Dynamic vibration absorbers (DVAs) can effectively suppress unwanted vibrations in primary structures. However, traditional DVAs struggle to adapt to variable operating requirements due to their fixed damping and susceptibility to wear. In this paper, a tunable DVA based on Electromagnetic Shunt Damping (EMSD) is proposed. By establishing a nonlinear electromechanical coupling model that considers spatial magnetic field distribution, the analytical relationship between the induced electromotive force (EMF) and the electromagnetic damping force is derived. Subsequently, the Harmonic Balance Method (HBM) is employed to determine the steady-state response of the system under harmonic excitation, and the accuracy of the theoretical model is verified through Runge-Kutta numerical simulations. Based on the principle of periodic average energy dissipation equivalence, an equivalent linearization tuning strategy is proposed to transform the nonlinear damping into linear equivalent damping. Furthermore, the Newton iteration method is employed to achieve optimal parameter matching for the damped main system, effectively overcoming the limitations of the traditional Den Hartog fixed-point theory. Finally, numerical studies are performed to evaluate the applicability and limitations of the proposed optimal design method for the EMSD-DVA, with particular attention given to the optimal design conditions under varying geometric parameters. This study provides theoretical guidance for the design and tuning of EMSD-DVA.

The quasi-zero-stiffness (QZS) harvester-absorber system (HAS) has proven effective in simultaneously suppressing low-frequency vibrations and harvesting energy. However, to expand its applicability in engineering applications, the performance of the QZS HAS requires further enhancement. To overcome this drawback, this paper puts forward an innovative QZS dual torsional HAS (DTHAS) in series to enhance the performance of suppressing low-frequency torsional vibrations while harvesting energy. The QZS characteristics are achieved by integrating four piezoelectric beams and two pairs of magnet tiles in parallel. First, theoretical formulations are developed to evaluate the restoring force and stiffness of piezoelectric beams and magnet tiles and validated through finite element simulations (FES). Based on the theoretical analysis, the QZS characteristics are realized through parametric design. Subsequently, the nonlinear electromechanical equations for the QZS DTHAS are formulated based on Kirchhoff's and Newton's laws. And solutions of electromechanical equations are derived by using the harmonic balance method (HBM) in combination with the pseudo arc-length continuation method. According to the theoretical solutions, a detailed analysis is conducted on the effects of critical mechanical parameters, including the torsional inertia ratios (mu 1, mu 2), damping ratios (41, 42), and frequency ratios ((11, (12). Finally, design optimization is performed using a multi-objective genetic algorithm (MOGA) integrated with the technique for order of preference by similarity to the ideal solution (TOPSIS). The optimized results exhibit the superior performance of the QZS DTHAS in both energy harvesting and vibration mitigation. Notably, with a dimensionless excitation amplitude of 0.8 and a vibration suppression weight of 0.9, the host oscillator's maximum resonance peak decreases by 64.5 %, whereas the maximum output power rises by 580 %.

The vibration energy, which is widely found in mechanical equipment and engineering structures, is typically low-frequency and broadband. The traditional approaches to energy harvesting are not effective in capturing low-frequency vibration energy across a wide frequency bandwidth. This paper introduces the negative-stiffness mechanism into triboelectric nanogenerator to propose a lantern-inspired bistable triboelectric nanogenerator (LBTENG). Its objective is to efficiently collect low-frequency vibration energy spanning a broad frequency range. The LBTENG's design concept and working principle are first explained, and its electromechanical coupling model is established. Then, its static characteristic, dynamic behavior, and electrical performance are investigated numerically. Next, the LBTENG prototype is fabricated, and the experimental platform is built to verify its output performance and demonstrate its applications in low-frequency vibration and human motion. In the final stage, an in-depth analysis is conducted on how the key parameters influence the performance of the LBTENG. The results show that the LBTENG can achieve interwell oscillation and efficiently harvest vibration energy in the 7-27 Hz frequency range. At 22 Hz and with a 10 M Omega load resistance, the LBTENG delivers a maximum output power of 2.08 mW. The LBTENG can power LED arrays, temperature and humidity sensors, and wearable smart devices under low-frequency vibration and human motion. Therefore, the LBTENG has potential in structural-health monitoring and human-health monitoring.

