, machinery, marine, aviation and aerospace. The serious torsional resonance may generate the additional cyclic stress in the transmission system in operation, subsequently leading to damage or failure. In this paper, a novel torsional hollow stepped shaft design method is proposed to effectively attenuate the torsional vibration amplitude, inspired by the bending beam with the acoustic black hole (ABH) profile. By comparing dynamic equations of the bending beam to the torsional shaft with the ABH profile, it can be concluded that both dynamic equations exhibit similarities. Three types of torsional shafts with the ABH profile are designed and fabricated by additive manufacturing. Transient torsional experiments are conducted with a high-torque torsional experimental apparatus, and amplitude attenuation characteristics are investigated by finite element method (FEM), with solutions compared against experimental results. The comparison between the shaft with epoxy resin and the pure aluminum alloy shaft further confirms that the power law cross section with an ABH profile is the primary mechanism for vibration attenuation, while the epoxy resin merely plays a supplementary role. Accordingly, three engineering torsional shafts with the ABH profile are designed and subjected to numerical solutions. Results indicate that torsional natural frequencies of all three novel shafts are significantly reduced compared to conventional shafts. Moreover, whether subjected to the periodic impact load or the irregular transient load, all three novel shafts present significant vibration attenuation advantages, which can be flexibly selected under the different operating conditions.
In cable-supported bridge systems, stay cables and hangers are critical load-carrying components, and their fatigue deterioration can directly affect the overall service life of the bridge. Fatigue testing is time-consuming and costly, while continuum mechanics-based numerical methods also exhibit limitations in handling crack-induced discontinuities. Peridynamics (PD), owing to its inherent capability in modeling discontinuities, has been increasingly adopted for fatigue life prediction. Nevertheless, most existing PD-based fatigue studies focus on individual materials or components, and investigations targeting components in in-service structures at the structural level remain limited. This study integrates moving-load dynamic analysis with a PD-based finite element (PD-FE) model to evaluate the fatigue life of high-strength steel wires (HSSWs) in in-service bridge cables under moving train load. An urban rail transit extradosed cable-stayed bridge is taken as an engineering case study. Cable stress time histories are obtained via moving-load simulations, and the equivalent stress amplitude is determined using rainflow counting combined with Miner’s linear damage rule. The resulting equivalent cyclic loading is then applied to the PD-FE model to simulate fatigue crack growth and fatigue life. The results demonstrate the feasibility of the proposed PD-based method for fatigue life prediction of cable wires in in-service bridges. In addition, the effects of train speed, train formation and axle load, traffic loading frequency, and train-meeting conditions on wire fatigue life are investigated. This study provides an effective framework for fatigue performance assessment of in-service bridge cables subjected to moving train load.
Bridges are critical transportation infrastructure whose structural safety directly impacts public safety. Recently, non-contact measurement technologies have gained prominent attention in bridge structural health monitoring due to their high efficiency and automation. This paper presents a Multi-frequency Phase Unwrapping-based bridge vibration monitoring method (MB-PM) to address phase distortion and weak signal extraction challenges inherent in traditional phase-based methods under complex environments. The core Multi-frequency Phase Unwrapping (MPU) technique couples an adaptive reliability-weighted sub-band fusion strategy with a temporal phase unwrapping approach to resolve phase wrapping and noise interference. Mechanistically, the framework extracts local phase temporal information by applying an enhanced Phase-Based Motion Estimation (PME) approach via Complex Steerable Pyramid (CSP) decomposition across multiple Regions of Interest (ROIs). The MPU technique then fuses multi-scale and multi-directional phase information, while an adaptive frequencydomain filtering algorithm enhances system robustness. Subsequently, a dynamic reference benchmark unifies phase responses across multiple monitoring points, complemented by Phase-based Motion Magnification (PMM) to amplify weak vibration signals for subsequent spectral analysis. Under intense illumination interference, MB-PM limits the displacement-monitoring NRMSE to 0.61%, compared with 2.96% for traditional PME; in the ablation test, enabling MPU further reduces the NRMSE from 1.03% to 0.49%, confirming the effectiveness of the multi-frequency fusion strategy. Field application confirms that synchronous multi-point monitoring successfully captures loadinduced transient vibration responses, validating the practical engineering applicability of the proposed method.
