Membrane-type acoustic metamaterials (MAMs) have recently received widespread attention due to their good low-frequency sound-transmission-loss (STL) performance. A fast prediction method for the STL of rectangular membranes loaded with masses of arbitrary shapes and surface density values is proposed as a semi-analytical model for calculating the STL of membrane-type acoustic metamaterials. Through conformal mapping theory, the mass blocks of arbitrary shapes were transformed into regular shapes, which simplified the calculation model of acoustic propagation loss prediction, and the prediction results were verified by finite element simulations. The results show that the change in mass surface density was closely related to the size and frequency distribution of STL. The influence of the mass center on the STL and characteristic frequency of the film metamaterial is discussed.

Product performance, function, cost, and the level of module generalization are all significantly influenced by product modular design, but different goods require different division indicators and techniques. The purpose of this study is to provide a set of appropriate modular division techniques for FDM 3D printers. This research offers an ecologically friendly module division index and uses module clustering as the module division principle in accordance with the current industrial development trend and the fundamental requirements of FDM 3D printer consumers in the current market. The K-means algorithm is used to use the Jaccard similarity coefficient as the metric of similarity of the DSM clustering process to realize the module division of the FDM 3D printer after studying the function–behavior–structure mapping model of the 3D printer. Additionally, the elbow method–cluster error variance and average contour coefficient evaluation systems were built, respectively, in order to verify the viability of the FDM 3D printer module division method and obtain the best module division results. By analyzing these two systems, it was discovered that when the FDM 3D printer was divided into three modules, the in-cluster error variance diagram obviously had an inflection point, and the average profile coefficient and other modular approaches that need to be adjusted to their respective goods can use this division method as a theoretical foundation and point of reference.

A gradient composite laminate that was composed of two-phase fibers, a shape memory alloy (SMA), and graphite was prepared to investigate modal performance and improve vibration behavior. The stress-strain relation of the single-layer composite plates was derived from Kirchhoff thin plate theory and the material constitutive of the SMA. A gradient distribution model and the eigenvalue equations of gradient composite laminates were developed. The influence of the fiber component content gradient distribution, pre-strain, the two-phase fiber volume fraction, and geometric parameters on the modal performance was analyzed. This study provides a method to avoid the structural resonance of composite laminates that are embedded with an SMA through the gradient distribution of two-phase fiber content that leads to the interaction of the material properties.

Honeycomb core sandwich plates are widely used as a lightweight, high-strength sound insulation material. However, they do not perform well in specific frequency bands. Acoustic metamaterials can break the law of mass in specific frequency bands and have high sound transmission loss (STL); however, the resonance frequency is difficult to regulate. To solve this problem, this paper first proposes an infinitely large metamaterial honeycomb core sandwich plate, which can generate newly tuned piezoelectric resonance frequencies, and we study its STL. The structure has piezoelectric patches arranged in sub-wavelength arrays with inductance shunting circuits that are elastically connected to both sides of the honeycomb core sandwich plate. The effective dynamic mass density and effective dynamic bending stiffness of the metamaterial plates were obtained using the effective medium (EM) method. A theoretical model for the numerical calculation of oblique STL and diffuse-field STL was established by the structural bending wave method. The finite element simulation method was used to verify that the metamaterial plates can generate three peaks at 1147 Hz, 1481 Hz and 1849 Hz in oblique or diffuse-field STL curves, which reached 57 dB, 86 dB and 63 dB, respectively, and are significantly better than the plate rigidly connected with piezoelectric sheets and the bare plate with the same mass. In order to better understand the characteristics of STL, the explicit functions of the resonance frequencies were derived. Key influencing factors were analyzed, and the regulation law of new piezoelectric resonance frequencies was clarified.