This study introduces a versatile trapezoidal X-mechanism with three degrees-of-freedom (DOFs) to enable practical nonlinear manipulation using standard mechanical components. When integrated springs and rods are arranged in a trapezoidal configuration, the mechanism exhibits rich nonlinear characteristics along multiple directions and can be flexibly configured into trapezoidal, quadrilateral, or triangular forms, encompassing the known X-shaped variants in the literature. Compared with classic single-DOF X-structures, the proposed design offers superior versatility, compactness, and a self-contained spring-rod architecture without additional connections, while achieving comparable nonlinear dynamics. Analytical modeling, numerical simulations, and experimental validations demonstrate that the trapezoidal X-mechanism can be readily implemented with common spring-slider units, eliminating the need for custom rod fabrication. The structure enables tunable stiffness profiles, including positive, quasi-zero, zero, and negative stiffnesses across multiple directions, providing an expanded and adjustable quasi-zero stiffness (QZS) range. These features enhance the practicality and flexibility of engineering applications for noise, vibration, and stability control, offering a robust framework for designing nonlinear systems using widely available components.

This paper presents a lattice sandwich metamaterial beam with embedded active mass-rubber resonators, enabling automatic bandgap tuning in response to the excitation frequency. Unlike existing tunable metamaterials that rely on open-loop thermal regulation, the proposed closed-loop frequency-temperature feedback control strategy achieves adaptive bandgap tuning with only an ultra-low voltage and a simple structural design. With the energy method, the dispersion relations and bandgap edges are analytically derived for the sandwich metamaterial beam. Experimental measurements are conducted to quantify the temperature dependence of the rubber elastic modulus and the resonator natural frequencies, as well as the correlation between the applied voltage and rubber temperature. From these relationships, a frequency-to-voltage transfer function that enables the required tuning voltage for any target excitation frequency within the operational bandwidth is derived. A closed-loop frequency-temperature feedback control strategy is then proposed to achieve bandgap adaptation. Both theoretical analyses and experimental validations confirm that the proposed frequency-temperature feedback control strategy enables adaptive bandgap control at extremely low voltages. The proposed metamaterial beam and the control method exhibit advantages such as structural simplicity, low voltage requirements, and high control efficiency, which can be used in a wide range of engineering applications such as active vibration suppression, broadband acoustic absorbers, and tunable metamaterial filters.

Low-frequency vibration suppression under multidirectional excitations remains a major challenge in engineering systems. To address this issue, a novel bidirectional quasi-zero-stiffness (QZS) X-shaped linkage isolator incorporating torsional positive springs and a torsional magnetic negative stiffness (TMNS) mechanism connected in parallel is proposed. The parallel torsional positive-negative-stiffness strategy enables simultaneous QZS characteristics in both horizontal and vertical directions. An analytical model describing the coupled in-plane dynamics is established and validated through ADAMS simulations. The stability analysis shows that the stable potential well disappears under horizontal-torsional coupling when the vertical static equilibrium displacement exceeds a critical threshold. With the torsional motion constrained, the coupled dynamic behavior and transmissibility under bidirectional excitations are further investigated. Compared with previous structures, the proposed isolator achieves superior bidirectional low-frequency vibration-isolation performance. The experimental results agree well with the theoretical predictions, confirming the effectiveness of the proposed bidirectional vibration-isolation mechanism.

Particle damping (PD) attenuates structural vibration through momentum exchange and dissipative contacts in a confined granular bed. Unlike reviews organized mainly by devices, models, or applications, this review uses the granular motion regime to link contact mechanics, model choice, parameter effects, response metrics, and validation. The excitation direction and level, effective gravity, clearance, fill ratio, and cavity geometry determine access to impact-timed, dense friction-active, and dilute gas-like regimes, whose contact schedules govern dissipation and apparent dynamic mass. This review compares contact-resolved discrete element method (DEM) simulations, reduced-order and effective models, coupled particle-structure simulations, and data-refined surrogates within their calibration envelopes. It develops a preliminary screen for multi-axis impact-shear competition. It also clarifies when explicit non-spherical geometry can reduce or replace rolling resistance as a shape surrogate and when a residual rolling term requires independent evidence. It also specifies staged calibration and long-duty qualification for wear, restitution drift, fragmentation, and dust. It distinguishes the loss factor, apparent dynamic mass, and transmissibility and treats the equivalent damping as a derived descriptor. The reported optima are operating-point properties, not intrinsic granular-material constants. Key requirements are transferable regime maps, identifiable contact parameters, and multi-axis, reduced-gravity, and durability validation.

