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 σs, the average diameter D2, and the total thickness T′all of the metal inner-outer tubes improves the mean crushing force (MCF) and SEA of the free internal inversion device almost linearly.
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.
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.
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.
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.
