Search Results (1,103)

Fractional-order models provide a powerful framework for capturing memory-dependent and viscoelastic dynamics in mechanical systems, which are often inadequately represented by classical integer-order characterizations. This study addresses the identification of dynamic parameters in both single-degree-of-freedom (1-DOF) and three-degree-of-freedom (3-DOF) Duffing oscillators with fractional damping, modeled using the Grünwald–Letnikov characterization. The 1-DOF system includes a cubic nonlinear restoring force and is excited by a harmonic input to induce steady-state oscillations. For both systems, time domain simulations are conducted to capture long-term responses, followed by Fourier decomposition to extract steady-state displacement, velocity, and acceleration signals. These components are combined with a GL-based fractional derivative approximation to construct structured regressor matrices. System parameters—including mass, stiffness, damping, and fractional-order effects—are then estimated using pseudoinverse techniques. The identified models are validated through a comparison of reconstructed and original trajectories in the phase space, demonstrating high accuracy in capturing the underlying dynamics. The proposed framework provides a consistent and interpretable approach for frequency domain system identification in fractional-order nonlinear systems, with relevance to applications such as mechanical vibration analysis, structural health monitoring, and smart material modeling. Full article

Aiming at the characteristics of limited actuation capability of the semi-active control system and strong nonlinearity of the hydro-pneumatic suspension, a constrained nonlinear control strategy of a semi-active hydro-pneumatic suspension system is proposed. According to the mathematical model of nonlinear hydro-pneumatic suspension, the static stiffness and linear damping coefficient based on the equivalent energy are calculated, and then the control-oriented dynamic equation whose expression minimizes the nonlinear term is constructed. Combined with actuation capacity constraints, an optimization model with constraints is established to minimize the deviation between the actual overall control force and the expected optimal control force, and the optimal approximation from nonlinear control to linear quadratic optimal control is realized. The control simulation results of various methods show that the nonlinear control with constraints of the semi-active hydro-pneumatic suspension system, which effectively combines the actuation capacity constraints and nonlinear characteristics of the system, achieves a good comprehensive control effect for the nonlinear suspension control with constraints. Full article

This paper presents an enhanced pseudo-rigid body model (PRBM) integrated with the LuGre friction law to analyze the dynamic behavior of flexure-hinge-based piezoelectric stick–slip actuators (PSSAs). The PRBM captures flexure compliance through Lagrangian dynamics, while Newtonian mechanics describe the piezoelectric stack and slider motion. Non-linear contact effects, including stick–slip transitions, are modeled using the LuGre formulation. A mass–spring–damper model (MSDM) is also implemented as a baseline for comparison. The models are solved in MATLAB Simulink version R2021a and validated against experimental data from a published prototype. The enhanced PRBM achieves strong agreement with experiments, with a root mean square error of 20.19%, compared to 51.65% for the MSDM. By reformulating the equations into closed-form expressions, it removes symbolic evaluations required in the standard PRBM, resulting in one to two orders of magnitude faster simulation time while preserving accuracy. Stable transient simulations are achieved at fine time steps ($\Delta t={10}^{-8}$ s). A systematic parametric study highlights preload force, flexure stiffness, friction coefficients, and tangential stiffness as dominant factors in extending the linear frequency–velocity regime. Overall, the PRBM–LuGre framework bridges the gap between computationally intensive finite element analysis and oversimplified lumped models, providing an accurate and efficient tool for design-oriented optimization of compliant piezoelectric actuators. Full article