Cylindrical indentation has become a common method for determining Young’s modulus and the adhesion energy of materials. In this study, an analytical method is developed for incompressible elastic thin layers based on Kerr’s model. The contact pressure is solved by Betti’s reciprocal theorem, with assistance from a reference solution without adhesion. Explicit relations among the indentation force F, the depth δ, and the contact half-width a are derived up to the second order. Furthermore, the pull-off force is determined, and a simple method for extracting Young’s modulus using two characteristic points (the pull-off point and the zero-force point) is provided. Comparisons with numerical results demonstrate that the second-order solutions are considerably more accurate than the first-order solutions for the F-a and δ-a relations. Finally, the indentation experiments are conducted, demonstrating that the proposed formulae are capable of determining Young’s modulus and the adhesion energy based on the experimental data.

Internal uncertainties are inevitable in rotor systems, and may significantly affect their dynamic characteristics and render conventional deterministic optimization approaches inapplicable. Meanwhile, existing uncertainty optimization methods often entail prohibitive computational costs. In view of the above issues, in this paper, an efficient interval structural analysis method is proposed based on a surrogate model, and an uncertain multi-objective optimization framework is established. The framework improves the computational efficiency by providing a surrogate-based method for interval evaluation, which avoids the need for the nested optimization loop and reduces the reliance on the direct invocations of the computationally expensive high-fidelity model. The numerical examples illustrate the potential of the proposed method to balance the computational accuracy with efficiency. The subsequent application to the dynamic optimization of an uncertain rotor system demonstrates its engineering applicability and computational economy, offering a computationally efficient approach for robust design of such systems.

Lightweight structures can offer many enhanced mechanical characteristics, including load-bearing capability and impact resistance. However, achieving a high specific energy absorption (SEA) and a stable force level is challenging. Here, to overcome these limitations, a novel collapse-resistant structure of the metal foam-filled sandwich tube (MFFST) under free internal inversion is proposed. According to the energy conservation, an analytical model is established to predict the inversion force of the MFFST. The numerical simulations are conducted, and the analytical model captures the numerical results. In addition, the effects of the parameters on the free internal inversion of the MFFST are discussed in detail. It is demonstrated that increasing the yield stress {\sigma }_{\text{s}}, the average diameter D₂, and the total thickness T_{\text{all}}^{\prime } of the metal inner-outer tubes improves the mean crushing force (MCF) and SEA of the free internal inversion device almost linearly.

A space flexible manipulator (SFM) is a key development for on-orbit operations, yet even low-speed motions trigger significant structural vibrations in complex space environments. This paper proposes a vibration control method based on stiffness modulation of a flexible manipulator. The SFM is modeled as a hub-beam system with variable stiffness, and two typical modulation forms are considered: single stiffness modulation and periodic stiffness modulation. Single stiffness modulation exhibits excellent vibration suppression performance, for which an approximate analytical solution for the optimal modulation is derived. For the periodic form, resonance-like behaviors are observed, and the relationship between the variable-stiffness parameters and the resonance behaviors is identified. A Floquet-based stability analysis is adopted to theoretically determine the parametric resonance frequencies, revealing the underlying mechanism governing the observed resonance phenomena. Furthermore, the optimal periodic stiffness modulation that suppresses vibrations by avoiding resonance regions is presented. This study offers valuable insights into the design of SFMs with variable stiffness for effective vibration suppression.