Low-frequency sound insulation is in urgent demand for engineering equipment. However, it is still a challenge to achieve sound insulation in low-frequency range. To resolve such an issue, this study proposes a quasi-zerostiffness (QZS) locally resonant acoustic metastructure (LRAM). The QZS LRAM is constructed by a sandwich plate compounded with the Helmholtz resonant cavity and the QZS locally resonator in parallel. An analytical model is developed using the space-harmonics method, to evaluate the sound transmission loss (STL) of the QZS LRAM under normal and diffuse sound field excitation, respectively. Both finite element simulations and experimental tests are conducted to validate the analytical model. The results show that the QZS LRAM breaks the mass law limit and achieves two distinct STL peaks in the low-frequency range from 50 Hz to 250 Hz, due to the combined effects of the Helmholtz resonant cavity and the QZS local resonator. Moreover, the geometric parameters can be tailored to tuning the sound insulation performance, demonstrating significant potential for applications of low-frequency sound insulation.

Multi-directional in-plane low-frequency vibration exerts a substantial impact on the precision of instruments. The in-plane stiffness is always reduced to isolate low-frequency vibration, while sacrificing the load-bearing capacity out of plane. To ad-dress such a challenge, this paper proposes an in-plane low-frequency (IPLF) vibration isolator with quasi-zero stiffness (QZS) supports. Firstly, the QZS support is designed using three-segment flexible beams, and its shape and geometry is optimized to fulfill quasi-zero stiffness. Subsequently, the QZS support structure is integrated with linear springs to construct the IPLF vibration isolator. Both the static and dynamic analyses of the IPLF vibration isolator are conducted to reveal its in-plane and out-of-plane stiffness properties and vibration isolation performance. Finally, a prototype of the IPLF vibration isolator is fabricated, and experiments are conducted to validate the design concept and theoretical predictions. The results demonstrate that the initial vibration isolation frequency of the IPLF vibration isolator is 8 Hz, which is far lower than 57 Hz exhibited by the isolator consisting of only linear springs with equivalent support stiffness. This significant frequency reduction indicates that the IPLF isolator exhibits desired low in-plane stiffness and superior loadbearing capability, and also highlights the unique advantage of the IPLF isolator in lowfrequency scenarios. Therefore, the IPLF vibration isolator integrates excellent low-frequency vibration isolation performance with sufficiently high load-bearing stiffness, thereby providing a viable solution for in-plane low-frequency vibration isolation.

Vibration systems with time-varying mass are prevalent in engineering practice, exemplified by rockets with fuel depletion, vehicles with changing mass, and systems with cable-hoisted payloads. However, progress has been constrained by the lack of an end-to-end approach capable of integrating modeling, closed-form analysis, numerically stable calculations, and isolation design. Focusing on a typical system involving rocket fuel combustion with linear mass depletion, we first derive the equations of motion from the momentum theorem. A parameter transformation, constructed via the method of undetermined coefficients, converts the time-varying differential equation into a standard Bessel equation, yielding a closed-form analytical solution. To achieve reliable numerical solutions, a strategy combining variable upper-limit integration with grid-search-optimized lower bounds is deployed to replace indefinite integrals, thereby overcoming non-integrable products of Bessel functions. Benchmark comparisons with harmonic excitations show excellent agreement, validating the formulation and solution scheme. Building on the closed-form response, an end-to-end vibration isolation workflow is established via transmissibility and isolation failure-time-threshold (FTT) metrics, allowing for the selection of stiffness based on the instantaneous frequency ratio throughout the mass variation process. The resulting framework provides a general analytical tool for linear differential equations with time-varying mass and a practical pathway for vibration isolation design in mass-varying structures, with special relevance to aerospace applications.

Self-powered wireless sensing systems face a fundamental challenge in effectively harvesting multidirectional low-frequency vibrations—a dominant feature in environmental mechanical energy spectra—while maintaining compact form factors. Conventional energy harvesters often exhibit limited adaptability to multidirectional excitations and poor efficiency at low frequencies. Inspired by the adaptive petal morphology of flowers, this work presents a flower-like bidirectional energy harvester (FLB-EH) incorporating quasi-zero stiffness (QZS) mechanisms for enhanced low-frequency vibration energy conversion. Through an integrated approach combining biomimetic design, nonlinear dynamics modeling, and systematic experimentation, this study deciphers the unique architecture of the FLB-EH and its role in bidirectional energy conversion, establishes a nonlinear electromechanical coupling model to quantify stiffness effects on power generation, and demonstrates a prototype achieving dual functionality as both a power source and self-powered vibration sensor. The synergistic integration of bioinspired petal morphology and QZS design, effectively resolving the two long-standing challenges in vibration energy harvesting systems: orientation adaptability and the difficulty of capturing low-frequency vibration energy.

