The rapid advancement of wearable electronic devices has paved the way for a more intelligent and interconnected world. However, ensuring the sustainable energy supply for these devices remains a critical challenge, particularly for specialized populations and professionals in demanding environments, where a lack of power can pose life-threatening risks. Herein, we propose a mechanically intelligent biomechanical energy harvesting approach that adapts to complex human motion excitations, thereby improving the energy harvesting performance. Leveraging a mechanical intelligence mechanism, the energy harvester aligns with human physiological habits, selectively activating or deactivating as needed. The system can also adapt to excitations of varying directions, amplitudes, and frequencies. Furthermore, the string tension helps reduce the impact forces on the knee joint during foot strikes. A theoretical model for the biomechanical energy harvesting system is developed to describe its dynamic and electrical characteristics, and a prototype is fabricated and tested under diverse conditions. The experimental results are in good agreement with the simulation trends, validating the effectiveness of the theoretical model. A test subject running at 8 km/h for 90 seconds can successfully power a smartphone for 20 seconds, demonstrating the viability of self-powered applications. This mechanically intelligent biomechanical energy harvesting method holds a promising solution for the sustainable power supply for wearable electronic devices.
The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometric distortions, leading to a diminution in the predictive accuracy of the distorted similitude. To address this challenge, this study formulates a novel set of scaling laws, tailored to account for the intricate geometric distortions associated with elastic rings. The proposed scaling laws are formulated based on the intrinsic deformation characteristics of elastic rings, rather than the traditional systemic governing equations. Numerical and experimental cases are conducted to assess the efficacy and precision of the proposed scaling laws, and the obtained results are compared with those achieved by traditional methods. The outcomes demonstrate that the scaling laws put forth by this study significantly enhance the predictive capabilities for deformations of elastic rings.
Conventional rotary actuators mainly rely on electric or hydraulic/pneumatic motors to convert energy into mechanical motion, making them one of the most widely used actuation methods in industrial manufacturing, robotics, and automation control. However, these traditional actuators often suffer from limitations in operability and applicability due to their complex structures, bulky systems, high energy consumption, and severe mechanical wear. Liquid crystal elastomers (LCEs) have been increasingly used for programmable actuation applications, owing to their ability to undergo large, reversible, and anisotropic deformations in response to external stimuli. In this work, we propose a compact flexible rotary joint (FRJ) based on LCEs. To describe the thermo-mechanical coupled behaviors, a constitutive model is developed and further implemented for finite element analysis (FEA). Through combining experiments and simulations, we quantify the dynamic rotational behavior of the rotor rotating relative to the base driven by the induced strain of the FRJ under cyclic thermal stimuli. The proposed rotary joint features a simple structure, lightweight design, low energy consumption, and easy control. These characteristics endow it with significant potential for miniaturization and integration in the field of soft actuation and robotics.
This work presents a piezoelectric vibration energy harvester (PVEH) featuring a pre-shaped curved beam with clamped boundaries to investigate its energy harvesting mechanism based on the intrinsic snap-through behavior. Since the ability of the beam to exhibit meta-stable and bi-stable states strongly depends on its geometric parameters, the potential energies of models with varying thicknesses and initial apex heights are analyzed, followed by the derivations of electromechanical coupled equations for both meta-stable and bi-stable systems. The effects of the geometric parameters of the curved beam on the nonlinear dynamic behaviors and energy harvesting efficiencies under different external excitations are examined. Series of experiments are tested to validate the theoretical analyses. The research findings show that the separation between the potential wells in the bi-stable beam is mainly governed by the thickness and initial apex height, while the potential barrier height is affected by both the geometric and material properties. The optimal energy harvesting efficiencies in the transition analyses of meta-stable and bi-stable states are achieved by tuning specific geometric parameters. Design guidelines are provided to maximize the bandwidth and efficiency for energy harvesting applications.
