Designing, modeling, and analyzing novel nonlinear elastic elements for the nonlinear energy sink (NES) have long been an attractive research topic. Since gravity is difficult to overcome, previous NES research mainly focused on horizontal vibration suppression. This study proposes an origami-inspired NES. A stacked Miura-origami (SMO) structure, consisting of two Miura-ori sheets, is adopted to construct a nonlinear elastic element. By adjusting the initial angle and the connecting crease torsional stiffness, the quasi-zero stiffness (QZS) and load-bearing capacity can be customized to match the corresponding mass, establishing the vertical SMO-NES. The dynamic model of the SMO-NES coupled with a linear oscillator (LO) is derived for vibrations in the vertical direction. The approximate analytical solutions of the dynamic equation are obtained by the harmonic balance method (HBM), and the solutions are verified numerically. The parameter design principle of the SMO-NES is provided. Finally, the vibration reduction performance of the SMO-NES is studied. The results show that the proposed SMO-NES can overcome gravity and achieve quasi-zero nonlinear restoring force. Therefore, the SMO-NES has the ability of wide-frequency vibration reduction, and can effectively suppress vertical vibrations. By adjusting the initial angle and connecting the crease torsional stiffness of the SMO, the SMO-NES can be achieved with different loading weights, effectively suppressing the vibrations with different primary system masses and excitation amplitudes. In conclusion, with the help of popular origami structures, this study proposes a novel NES, and starts the research of combining origami and NES.
Metamaterials can control and manipulate acoustic/elastic waves on a subwavelength scale using cavities or additional components. However, the large cavity and weak stiffness components of traditional metamaterials may cause a conflict between vibroacoustic reduction and load-bearing capacity, and thus limit their application. Here, we propose a lightweight multifunctional metamaterial that can simultaneously achieve low-frequency sound insulation, broadband vibration reduction, and excellent load-bearing performance, named as vibroacoustic isolation and bearing metamaterial (VIBM). The advent of additive manufacturing technology provides a convenient and reliable method for the fabrication of VIBM samples. The results show that the compressive strength of the VIBM is as high as 9.71 MPa, which is nearly 87.81% higher than that of the conventional grid structure (CGS) under the same volume fraction. Moreover, the vibration and sound transmission are significantly reduced over a low and wide frequency range, which agrees well with the experimental data, and the reduction degree is obviously larger than that obtained by the CGS. The design strategy can effectively realize the key components of metamaterials and improve their application scenarios.
The metamaterial based on external meshing gears (MEG) is designed based on the principle of external meshing gear transmission. Based on the meshing transmission principle of external meshing gears and planetary gear trains, the internal and external gear rings are designed. Based on the internal and external gear rings, the metamaterial based on inner and outer planetary gear trains (MIP) is designed to study the shear modulus, Young's modulus, and amplitude-frequency characteristics of the metamaterial based on gears at different angles. The effects of the number of planetary gears on the physical characteristics of the MIP are studied. The results show that the MEG can be continuously adjusted by adjusting the shear modulus and Young's modulus due to its meshing characteristics. With the same number of gears, the adjustment range of the MIP is larger than the adjustment range of the MEG. When the number of planetary gears increases, the adjustment range of the MIP decreases. Moreover, when the metamaterial based on gears rotates, the harmonic response changes with the change of the angle.
A novel elastic metamaterial is proposed with the aim of achieving low-frequency broad bandgaps and bandgap regulation. The band structure of the proposed metamaterial is calculated based on the Floquet-Bloch theorem, and the boundary modes of each bandgap are analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the metamaterials with a low elastic modulus of ligaments can generate flexural wave bandgaps below 300 Hz. Multi-frequency vibrations can be suppressed through the selective manipulation of bandgaps. The dual-graded design of metamaterials that can significantly improve the bandgap width is proposed based on parametric studies. A new way that can regulate the bandgap is revealed by studying the graded elastic modulus in the substrate. The results demonstrate that the nonlinear gradient of the elastic modulus in the substrate offers better bandgap performance. Based on these analyses, the proposed elastic metamaterials can pave the way for multi-frequency vibration control, low-frequency bandgap broadening, and bandgap tuning.
Over the past decades, topological interface states have attracted significant attention in classical wave systems. Generally, research on the topological interface states of elastic waves is conducted in the lattices with symmetric elements. This paper proposes composite lattices with/without symmetric elements, and demonstrates the realization of tunable topological interface states of elastic waves via parametric systems. To quantize the topological characteristics of the bands, a modified Zak phase is defined to calculate the topological invariant by the eigenstates for the lattices with/without symmetric elements. The numerical results show that the tunable frequencies of topological interface states can be realized in composite lattices with/without symmetric elements through the modulation of the parametric excitation frequency. The tunable topological interface states can be introduced into the vibration energy harvesting to design efficient and steady energy harvesting systems.
