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In this paper, a novel design concept for active auto-adaptive metamaterial (AAAMM) plates is proposed based on an active auto-adaptive (AAA) control strategy guided by the particle swarm optimization (PSO) technique. The AAAMM plates consist of an elastic base plate and two periodic arrays of piezoelectric patches. The periodic piezoelectric patches placed on the bottom plate surface act as sensors, while the other ones attached on the top plate surface act as actuators. A two-dimensional (2D) simplified metamaterial (MM) plate model is established by the Hamilton principle. The finite element method (FEM) with quadratic shape functions is adopted for numerically solving the 2D simplified MM plate model, which is validated by two more accurate but also much more complicated FEM models using three-dimensional (3D) piezoelectric and 3D elastic solid elements, and by its 2D counterpart model solved by the plane wave expansion (PWE) method. The conventional displacement, acceleration and velocity feedback control methods are introduced and analyzed. Then, a novel AAA control strategy based on combining the displacement and acceleration feedback control methods and guided by the PSO technique is developed. The main objective of the present paper aims at the vibration or flexural wave suppression and isolation of elastic plate structures based on an auto-adaptive control strategy, which has wide-range engineering applications. Numerical results will be presented and discussed to show that the proposed AAAMM plates can automatically and intelligently evolve different feedback control schemes to adapt to different stimulations on demand. Compared to the conventional MM plates, the proposed AAAMM plates exhibit improved and enhanced band-gap characteristics and suppression performance for flexural waves at frequencies inside and outside the band-gaps. [ABSTRACT FROM AUTHOR]

Pyramid-core lattice sandwich structures (PCLSSs) have been widely used in various engineering fields due to their high stiffness-to-density ratio. Although the advantages of such structures are obvious, the rather poor vibration isolation property restricts their applications. In the present work, we develop the chessboard-designed and gradient PCLSSs in order to improve their out-of-plane vibration isolation performance. The numerical results are obtained by the finite element method (FEM). Our results show that the chessboard-designed PCLSS has a lower and wider band-gap for the out-of-plane vibration than the classical PCLSS. The effects of the geometry and material parameters on the band-gap are analyzed. A gradient PCLSS with the core radius varying linearly is proposed. Compared to the classical PCLSS, the gradient PCLSS can expand the frequency range of the band-gaps significantly while maintains the high stiffness-to-density ratio. Moreover, the spatial gradient of the pyramid-core is utilized to realize the rainbow trapping and the nonreciprocal transmission of the elastic flexural waves. The novel meta-designed PCLSSs show potential applications where both a good vibration isolation and a high stiffness-to-density ratio are needed.0 [ABSTRACT FROM AUTHOR]

• A control method based on the non-simplified equations of motion of the lattice sandwich structures with considering the effects of the sensors and actuators is established. • The effects of active feedback control on the band-gaps of the pyramidal core lattice sandwich structures based on the non-simplified equations of motion are investigated. • The results show that the proposed simple control strategy is sufficiently accurate, highly efficient and can significantly expand the band-gaps. In this paper, we propose a simple active adaptive feedback (AAF) control strategy to enhance the vibration mitigation and isolation properties of the conventional pyramid-core lattice sandwich structures (PSSs) and the modified chessboard-designed pyramid-core lattice sandwich structures (CPSSs) via the lead zirconate titanate (PZT) ceramic patches. The proposed simple AAF control strategy is based on the active feedback (AF) control by relating the AF control parameters to the frequency. Firstly, the effects of the AF control parameters on the band structures are analyzed. Subsequently, the mathematical expressions of the frequency-dependent AAF control parameters are derived by the curve fitting technique. The results show that the proposed simple AAF control strategy is sufficiently accurate, highly efficient and can significantly expand the band-gaps compared to the conventional AF control, hence leading to improved vibration mitigation and isolation properties of the PSSs and CPSSs. The proposed simple AAF control strategy provides a simplified and generalized method to enhance the vibration mitigation and isolation properties of the lightweight lattice sandwich structures (LSSs) while maintaining their high stiffness-to-density ratio, which may offer various potential applications in engineering sciences. [ABSTRACT FROM AUTHOR]

Sandwich structures (SSs) are widely deployed in engineering applications, such as for the low-frequency vibration or acoustic mitigation and isolation. However, it is challenging to enhance their low-frequency vibration mitigation and isolation performance while maintaining their multi-functionalities, such as lightweight, high bending stiffness, and high impact absorption ability, etc. To achieve this objective, local resonators are introduced into a hollow-tube core lattice sandwich structure (HLSS) in this paper, which is referred to as the metamaterial sandwich structure (MMSS-1). The proposed MMSS-1 is composed of periodically distributed thin-walled hollow tubes with attached resonators as the core, and two thin cover-plates or face-sheets. The band structures and the corresponding eigenmodes of the unit-cell of the MMSS show that both the Bragg scattering and the local resonance band-gaps coexist in the proposed MMSS-1. The influences of the key geometrical and material parameters of the MMSS-1 on the band-gaps are analyzed in details. Then, the piezoelectric patches are attached to the top and bottom face-plate surfaces of the MMSS-1 and resonators to form the MMSS-2, and they are shunted via an active feedback control to build the MMSS-3. The effects of the displacement feedback control gains on the band-gaps of the MMSS-3 are studied. Based on the active displacement feedback control and differential evolution (DE) optimization algorithm, a self-sensing and self-actuating strategy is developed to lend the self-adaptive capability to the MMSS-3, which is referred to as the self-adaptive MMSS. The vibration or flexural wave propagation in the finite-sized self-adaptive MMSS is numerically simulated to demonstrate its outstanding ability for low-frequency vibration mitigation and isolation. It shows that the proposed self-adaptive MMSS can evolve different control parameters automatically to widen and merge Bragg scattering band-gaps and local resonance band-gaps without human intervention. In addition, the vibration attenuation inside the band-gaps is also enhanced. The proposed self-sensing and self-actuating strategy can improve the vibration mitigation and isolation performance of the HLSSs significantly in the low-frequency range. The proposed self-adaptive MMSS may pave a novel and feasible way for the design and applications of the HLSSs for the low-frequency vibration mitigation and isolation in civil engineering, mechanical engineering, and aerospace engineering etc. Moreover, the proposed self-adaptive strategy via self-sensing and self-actuating can be also applied to other types of the SSs for improving their vibration mitigation and isolation performance, and for the NVH (noise, vibration and harshness) of vehicles, high-end equipment and high-precision instruments. [ABSTRACT FROM AUTHOR]