This study investigates the dynamical behavior of two parallel fluid-conveying pipes by developing a non-planar dynamical model of the two pipes coupled with an intermediate spring. A systematic analysis is conducted to evaluate the effects of spring parameters on the non-planar vibration characteristics and buckling behaviors of the coupled system. The nonlinear governing equations are derived with Hamilton’s principle, subsequently discretized through Galerkin’s method, and finally numerically solved by the Runge-Kutta algorithm. Based on the linearized equations, an eigenvalue analysis is performed to obtain the coupled frequencies, modal shapes, and critical flow velocities for buckling instability. Quantitative assessments further elucidate the effects of the spring position and stiffness coefficient on the coupled frequencies and critical flow velocities. Nonlinear dynamic analyses reveal the evolution of buckling patterns and bifurcation behaviors between the lateral displacements of the two pipes and the flow velocity. Numerical results indicate that the intermediate spring increases the susceptibility to buckling instability in the out-of-plane direction compared with the in-plane direction. Furthermore, synchronized lateral displacements emerge in both pipes when the flow velocity of one pipe exceeds the critical threshold. This work is expected to provide a theoretical foundation for the stability assessment and vibration analysis in coupled fluid-conveying pipe systems.
A drag-free satellite is an important platform for space-borne gravitational wave (GW) observation. To achieve the high-precision control of a drag-free satellite in practical engineering, an accurate dynamic model is essential. This paper presents a nonlinear model of the electrostatic effect between a satellite and a test mass (TM), and designs a model predictive controller based on the drag-free satellite model with the nonlinear electrostatic effect. To determine the analytical form of the electrostatic effect, a comprehensive theoretical analysis is performed for gravitational reference sensors (GRSs). An electrostatic force and a torque are simulated with the displacement as a varying parameter through a commercial software. Then, the results are fitted to derive the nonlinear expressions of the electrostatic effect. The model predictive controllers based on the models with the nonlinear and linear electrostatic effects are designed in the capture mode. Finally, the control results are given to show the advantages of the nonlinear electrostatic effect.
In quadrupeds, the cervical and lumbar circuits work together to achieve the speed-dependent gait expression. While most studies have focused on how local lumbar circuits regulate limb coordination and gaits, relatively few studies are known about cervical circuits and even less about locomotor gaits. We use the previously published models by Danner et al. (DANNER, S. M., SHEVTSOVA, N. A., FRIGON, A., and RYBAK, I. A. Computational modeling of spinal circuits controlling limb coordination and gaits in quadrupeds. eLife, 6, e31050 (2017)) as a basis, and modify it by proposing an asymmetric organization of cervical and lumbar circuits. First, the model reproduces the typical speed-dependent gait expression in mice and more biologically appropriate locomotor parameters, including the gallop gait, locomotor frequencies, and limb coordination of the forelimbs. Then, the model replicates the locomotor features regulated by the M-current. The walk frequency increases with the M-current without affecting the interlimb coordination or gaits. Furthermore, the model reveals the interaction mechanism between the brainstem drive and ionic currents in regulating quadrupedal locomotion. Finally, the model demonstrates the dynamical properties of locomotor gaits. Trot and bound are identified as attractor gaits, walk as a semi-attractor gait, and gallop as a transitional gait, with predictable transitions between these gaits. The model suggests that cervical-lumbar circuits are asymmetrically recruited during quadrupedal locomotion, thereby providing new insights into the neural control of speed-dependent gait expression.