Inspired by the self-organizing optimization mechanisms in nature, the leaf venation of the royal water lily exhibits a hierarchically branched fractal network that combines excellent mechanical performance with lightweight characteristics. In this study, a structural bionic approach was adopted to systematically investigate the venation architecture through macroscopic morphological observation, experimental testing, 3D scanning-based reverse reconstruction, and finite element simulation. The influence of key fractal geometric parameters under vertical loading on the mechanical behavior and energy absorption capacity was analyzed. The results demonstrate that the leaf venation of the royal water lily exhibits a core-to-margin gradient fractal pattern, with vein thickness linearly decreasing along the radial direction. At each hierarchical bifurcation, the vein width is reduced to 65–75% of the preceding level, while the bifurcation angle progressively increases with branching order. During leaf development, the fractal dimension initially decreases and then increases, indicating a coordinated functional adaptation between the stiff central trunk and the compliant peripheral branches. The veins primarily follow curved trajectories and form a multidirectional interwoven network, effectively extending the energy dissipation path. Finite element simulations reveal that the fractal venation structure of the royal water lily exhibits pronounced nonlinear stiffness behavior. A smaller bifurcation angle and higher fractal branching level contribute to enhanced specific energy absorption and average load-bearing capacity. Moreover, a moderate branching length ratio enables a favorable balance between yield stiffness, ultimate strength, and energy dissipation. These findings highlight the synergistic optimization between energy absorption characteristics and fractal geometry, offering both theoretical insights and bioinspired strategies for the design of impact-resistant structures. Full article

Fault activity represents a significant geological hazard to buried pipeline infrastructure. The associated stratigraphic dislocation may lead to severe deformation, instability, or even rupture of the pipeline, thereby posing a serious threat to the safe operation of oil and gas transportation systems. This study employs the 3D nonlinear finite element method to systematically investigate the mechanical behavior of buried steel pipes subjected to fault-induced dislocation, with particular emphasis on critical parameters including fault offset, internal pressure, and the diameter-to-thickness ratio. The study reveals that buried pipelines subjected to fault dislocation typically undergo a progressive failure process, transitioning from the elastic stage to yielding, followed by plastic deformation and eventual fracture. The diameter-to-thickness ratio is found to significantly affect the structural stiffness and deformation resistance of the pipeline. A lower diameter-to-thickness ratio improves deformation compatibility and enhances the overall structural stability of the pipeline. Internal pressure exhibits a dual effect: within a moderate range, it enhances pipeline stability and delays the onset of structural buckling; however, excessive internal pressure induces circumferential tensile stress concentration, thereby increasing the risk of local buckling and structural instability. The findings of this study provide a theoretical basis and practical guidance for the design of buried pipelines in fault-prone areas to withstand and accommodate ground misalignment. Full article

Dynamic compaction has been widely applied to reinforce soft soils in port areas due to its high efficiency and cost-effectiveness. However, a comprehensive understanding of the deformation mechanisms and stiffness evolution of treated soils under static and dynamic loading remains limited. This study integrated one-dimensional consolidation tests, resonant column tests, and bender element tests to systematically investigate the mechanical behavior of soft clay before and after dynamic compaction under varying stress levels and loading frequencies. The results show that dynamic compaction significantly enhances the compression modulus and consolidation stability of soft clay while reducing the settlement rate during primary consolidation. The shear modulus exhibits nonlinear degradation with increasing strain, whereas the damping ratio increases rapidly before reaching a plateau, indicating typical strain-dependent behavior. A three-parameter model and a second-order polynomial model effectively characterize the degradation of the shear modulus and the evolution of the damping behavior, respectively. Moreover, the strong consistency between the resonant column and bender element test results enables continuous characterization of the shear stiffness across small- to intermediate-strain ranges. These findings provide theoretical insight and practical guidance for modeling the dynamic response of soft clay and evaluating the effectiveness of dynamic compaction as a ground improvement technique. Full article

Diaphragm springs, as critical components in commercial vehicle clutch assemblies, directly determine the clutch’s working performance. The design of diaphragm springs, which possess a distinct symmetrical structure that underpins their mechanical behavior, centers on obtaining the large-end nonlinear load–displacement curve—a typical large deformation-induced nonlinear problem. Traditional design relies on the A-L formula, but studies show finite element analysis (FEA) yields results closer to actual measurements. This study established an FEA model of the diaphragm spring’s disc spring (excluding separation fingers) and validated its correctness by comparing it with the A-L formula. Then, using FEA on models with separation fingers, it analyzed factors influencing the large-end load–displacement characteristics. Leveraging the inherent symmetry of the diaphragm spring structure, particularly the symmetrical distribution of separation fingers, the analysis process efficiently captures uniform mechanical responses during deformation, while this symmetric arrangement also ensures balanced load distribution during clutch operation, a critical factor for stabilizing the load–displacement curve. Results indicate the separation finger root is a key factor, with larger root holes, square holes (compared to circular ones), and more separation fingers reducing stiffness to effectively adjust the curve; in contrast, the tip and length of separation fingers have little impact, making the latter unsuitable for design adjustments. Full article