This study presents an analytical investigation of the dynamic responses of a damped two-span continuous bridge subjected to successive moving loads, with particular emphasis on the role of bridge damping in internal and external cancellation phenomena and resonance conditions. The formulation is developed by exploiting the symmetric and antisymmetric modal characteristics of an equal-span bridge system, enabling analytical derivation of free vibration response in a two-span continuous bridge. A parametric study is conducted to quantify the effects of damping ratio, number of loads, and spacing of loads. The results demonstrate that bridge damping introduces a leaking effect that prevents complete vibration cancellation in damped systems, such that only minimum response levels can be achieved under cancellation conditions for both antisymmetric and symmetric modes. For small bridge damping ratios, cancellation and resonance conditions, as well as the optimal length ratios, remain essentially unaffected, indicating negligible influence of damping on critical speed parameters. Internal cancellation is shown to depend primarily on mode order, whereas external cancellation is governed by load number and spacing. Increasing bridge damping suppresses the occurrence of external cancellation, while increasing load number or spacing promotes it. The findings provide theoretical insight into vibration mitigation and dynamic design considerations for multi-span bridges under successive moving loads.
The elastoplastic buckling behavior of porous metallic rectangular thin plates is investigated accounting for pressure dependency of the material in plastic regime. The constitutive equations of two competitive theories including incremental theory (IT) and deformation theory (DT) of plasticity are proposed. To this end, related representative volume element of such materials with different porosities is constructed based on micromechanical averaging technique. The derived model is employed to study buckling of the plates with complex boundary conditions (BCs) under uniaxial and biaxial loading conditions. The current analytical solutions are restricted to the plates under Levy-type BCs. In this paper, a Hamiltonian system-based variational principle is reformulated for porous thin plates in the symplectic space. Three typical non-Levy-type BCs are studied for each of which two sub-problems are solved analytically using variable separation and symplectic eigen expansion methods. The results are validated against published literature. Comprehensive studies on the effects of plate’s aspect ratios, porosity factor and plasticity model on the buckling load and mode shapes have been carried out. It can be seen that the critical buckling load obtained from IT and DT are divergent especially for upper values of thicknesses. Also, the plastic buckling paradox is identified in which a significant disparity is observed between the DT and IT in calculating buckling loads for relatively thick plates.
Neural network techniques have been widely exploited to model structural dynamics. Among them, the continuous-time state-space neural network (CSNN) possesses great potential because of its advantage that a trained CSNN model can operate at different sampling rates without retraining. However, it has relatively low training efficiency due to the integration operations involved. To address this limitation, this study proposes a Wiener-type neural network (WNN) based on CSNN by reducing the nonlinear state derivative calculator present in CSNN to a linear equation. Based on this modification, an explicit state expression for WNN that discards high-order differentiable items for back propagation is derived, which not only facilitates rapid computation of the state variable but also greatly enhances training efficiency. The effectiveness of WNN is assessed through a numerical example of a cubic-stiffness structure, an on-site measurement example of a 6-story hotel building, and an experimental example of a magneto-rheological fluid damper. WNN models are compared with different models for these examples, and the results indicate that WNN models achieve high and consistent prediction accuracy, with Pearson correlation coefficients exceeding 0.85 and normalized root mean square errors below 0.06 across all cases. Meanwhile, the WNN model exhibits up to an 83% reduction in training time relative to the CSNN model. The developed WNN effectively balances prediction accuracy and training efficiency, making it a promising approach for dynamic modeling of large and complex systems.