Traditional energy harvesters struggle with inefficiency in low-frequency vibration energy harvesting and often feature bulky designs. To address these limitations, this study innovatively combines flexible beams and magnets to achieve negative stiffness, constructs a bistable structure, and proposes a compact bistable triboelectric energy harvester (CBTEH). This design minimizes mechanical connections while achieving bistability within a compact size. Leveraging the bistable mechanism, the CBTEH can transform small-amplitude and low-frequency vibrations into large-amplitude and high-velocity motion, thereby effectively converting low-frequency vibrations into electrical energy. The research begins with an introduction to the design concept and modeling of the CBTEH. Theoretical analyses of its mechanical behavior and electrical performance uncover the interaction between motion responses and electrical outputs. The impacts of key parameters on the CBTEH's performance are also explored, revealing mechanism to boost energy-harvesting performance. A series of experiments are carried out to confirm the theoretical model's precision, prove the prototype's durability, and show its capability to drive low-power electronic devices. Notably, the CBTEH generates 0.50 mW of power at 12 Hz and 60 M Omega, and the corresponding power density is 0.926 W/m2. Through optimal parameter selection, the CBTEH can effectively improve energy-harvesting performance. Its ability to power micro-sensors highlights its potential in intelligent sensing.

Achieving low-frequency vibration control in flywheel rotor systems under harsh aerospace conditions poses a substantial engineering challenge. This paper introduces a viscous quasi-zerostiffness (QZS) isolator with an exceptionally minimalist design. Notably, a broad QZS region can be attained simply by adjusting the length ratio and inclination angle of two straight beams, while the structure remains straightforward to manufacture and install. A prototype is manufactured using the viscoelastic material thermoplastic polyurethane (TPU), and its dynamic performance is experimentally investigated. Subsequently, a high-fidelity viscoelastic model is established and validated through dynamic experiments. This study also explores the nonlinear dynamic response characteristics of viscous QZS isolators under various excitation conditions. Results indicate that the viscoelastic properties of TPU suppress structural nonlinearity, contributing to the maintenance of low-frequency isolation performance in complex environments. Flywheel vibration isolation experiments verify that the proposed isolator achieves effective vibration isolation across wheel speeds ranging from 300 to 3300 RPM, with an average isolation of -15.72 dB and a peak isolation of -47.36 dB. Consequently, the design methodology and modeling framework presented in this study offer a viable technical pathway for enhancing the performance of flywheel vibration isolators.

Efficiently collecting low-frequency vibration energy has been a significant challenge in the aera of energy harvesting. In response to this issue, a pendulum-inspired bistable triboelectric vibration energy harvester (PBTVEH) is presented in this paper. Its ingenuity lies in the nonlinear mechanical design, which enables effective harvesting of low-frequency vibration energy. First, the design thought of the PBTVEH is described and its theoretical model is established. Next, by solving this model, the nonlinear dynamic features and energy harvesting performance of the PBTVEH are explored in depth to reveal the interaction between its dynamical and electrical behaviors. Besides, the impacts of parameters on the mechanical and electrical characteristics of the PBTVEH are examined. Finally, a prototype is developed, and the experimental platforms are constructed for performance testing and validation experiments, along with application demonstrations. The results indicate that during large-amplitude nonlinear dynamic responses (interwell oscillations), the PBTVEH delivers outstanding electrical performance, achieving a greatest power of 0.115mW at 8Hz. A large excitation amplitude, low damping coefficient, and appropriate design parameter (e.g., structural dimensions and stiffness) are conducive to improving the PBTVEH’s energy harvesting efficiency and widening its high-efficiency energy harvesting bandwidth. Capable of converting ambient vibration energy into electricity to power low-energy-consuming electronic devices and sensors, the PBTVEH holds considerable promise for structural health monitoring in civil infrastructures such as bridges.