To address the collaborative demand for low-frequency vibration control and energy recovery, this paper proposes a dual-functional structure integrating low-frequency vibration isolation and broadband energy harvesting. The structure consists of two core components: one is a quasi-zero stiffness (QZS) vibration isolation module composed of a linkage-horizontal spring (negative stiffness) and a vertical spring; the other is an energy-harvesting component with an array of parameter-differentiated piezoelectric cantilever beams. Aiming at the conflict between the structural dynamic stiffness approaching zero and broadening the effective working range, this paper establishes a dual-objective optimization function based on the Pareto principle on the basis of static analysis and uses the grid search method combined with actual working conditions to determine the optimal parameter combination. By establishing a multi-degree-of-freedom electromechanical coupling model, the harmonic balance method is used to derive analytical solutions, which are then verified by numerical simulations. The influence laws of external excitations and system parameters on vibration isolation and energy-harvesting performance are quantitatively analyzed. The results show that the optimized structure has an initial vibration isolation frequency below 2 Hz, with a vibration isolation rate exceeding 60% in the 3 to 5 Hz ultra-low frequency range and a minimum transmissibility of the order of 10⁻² (vibration isolation rate > 98%). The parameter-differentiated piezoelectric array effectively broadens the energy-harvesting frequency band, which coincides with the vibration isolation range. Synergistic optimization of both performances can be achieved by adjusting system damping, parameters of piezoelectric vibrators, and load resistance. This study provides a theoretical reference for the integrated design of low-frequency vibration control and energy recovery, and its engineering implementation requires further experimental verification. Full article

Pumping station structures are widely employed to supply circulating cooling water systems in nuclear power plants (NPPs) throughout China. Investigating their seismic performance under complex heterogeneous site conditions and load scenarios is paramount to meeting nuclear safety design requirements. This study proposes and implements a novel, efficient, and accurate viscous-spring boundary methodology within the ANSYS 19.1 finite element software to assess the seismic safety of NPP pumping station structures. The Maximum Initial Time-step (MIT) method, based on Newmark’s integration scheme, is employed for nonlinear analysis under coupled static–dynamic excitation. To account for radiation damping in the infinite foundation, a Compact Viscous-Spring (CVs) element is developed. This element aggregates stiffness and damping contributions to interface nodes defined at the outer border of the soil domain. Implementation leverages of ANSYS User Programmable Features (UPFs), and a comprehensive static–dynamic coupled analysis toolkit is developed using APDL scripting and the GUI. Validation via two examples confirms the method’s accuracy and computational efficiency. Finally, a case study applies the technique to an NPP pumping station under actual complex Chinese site conditions. The results demonstrate the method’s capability to provide objective seismic response and stability indices, enabling a more reliable assessment of seismic safety during a Safety Shutdown Earthquake (SSE). Full article

The harmonic balance method (HBM) is a widely used method for determining the forced response of non-linear systems such as bladed disks. This paper focuses on analyzing the sensitivity of this method to key computational parameters and its robustness. HBM and HBM coupled with pseudo arc length continuation are used in this paper to solve the equation of motion of a test case. The pseudo arc length continuation is necessary because when intermittent contact occurs, natural continuation cannot guarantee solver convergence. Intermittent contact, in addition to turning points, introduces further problems, which are caused by an infinite sequence of decaying, but not zero, Fourier coefficients. This results in the need to oversample the non-linear force time signal to avoid convergence problems. The computational parameters investigated in this paper are the samples per period, which determine the number of points in which the time signal is discretized, and the harmonic truncation order. In addition, the connection of contact parameters, such as friction and contact stiffness, with computational parameters is analyzed. This study shows that the number of time samples per period is the most limiting parameter when intermittent contact occurs; whereas, in the absence of intermittent contact convergence, problems can be avoided with a reasonable number of time points. Poor discretization of the signal leads to a bad computation of Fourier coefficients and thus a lack of convergence. Sensitivity analysis shows that the samples per period depend on the contact parameters, especially normal stiffness. To ensure the solver robustness, it is important to set the computation parameters appropriately to ensure the convergence of the solver while avoiding unnecessary computation effort. Full article