Traditional methods for measuring single-cell mechanical characteristics face several challenges, including lengthy measurement times, low throughput, and a requirement for advanced technical skills. To overcome these challenges, a novel machine learning (ML) approach is implemented based on the convolutional neural networks (CNNs), aiming at predicting cells' elastic modulus and constitutive equations from their deformations while passing through micro-constriction channels. In the present study, the computational fluid dynamics technology is used to generate a dataset within the range of the cell elastic modulus, incorporating three widely-used constitutive models that characterize the cellular mechanical behavior, i.e., the Mooney-Rivlin (M-R), Neo-Hookean (N-H), and Kelvin-Voigt (K-V) models. Utilizing this dataset, a multi-input convolutional neural network (MI-CNN) algorithm is developed by incorporating cellular deformation data as well as the time and positional information. This approach accurately predicts the cell elastic modulus, with a coefficient of determination R2 of 0.999, a root mean square error of 0.218, and a mean absolute percentage error of 1.089%. The model consistently achieves high-precision predictions of the cellular elastic modulus with a maximum R2 of 0.99, even when the stochastic noise is added to the simulated data. One significant feature of the present model is that it has the ability to effectively classify the three types of constitutive equations we applied. The model accurately and reliably predicts single-cell mechanical properties, showcasing a robust ability to generalize. We demonstrate that incorporating deformation features at multiple time points can enhance the algorithm's accuracy and generalization. This algorithm presents a possibility for high-throughput, highly automated, real-time, and precise characterization of single-cell mechanical properties.
Broadband vibration attenuation is a challenging task in engineering since it is difficult to achieve low-frequency and broadband vibration control simultaneously. To solve this problem, this paper designs a piezoelectric meta-beam with unidirectional electric circuits, exhibiting promising broadband attenuation capabilities. An analytical model in a closed form for achieving the solution of unidirectional vibration transmission of the designed meta-beam is developed based on the state-space transfer function method. The method can analyze the forward and backward vibration transmission of the piezoelectric meta-beam in a unified manner, providing reliable dynamics solutions of the beam. The analytical results indicate that the meta-beam effectively reduces the unidirectional vibration across a broad low-frequency range, which is also verified by the solutions obtained from finite element analyses. The designed meta-beam and the proposed analytical method facilitate a comprehensive investigation into the distinctive unidirectional transmission behavior and superb broadband vibration attenuation performance.
A physics-informed neural network (PINN) is a powerful tool for solving differential equations in solid and fluid mechanics. However, it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives. In this paper, we introduce Chien's composite expansion method into PINNs, and propose a novel architecture for the PINNs, namely, the Chien-PINN (C-PINN) method. This novel PINN method is validated by singularly perturbed differential equations, and successfully solves the well-known thin plate bending problems. In particular, no cumbersome matching conditions are needed for the C-PINN method, compared with the previous studies based on matched asymptotic expansions.
To achieve stability optimization in low-frequency vibration control for precision instruments, this paper presents a quasi-zero stiffness (QZS) vibration isolator with adjustable nonlinear stiffness. Additionally, the stress-magnetism coupling model is established through meticulous theoretical derivation. The controllable QZS interval is constructed via parameter design and magnetic control, effectively segregating the high static stiffness bearing section from the QZS vibration isolation section. Furthermore, a displacement control scheme utilizing a magnetic force is proposed to regulate entry into the QZS working range for the vibration isolation platform. Experimental results demonstrate that the operation within this QZS region reduces the peak-to-peak acceleration signal by approximately 66.7% compared with the operation outside this region, thereby significantly improving the low frequency performance of the QZS vibration isolator.
Multilayered van der Waals (vdW) materials have attracted increasing interest because of the manipulability of their superior optical, electrical, thermal, and mechanical properties. A mass-spring model (MSM) for elastic wave propagation in multilayered vdW metamaterials is reported in this paper. Molecular dynamics (MD) simulations are adopted to simulate the propagation of elastic waves in multilayered vdW metamaterials. The results show that the graphene/MoS2 metamaterials have an elastic wave bandgap in the terahertz range. The MSM for the multilayered vdW metamaterials is proposed, and the numerical simulation results show that this model can well describe the dispersion and transmission characteristics of the multilayered vdW metamaterials. The MSM can predict elastic wave transmission characteristics in multilayered vdW metamaterials stacked with different two-dimensional (2D) materials. The results presented in this paper offer theoretical help for the vibration reduction of multilayered vdW semiconductors.