Vibrational energy from human motion represents a pervasive and promising source of distributed power for wearable electronics, yet harnessing it efficiently remains a significant challenge due to its typically low-frequency, low-amplitude, and non-stationary characteristics, coupled with strict constraints on device integration. To address these limitations, this work proposes a wearable-oriented adaptive sliding-impact triboelectric nanogenerator with quasi-zero-stiffness (SIQZS-TENG). By synergistically integrating a quasi-zero-stiffness (QZS) mechanism with a hybrid sliding-impact operational mode, the device achieves exceptional sensitivity to weak and low-frequency excitations while substantially broadening the high-output frequency bandwidth. This unique combination effectively addresses the critical challenge of inefficient energy harvesting under off-resonance conditions, making it suitable for body-mounted applications. Guided by static analysis and experimental validation, key governing parameters are identified. Subsequently, comprehensive dynamic and electrical models are established, with theoretical predictions closely matching experimental results, enabling an in-depth analysis of frequency-domain response and parameter influence. Electrical characterization confirms that the impact mode enhances high-frequency energy harvesting, extending the operating bandwidth. Furthermore, the developed prototype successfully demonstrates its capability to power low-power electronic devices. This study highlights the substantial potential and wide application prospects of combining QZS structures with sliding-impact hybrid TENGs for efficient broadband vibrational energy harvesting from human motion in wearable systems.

This study systematically investigates the free vibration characteristics of sandwich beams/panels subjected to initial in-plane compressive loads, revealing a novel phenomenon of modal reordering. A new analytical model is developed to accurately characterize the dynamic behavior of sandwich structures under in-plane compressive loading and to determine their natural frequencies. Through dimensional analysis, the study identifies key dimensionless parameters governing the free vibration response, including the thickness ratio, stiffness ratio, and the ratio of compressive load to critical buckling load. The complex interplay among these parameters and their impact on the vibration behavior is subsequently explored in depth. A key finding of this study lies in uncovering the underlying mechanism of modal reordering. The results demonstrate that sandwich beams/panels with larger thickness ratios are more susceptible to mode transitions under compressive loading, while the stiffness ratio dictates the characteristics of higher-order modes prone to transition. As the compressive load increases, the frequency curves of these initially high-order modes progressively approach and eventually intersect with those of lowerorder modes, leading to a reordering of the modal sequence, wherein originally high-order modes shift to lower frequencies. However, this phenomenon has largely been overlooked in prior research, primarily due to limitations in experimental studies, where the selection of sandwich structures did not encompass the parameter range necessary to observe modal reordering. Finally, a comparative analysis with experimental data and finite element simulations further validates confirms the accuracy of the theoretical predictions and the existence of the modal reordering phenomenon.

This paper proposes a novel Weighted Delayed Visibility Graph (WDVG) method to enhance the noise robustness and data structural capture capability of visibility-based graph analysis for continuous dynamical systems. Unlike conventional visibility graph methods, which are sensitive to minor fluctuations in densely sampled signals and limited to binary visibility relationships, the WDVG introduces two key innovations: first, a "visibility margin" metric is proposed to quantify the strength of visibility between nodes. This approach goes beyond the traditional binary visibility relationship by capturing more detailed dynamical features. Second, a delayed visibility rule that ignores the influence of adjacent vertices when establishing links is proposed, thereby reducing noise interference. A parameter selection strategy based on autocorrelation analysis is also developed to systematically determine the optimal delay. Validation on the Rössler system shows that the proposed method achieves high robustness under noise contamination and can detect detailed dynamical structures. Furthermore, when applied to epileptic seizure classification based on the Temple University Hospital EEG Seizure Corpus, the WDVG achieves a state-of-the-art weighted F1 score of 0.982, confirming its effectiveness in real-world signal analysis.

Topological phases in phononic systems enable robust and unconventional control of wave propagation. However, realistic acoustic, elastic, and mechanical platforms are open, while loss or gain, active feedback, and spatiotemporal modulation provide tunable routes to non-hermiticity and nonreciprocity. Non-hermiticity reshapes complex-frequency spectra, eigenstates, and bulk-boundary correspondence beyond conventional Hermitian band theory, thereby giving rise to a wide range of unconventional wave phenomena. In this review, we provide a unified overview of topological non-Hermitian phononic crystals (PCs) and metamaterials from one to three dimensions, emphasizing physical mechanisms. In one-dimensional (1D) systems, non-Hermitian extensions of the Su–Schrieffer–Heeger (SSH) model reveal the emergence of the non-Hermitian skin effect (NHSE) and the breakdown of conventional Bloch band theory, necessitating the generalized Brillouin zone (GBZ) formalism and non-Bloch topological invariants. In two-dimensional (2D) systems, the interplay of non-hermiticity with lattice symmetry gives rise to exceptional degeneracies, anisotropic and higher order skin localization, and valley- and pseudospin-dependent transport. In three-dimensional (3D) systems, non-Hermitian Weyl phases support exceptional rings, complex Fermi arcs, and surface states governed by biorthogonal topology. Finally, we discuss non-hermiticity in space–time-modulated systems, non-Abelian exceptional-point braiding, and synthetic Landau-level physics as emerging directions. This review aims to offer a unified perspective on non-Hermitian topology in PCs and to stimulate further developments toward next-generation intelligent elastic metamaterials and topological wave devices.