The growing demand for low-frequency, broadband vibration and noise suppression technologies in next-generation mechanical equipment has become increasingly urgent. Effective negative mass locally resonant structures represent one of the most paradigmatic classes of acoustic metamaterials. Their unique elastic wave bandgaps enable efficient suppression of low-frequency vibrations, while inherent nonlinear effects provide significant potential for the design and tunability of these bandgaps. To achieve ultra-low-frequency and ultra-broadband vibration attenuation, this study employs Duffing oscillators exhibiting negative-stiffness characteristics as structural elements, establishing a bistable nonlinear acoustic-metamaterial mechanical model. Subsequently, based on the effective negative mass local resonance theory, the perturbation solution for the dispersion curves is derived using the perturbation method. Finally, the effects of mass ratio, stiffness ratio, and nonlinear term on the starting and cutoff frequencies of the bandgap are analyzed, and key geometric parameters influencing the design of ultra-low vibration reduction bandgaps are comprehensively investigated. Subsequently, the influence of external excitation amplitude and the nonlinear term on bandgap formation is analyzed using numerical computation methods. Finally, effective positive mass, negative mass, and zero-mass phenomena within distinct frequency ranges of the bandgap and passband are examined to validate the theoretically derived results. The findings demonstrate that, compared to a positive-stiffness system, the bandgap of the bistable nonlinear acoustic metamaterial incorporating negative-stiffness Duffing oscillators shifts to higher frequencies and widens by a factor of $\sqrt{2}$. The external excitation amplitude F changes the bandgap starting frequency and cutoff frequency. As F increases, the starting frequency rises while the cutoff frequency decreases, resulting in a narrowing of the bandgap width. Within the frequency range bounded by the bandgap starting frequency and cutoff frequency, the region between the resonance frequency and cutoff frequency corresponds to an effective negative mass state, whereas the region between the bandgap starting frequency and resonance frequency exhibits an effective positive mass state. Critically, the bandgap encompasses both effective positive mass and negative mass regions, wherein vibration propagation is suppressed. Concurrently, a zero-mass state emerges within this structure, with its frequency precisely coinciding with the bandgap cutoff frequency. This study provides a theoretical foundation and practical guidelines for designing nonlinear acoustic metamaterials targeting ultra-low-frequency and ultra-broadband vibration and noise mitigation. Full article

This study investigates the elastoplastic behavior of phenol formaldehyde/polyvinyl butyral matrix (70% PF/30% PVB) reinforced with Kevlar^® fibers through comprehensive in-plane tensile testing. Cyclic loading–unloading tests were conducted at a 100%/min strain rate using a universal testing system at room temperature on $\left(0_4\right)$, $\left({90}_4\right)$, and ${\left(\pm 45\right)}_s$ laminates. The experimental results revealed significant nonlinear hardening behavior beyond yield stress, accompanied by yarn stiffening effects during loading cycles. A novel elastoplastic constitutive model was developed, incorporating Hill’s yield criterion adapted for orthotropic materials and an isotropic hardening function that accounts for equivalent plastic strains and progressive yarn stiffening. Laminates with other stacking sequences were also tested and the accuracy of the predictions of the nonlinear behavior was assessed. In these laminates, delaminations took place and the model provided an overestimation of the stress–strain response. Since the model could not predict delamination onset and propagation, an adaptation of the model considering fully delaminated interfaces brought a lower bound of this response. Despite the limitations of the model, it can be used to provide reasonable limits to the stress–strain response of laminates accounting for plastic strains within plies. This study provides essential mechanical properties and constitutive relationships for designing Kevlar^® composite structures with tailored stiffness characteristics for impact-resistant applications. Full article