Eliminating the effects of gravity and designing nonlinear energy sinks (NESs) that suppress vibration in the vertical direction is a challenging task with numerous damping requirements. In this paper, the dynamic design of a vertical track nonlinear energy sink (VTNES) with zero linear stiffness in the vertical direction is proposed and realized for the first time. The motion differential equations of the VTNES coupled with a linear oscillator (LO) are established. With the strong nonlinearity considered of the VTNES, the steady-state response of the system is analyzed with the harmonic balance method (HBM), and the accuracy of the HBM is verified numerically. On this basis, the VTNES prototype is manufactured, and its nonlinear stiffness is identified. The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally. The results show that the VTNES has better damping effects when strong modulation responses (SMRs) occur. Moreover, even for small-amplitude vibration, the VTNES also has a good vibration suppression effect. To sum up, in order to suppress the vertical vibration, an NES is designed and developed, which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.
Second-generation high-temperature superconducting (HTS) conductors, specifically rare earth-barium-copper-oxide (REBCO) coated conductor (CC) tapes, are promising candidates for high-energy and high-field superconducting applications. With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components, the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields. Traditional numerical models include homogenized orthotropic models, which simplify overall field calculation but miss detailed multi-physics aspects, and full refinement (FR) ones that are thorough but computationally demanding. Herein, we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils. This approach combines a global homogenization (GH) scheme based on the homogenized electromagnetic T-A model, a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A, and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale. We then identify "dangerous regions" at the macroscopic scale and obtain finer details using a local refinement (LR) scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale. The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature, indicating that the present approach is accurate and efficient. The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.
The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors. The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified. The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated, and the four-dimensional (4D) nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method. The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed. The discussion focuses on investigating the effects of key parameters, e.g., excitation amplitude, damping coefficient, and detuning parameters, on the resonance responses. The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system. Furthermore, the significant motions under particular excitation conditions are visualized by bifurcation diagrams, time histories, phase portraits, three-dimensional (3D) phase portraits, and Poincare maps. Finally, the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell, yielding results that are qualitatively consistent with the theoretical results.
With its complex nonlinear dynamic behavior, the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression, and has attracted a lot of attention. In this paper, an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks (NESs) for the first time. The proposed asymmetric tristable NES (ATNES) is composed of a pair of oblique springs and a vertical spring. Then, the three stable states, symmetric and asymmetric, can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs. The governing equations of a linear oscillator (LO) coupled with the ATNES are derived. The approximate analytical solution to the coupled system is obtained by the harmonic balance method (HBM) and verified numerically. The vibration suppression efficiency of three types of ATNES is compared. The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states. In addition, compared with the symmetrical tristable NES (TNES), the ATNES can effectively control smaller structural vibrations. In other words, the ATNES can effectively solve the threshold problem of TNES failure to weak excitation. Therefore, this paper reveals the vibration reduction mechanism of the ATNES, and provides a pathway to expand the effective excitation amplitude range of the NES.
Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment, along with the advances in additive manufacturing (AM) technologies. In this work, a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes. The parametric model takes the basic unit of the triple periodic minimal surface (TPMS) lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies, which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity, and therefore is referred to as a TPMS-like plate lattice (TLPL). Furthermore, a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints. In this method, the genetic algorithm for the optimization is utilized for global search capability, and an artificial neural network (ANN) model for individual fitness estimation is integrated for high efficiency. A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting (SLM) fabricated samples. It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.
In this paper, a novel efficient energy absorber with free inversion of a metal foam-filled circular tube (MFFCT) is designed, and the axial compressive behavior of the MFFCT under free inversion is studied analytically and numerically. The theoretical analysis reveals that the energy is mainly dissipated through the radial bending of the metal circular tube, the circumferential expansion of the metal circular tube, and the metal filled-foam compression. The principle of energy conservation is used to derive the theoretical formula for the minimum compressive force of the MFFCT over free inversion under axial loading. Furthermore, the free inversion deformation characteristics of the MFFCT are analyzed numerically. The theoretical steady values are found to be in good agreement with the results of the finite element (FE) analysis. The effects of the average diameter of the metal tube, the wall thickness of the metal tube, and the filled-foam strength on the free inversion deformation of the MFFCT are considered. It is observed that in the steady deformation stage, the load-carrying and energy-absorbing capacities of the MFFCT increase with the increase in the average diameter of the metal tube, the wall thickness of the metal tube, or the filled-foam strength. The specific energy absorption (SEA) of free inversion of the MFFCT is significantly higher than that of the metal tube alone.
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