Metamaterials with local resonance show promising application prospects in low-frequency vibration attenuation. However, with the drawback of narrow band gap, such potential is greatly limited. In order to broaden the local resonant band gap, a semi-active graded magnetorheological elastomer (MRE) metamaterial sandwich beam (GMREMSB) with real-time tunable graded stiffness was proposed and investigated in this study. For theoretical calculation, a mass-spring model was established for the GMREMSB. Then the calculated band gap and transmissibility using Timoshenko beam theory and spectral element method were compared. An experimental test was also conducted for verification. The results show that the bandwidth of the proposed GMREMSB can be widened by the graded stiffness arranged in ascending order. The experimental band gap of the GMREMSB under the graded current of 0.0–0.5–1.0 A is 6.4 Hz wider than the band gap of the periodic structure with the single current of 0.0 A and is 5.0 Hz wider than that of 1.0 A. The growth rate reaches 15.06% and 11.39%, respectively.

Incremental sheet metal forming characterized as increased flexibility and local plastic deformation is well suitable for low-production-run manufacturing and a new sample trial production of complex shapes. Thickness thinning is still an obstacle to the application of incremental forming. In this study, a novel mathematical algorithm based on a non-uniform rational B-spline (NURBS) surface was proposed and implemented which focuses on predicting and calculating the final thickness for arbitrary parts in incremental forming. In order to evaluate the validity of the proposed model, the finite element simulation and forming experiments of three kinds of parts, such as truncated cones, truncated pyramids and ellipsoid parts, were conducted. The thickness of theoretical prediction was compared with that of finite element simulation and experiment, and good agreements were obtained. The results show that the proposed model and the method are effective and robust for predicting the thickness of the formed parts in incremental sheet metal forming.

Acoustic metamaterials are capable of generating bandgaps at specific frequency ranges, which makes them have good applications in the field of vibration isolation. The bandgaps can be further broadened with active control, nonlinear components and graded structures, such as: controllable stiffness by magnetorheological elastomer (MRE) and graded stiffness. However, the current approaches to reducing the bandgaps have limitations. Both the reduction in structural stiffness and the increase in mass will reduce the overall stability of the acoustic metamaterial. In this research, a novel inerter-based acoustic metamaterial MRE isolator (IAM-MREI) was designed and prototyped to lower the bandgap. Inerters can generate a large equivalent mass with very light weight. Moreover, it is discovered that elements containing quadratic frequency terms are added to the dispersion matrix of the IAM-MREI due to the frequency-independent force applied to the resonators, which is generated by the inerters. By this way, the bandgap calculated by this dispersion matrix is greatly lowered and broadened, which cannot be achieved only with extra equivalent mass. The effects of the inerters on the overall performance of the IAM-MREI was thoroughly investigated and validated both theoretically and experimentally. The evaluation experiments confirmed that the IAM-MREI possesses a low-frequency bandgap and can provide great vibration isolation performance.

To address the issues of excessive sheet metal thinning and geometric deviation in single point incremental forming (SPIF), this paper proposed a bi-objective process parameter optimization framework for Al1060 sheet based on a multilayer perceptron (MLP) surrogate model and an improved multi-objective grey wolf optimization (IMOGWO) algorithm. Finite element simulations based on ABAQUS were conducted to generate a dataset considering variations in tool radius, initial sheet thickness, tool path strategy, step depth and forming angle. The trained MLP was used as the objective function in the optimization process to enable the rapid prediction of forming quality. The IMOGWO algorithm, enhanced by the Spm chaotic mapping initialization, an improved convergence coefficient updating mechanism and associative learning mechanism, was then employed to efficiently search for Pareto optimal solutions. For a truncated conical component case, optimal parameter sets were selected from the Pareto front via the entropy-weighted TOPSIS method for order preference by similarity to an ideal solution. Experimental verification showed close agreement with the simulated results, with relative errors of only 0.58% for the thinning rate and 3.10% for the geometric deviation. This validation demonstrates the feasibility and potential of the proposed method and its practical potential for improving the quality of SPIF forming.