Multi-constrained pipes conveying fluid, such as aircraft hydraulic control pipes, are susceptible to resonance fatigue in harsh vibration environments, which may lead to system failure and even catastrophic accidents. In this study, a machine learning (ML)-assisted weak vibration design method under harsh environmental excitations is proposed. The dynamic model of a typical pipe is developed using the absolute nodal coordinate formulation (ANCF) to determine its vibrational characteristics. With the harsh vibration environments as the preserved frequency band (PFB), the safety design is defined by comparing the natural frequency with the PFB. By analyzing the safety design of pipes with different constraint parameters, the dataset of the absolute safety length and the absolute resonance length of the pipe is obtained. This dataset is then utilized to develop genetic programming (GP) algorithm-based ML models capable of producing explicit mathematical expressions of the pipe’s absolute safety length and absolute resonance length with the location, stiffness, and total number of retaining clips as design variables. The proposed ML models effectively bridge the dataset with the prediction results. Thus, the ML model is utilized to stagger the natural frequency, and the PFB is utilized to achieve the weak vibration design. The findings of the present study provide valuable insights into the practical application of weak vibration design.
Vibration energy harvesting presents a significant opportunity for powering wireless sensor networks and internet of things (IoT) devices, offering a sustainable alternative to traditional battery-based power sources. However, environmental vibrations are predominantly low-frequency, which presents a significant challenge to the efficient conversion of such energy. To address this challenge, this paper proposes a novel two-degree-of-freedom (2-DOF) energy harvester. The first layer of the harvester incorporates a piezoelectric composite beam (PCB) paired with permanent magnets to form a negative stiffness mechanism (NSM), which counteracts the stiffness of linear springs, thereby achieving quasi-zero stiffness (QZS) or bistable characteristics. The second layer integrates piezoelectric transduction units with triboelectric nanogenerator (TENG) units to further enhance the efficiency of low-frequency vibration energy conversion. By considering the modal characteristics of the PCB, this paper establishes the electromechanical coupling equations of the harvester from an energy perspective. The mechanical responses of the masses in both layers, as well as the electrical outputs of the PCB, are analytically solved. Furthermore, the effects of the system parameters on the efficiency of low-frequency vibration energy harvesting are thoroughly analyzed. This work provides a theoretical foundation for the development of self-powered IoT sensor nodes, enabling efficient energy harvesting from ambient low-frequency vibrations.
In order to obtain a lower frequency band gap, this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor. An improved cam-roller structure is designed in this meta-beam to achieve the softening nonlinear stiffness of the local oscillators. Firstly, based on Hamilton's principle and the Galerkin method, the control equations for the coupled system are established. The theoretical band gap boundary is then derived with the modal analysis method. The theoretical results reveal that the band gap of the meta-beam shifts towards lower frequencies due to the presence of a softening nonlinear factor, distinguishing it from both linear metamaterials and those with hardening nonlinear characteristics. Then, the vibration attenuation characteristics of a finite size meta-beam are investigated through numerical calculation, and are verified by the theoretical results. Furthermore, parameter studies indicate that the reasonable design of the local oscillator parameters based on lightweight principles helps to achieve further broadband and efficient vibration reduction in the low-frequency region. Finally, a prototype of the meta-beam is fabricated and assembled, and the formations of the low-frequency band gap and the amplitude-induced band gap phenomenon are verified through experiments.
Re-entrant honeycombs are widely used in safeguard structures due to their geometric simplicity and excellent energy absorption capacities. However, traditional re-entrant honeycombs exhibit insufficient stiffness and stability owing to the lack of internal support. This paper proposes a new hybrid honeycomb by integrating a chiral component inside the re-entrant honeycomb. Since Young's modulus is a key parameter to evaluate the energy absorption performance and stiffness, an analytical model is given to predict the effective Young's modulus of the proposed hybrid honeycomb. It is found that the optimal design scheme is to directly insert a circular ring inside the re-entrant honeycomb. The normalized specific energy absorption (SEA) of the hybrid honeycomb is 95% larger than that of the traditional re-entrant honeycomb. The normalized SEA first increases to a peak value and then decreases with the cell wall thickness. The optimal thickness of the cell wall for the maximum SEA is derived in terms of the geometric configuration of the unit cell. The normalized SEA first decreases to a valley value and then increases with the re-entrant angle. A longer horizontal cell wall results in a smaller normalized SEA. This paper provides a new design method for safeguard structures with high stiffness and energy absorption performance.
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.
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