Double-Track Bridges (DTBs) are widely used in heavy-haul railways to accommodate bidirectional traffic. Under asymmetric train loading, DTBs may experience pronounced torsional deformation and unbalanced bearing reactions, which can intensify train–track–bridge dynamic interaction. At the same time, the large structural scale of DTBs requires high computational efficiency. This study investigates the dynamic interaction characteristics of the Heavy-Haul Train-Double-Track Bridge System (HTDTBS) by developing a high-efficiency coupled dynamics model. The governing vibration equations of the heavy-haul train subsystem are derived from the D’Alembert principle. A multi-span double-track simply supported bridge is modeled by the Component Mode Synthesis (CMS) method to enable efficient simulation of large-scale bridge structures. The HTDTBS is coupled through nonlinear wheel–rail contact and equivalent track–bridge connection relationships. Based on this framework, the dynamic responses of the HTDTBS are examined in the time and frequency domains through theoretical analysis and field testing, and the measured data are used to validate the proposed model. Parametric analyses are then conducted to identify key design parameters that improve the dynamic performance of the HTDTBS. The results indicate that good consistency is observed between the simulation outputs of the established dynamic model and field test data. Asymmetric loading from heavy-haul trains generates notable torsional responses in DTBs. The rotation angle under loaded train conditions exceeds three times that under empty conditions. To guarantee favorable dynamic performance of DTBs, the recommended stiffness values are 140–180[Formula: see text]MN/m for rail fastener pads and over 800[Formula: see text]MN/m for bridge bearings.
The rapid development of waterborne transportation has increased the risk of vessel-bridge collisions, posing significant threats to bridge safety. However, existing protective installations often suffer from limited adaptability and high maintenance costs. Inspired by the superior compressive strength of the elytral joint structure of the iron-ringed beetle, a novel biomimetic thin-walled honeycomb energy-absorbing system was developed by integrating this joint structure with hexagonal and concave honeycomb cells. The mechanical performance of the proposed system was systematically investigated through quasi-static compression experiments and finite element (FE) simulations. By controlling the relative density, the influence of cross-sectional dimensional variations on the mechanical response was further analyzed. Results show that the system exhibits a distinctive secondary plateau stress during impact loading, with the second plateau stress increasing by 328% compared to the first. Furthermore, a pier protection device based on the proposed structure was designed and applied to the Jinma Bridge. Numerical simulations indicate that the peak vessel impact force can be reduced by up to 63.4%. Compared with conventional monolithic protection systems, the proposed interlocking modular system allows discrete unit assembly, providing improved adaptability, reduced material consumption, and higher replacement efficiency. This study offers a novel biomimetic design strategy for bridge protection systems subjected to impact loading.
With the increasing demand for high-performance vibration control in modern structures, inerter-based systems have attracted significant attention due to their pronounced inertia amplification and compact configuration. However, existing inerter systems, such as tuned viscous mass dampers (TVMDs) and tuned inerter dampers (TIDs), still suffer from limited effective bandwidth, high sensitivity to parameter variations, and possible dynamic coupling problems under strong excitations. To overcome these limitations and achieve higher vibration mitigation efficiency, this study proposes a novel dual-tuned inerter system (DTIS), which introduces a two-stage resonance mechanism into the energy transfer path to achieve broadband vibration control and improved dynamic stability. A simplified analytical model describing the interaction between the structure and DTIS is developed, and closed-form solutions of the frequency response function (FRF) are derived. The influences of key design parameters on vibration mitigation performance are systematically examined. Furthermore, a refined finite element (FE) model of a five-story reinforced concrete (RC) frame structure is established, and natural earthquake records are adopted to evaluate the seismic performance of different DTIS configurations. The results indicate that the proposed DTIS provides significantly enhanced vibration suppression and dynamic stability compared with conventional inerter-based systems. This study deepens the theoretical understanding of multi-resonant inerter mechanisms and offers a reliable basis for the design and practical implementation of high-efficiency vibration control devices in structural engineering.
The stability of thin-walled structures can be significantly affected by the uncertainties induced in the fabrication process. Uncertainties in the stability design of thin-walled structures present significant challenges. An AI-assisted analytical method is proposed for the reliable stability design in the fabrication of thin-walled structures with uncertainties. The moment estimation method and the least squares method are used in combination with the autoregressive model to evaluate the uncertainties. The GA-ACO-BP hybrid algorithm is proposed by combining the global search ability of genetic algorithm (GA) and the local search ability of ant colony algorithm (ACO). This algorithm transforms uncertain deformations into computable physical correction terms, achieving a regression coefficient (R2) of up to 0.956 and converging within 15 generations, which significantly outperforms traditional GA-BP and PSO-BP algorithms. Based on the 'formula degradation-physical mechanism' verification strategy, the experiment proves that the simulation benchmark error is only 5.61%, and the prediction error is reduced to 5.01% after geometric factor correction. This method can effectively realize the accurate compensation and rapid design of complex structural uncertainty through high-fidelity indirect verification.