The dynamic behaviors of a wing structure incorporating both nonlinear and viscoelastic damping under extreme random loads are investigated, and the unrealistic white Gaussian noise assumption, which is an issue that leads to inaccurate designs for aircraft wings, is addressed. The extreme random loads are quantified by the colored Lévy noise, which possesses inherent heavy-tailed characteristic and temporal correlation, thereby enhancing the realism of the modeled load environment. A multi-scale method is adopted to derive the theoretical amplitude-frequency characteristics of the corresponding deterministic case. Subsequently, the effects of nonlinear damping, viscoelastic damping, and colored Lévy noise on the wing’s dynamics are studied. The results highlight the potential application of nonlinear damping in the design of vibration isolations for aircraft wing structures. In contrast to linear viscous damping, nonlinear damping effectively suppresses the resonance peaks of the airfoil system, while exponential viscoelastic damping increases these resonance peaks. Within the bistable region of amplitude-frequency response curves, we uncover that both the noise intensity and the correlation time of the colored Lévy noise can induce undesirable stochastic transitions. We reveal that a lower stability index, a higher noise intensity, or a shorter correlation time reduces the mean first passage time (MFPT) and raises the residence probability (RP), thereby elevating the likelihood of transitions. Notably, the colored noise causes a larger MFPT and a smaller RP than the white noise without temporal correlation, indicating a lower propensity for triggering the unexpected transitions. Compared with the colored Gaussian noise, the colored Lévy noise reduces the MFPT and raises the RP, owing to the presence of large jumps. Our findings provide a theoretical foundation for the safety design of aircraft wing structures operated under extreme conditions, enabling the effective avoidance of structural redundancy and the improvement of design margins.

Quantile-based sequential optimization and reliability assessment can efficiently optimize the reliability-based design, and the key is to obtain the performance function quantile with respect to the target probability. Since high-end equipment usually requires an extremely low target failure probability and its performance function often includes a high-dimensional random input vector, efficient algorithms for this scenario are lacking. To address this issue, a stratified clustering dimension reduction importance sampling (DRIS) method based on the radial basis function neural network (RBFNN), called S-DRIS-RBFNN for short, is proposed. Its innovations are as follows. (i) A progressive iteration strategy is developed to efficiently search for the target quantile based on a set of intermediate quantiles. By evolutionarily filtering out the regions without the target quantile, this strategy avoids the heavy computational burden of directly exploring the rare regions with respect to the extremely low target failure probability. (ii) A stratified clustering algorithm is proposed for constructing the DRIS density (DR-ISD), and the importance sampling (IS) variance reduction involved can improve the efficiency of calibrating the failure probability at each intermediate quantile. (iii) A strategy of sharing DR-ISD sample information is designed to further enhance the efficiency of searching for the target quantile while incorporating an adaptive RBFNN to reduce the number of model evaluations. Examples indicate that, owing to the above innovations, the proposed S-DRIS-RBFNN is superior to the existing methods.

Local self-similar solutions provide a reduced description of chemically reacting high-enthalpy boundary layers, although finite-rate chemistry limits strict global similarity. At a fixed station, the converged local solution serves as a controlled framework for probing how transport and chemistry entries reshape boundary-layer profiles. More specifically, the five-species reacting balances are recast as a flux-based first-order boundary value problem (BVP) and solved with source-term continuation for finite-rate chemistry. The solution is verified through three complementary checks, from the classical compressible Blasius limit to a finite-rate reacting benchmark. The transport entries C, C_{\lambda }, and C_{D_i}, together with the stationwise finite-rate chemistry-source entry, are then scaled one at a time, and the reconverged changes are reported as local logarithmic sensitivities. For the selected baseline station, the density-weighted viscous and heat-conduction entries give the largest local first-order thermal responses with nearly equal and opposite signs, the species-diffusion entry mainly redistributes composition, and the chemistry-source entry changes the thermal and radical states while weakly affecting velocity. The same pattern holds at the second, hotter station, supporting the interpretation that this near cancellation is a structural feature of the transformed energy balance rather than an artifact of the chosen baseline. Therefore, the resulting sensitivities compare how individual transport and chemistry pathways act within the coupled local balances, while retaining the operator responses of the local BVP rather than independent material-property perturbations or global mechanism rankings.