To meet the requirements of geometric nonlinear modeling and bending–torsion coupling analysis of long, flexible offshore blades, this paper develops a high-precision engineering simplified model based on the Absolute Nodal Coordinate Formulation (ANCF). The model considers nonlinear variations in linear density, stiffness, and aerodynamic center along the blade span and enables efficient computation of 3D nonlinear deformation using 1D beam elements. Material and structural function equations are established based on actual 2D airfoil sections, and the chord vector is obtained from leading and trailing edge coordinates to calculate the angle of attack and aerodynamic loads. Torsional stiffness data defined at the shear center is corrected to the mass center using the axis shift theorem, ensuring a unified principal axis model. The proposed model is employed to simulate the dynamic behavior of wind turbine blades under both shutdown and operating conditions, and the results are compared to those obtained from the commercial software Bladed. Under shutdown conditions, the blade tip deformation error in the y-direction remains within 5% when subjected only to gravity, and within 8% when wind loads are applied perpendicular to the rotor plane. Under operating conditions, although simplified aerodynamic calculations, structural nonlinearity, and material property deviations introduce greater discrepancies, the x-direction deformation error remains within 15% across different wind speeds. These results confirm that the model maintains reasonable accuracy in capturing blade deformation characteristics and can provide useful support for early-stage dynamic analysis. Full article

Accidental surface surcharge will generate additional load in the stratum, which then leads to unfavorable impacts on the underlying shield tunnel. This paper proposes a probabilistic analysis method to address this problem. In this framework, an improved soil–tunnel interaction model considering the nonlinearity of the subgrade is established at first, and the Newton–Raphson iterative solution algorithm is employed to acquire tunnel responses. Then, the random field models of the initial stiffness and the ultimate reaction of the subgrade are constructed to realize the spatial variability of soil properties. Finally, with the aid of the Monte Carlo Simulation method, the probabilistic analyses on tunnel responses are performed by combining the improved soil–tunnel interaction model and the random field model of subgrade parameters. The applicability and the superiority of the improved soil–tunnel interaction model are validated by a historical case from Shanghai Metro Line 9. The results prove that the traditional linear foundation model will overestimate the bearing capacity of the subgrade, thereby leading to overly optimistic assessments of surcharge-induced tunnel responses. This shortcoming could be addressed by the improved nonlinear soil–tunnel interaction model. The influences of spatial variability of soil properties on tunnel responses are nonnegligible. The stronger the uncertainties of subgrade parameters, in terms of the initial stiffness and the ultimate reaction concerned in this work, the higher the failure risk of the shield tunnel subjected to the surcharge. The failure modes of the tunnel subjected to the surcharge are controlled by the longitudinal curvature radius of the tunnel within the current assessment criteria, which means if this evaluation indicator can be restricted within the allowable value, then the opening of the circumferential joint and the longitudinal settlement can also meet the requirements. Compared with the influences of the uncertainty of the subgrade ultimate reaction, the spatial variability of the subgrade initial stiffness has greater influences on tunnel failure risk under the same conditions. An increase in the range of surcharge will raise the risk of tunnel failure, while the influence of tunnel burial depth is just the opposite. Full article

This article investigates the problem of bending failure in a rectilinear thin-walled rod consisting of a multimodular material exhibiting different elastic properties in tension and compression, with applications to the structural design of space satellites, unmanned aerial vehicles, aeronautical systems, and nano- and micro-class satellites. Nonlinear differential equations have been formulated to describe the propagation of the failure front under transverse loading. Formulas for determining the incubation period of the failure process have been derived, and the problem has been solved. Based on the developed model, new analytical expressions have been obtained for the displacement of the neutral axis, the stiffness of the rod, the distribution of maximum stresses, and the motion of the failure front. The influence of key parameters—such as the singularity coefficient of the damage nucleus and the ratio of the elastic moduli—on the service life and failure dynamics of the rod has been analyzed. Using the obtained results, the effect of the multimodular properties on the long-term strength of thin-walled rods under pure bending has been thoroughly studied. The analysis of the constructed curves shows that an increase in the “fading of memory” (memory-loss) parameter, which characterizes the material’s ability to quickly “forget” previous loadings and return to equilibrium, can, in certain cases, lead to a longer service life. Full article