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.

While the quasi-zero-stiffness (QZS) property has been widely incorporated into locally resonant (LR) metamaterials to facilitate the opening of low-frequency band gaps, the resulting gap widths typically remain narrow. In response to this limitation, here we introduce a new type of QZS LR metamaterial. In our design, the compression of resonators is systematically modulated by a quasiperiodic pattern, leading to the emergence of the well-known Hofstadter butterfly spectrum with a fractal network of frequency gaps. These fractal gaps, elucidated by the integrated density of states (IDS), exhibit topologically nontrivial characteristics and are traversed by edge-localized modes. Leveraging the advantageous fractal effect, we optimize the modulation parameters of the quasiperiodic pattern. The optimized quasiperiodic configuration demonstrates the ability to open a low-frequency and wide band gap—a significant increase (465%) in width compared to a periodic configuration with a compression of 5 mm. This work is anticipated to serve as a valuable guide for designing broad low-frequency band gaps, thus offering potential applications in vibration reduction and wave attenuation purposes.

The torsional vibration widely exists in shafting and human joint motion, however, it is a significant challenge to harvest low-frequency torsional vibration energy over a broad frequency range by utilizing traditional triboelectric nanogenerator (TENG). Herein, a compact torsional disc-triboelectric nanogenerator (TD-TENG) with magnetic tristable mechanism is proposed, which has a low potential barrier and can efficiently convert low-frequency torsional vibration energy into electrical energy over a broad frequency range. The design inspiration of the TDTENG is introduced firstly and then the working principle is presented. The theoretical model of the TD-TENG is established based on the Newton's second law of motion and the theory of the TENG. The mechanical and electrical performances of the TD-TENG are obtained by using numerical simulations. The theoretical output voltages are validated by the electrical responses carried out using Simulink circuit model. Subsequently, the influences of the key parameters on the performance of the TD-TENG are studied. The prototype is fabricated and the experiment is conducted to validate the accuracy of the theoretical model of the TD-TENG. Furthermore, the output performance of the TD-TENG under human motion is tested, and the TD-TENG is used to power the LEDs and drive the temperature and humidity sensors under human motion. The results show that the TD-TENG can achieve a maximum output power of 0.64 mW, and its energyharvesting bandwidth is four times wider than that of the bistable TENG. In addition, the TDTENG exhibits superior output performance under human motion, capable of powering the LEDs and driving the temperature and humidity sensors, thus holding potential application prospects in the field of human health monitoring.

Photovoltaic driven air conditioning (PVAC) systems provide significant opportunities for sustainable building energy management, but optimizing their operational parameters remains challenging. Current control methods often lack flexibility in adapting to dynamic environmental conditions and occupancy requirements. This study introduces a novel optimization framework integrating a large language model (LLM) with a rule-based adaptive control strategy for PVAC systems. A comprehensive simulation model, coupling detailed building thermal dynamics and air conditioning behavior, is developed and experimentally validated. The LLM is requested to determine optimal operational parameters. The LLM is systematically evaluated across varying scenarios, including initial settings for temperature setpoints, comfort ranges, hysteresis bands, and communication intervals. Results indicated that the LLM consistently converged on optimal control configurations, notably temperature setpoints around 24-25 degrees C, comfort ranges of approximately 1-2 degrees C, and hysteresis bands of about 0.3-0.5 degrees C, achieving high thermal comfort satisfaction and substantial energy cost savings. Furthermore, the model demonstrated excellent repeatability and operational stability across diverse climatic conditions. This research confirms the viability of integrating LLM-assisted adaptive control into PVAC systems. The LLM provides a promising opportunity for enhanced building energy efficiency and occupant comfort in practical applications.

Photovoltaic-driven Air Conditioner (PVAC) systems suffer from a dynamic mismatch between Photovoltaic (PV) generation and Air conditioner (AC) consumption power. To address this challenge and investigate the potential in achieving carbon neutrality, this study proposed an adaptive control method for a PVAC system. An experimental facility and a numerical model were developed. This paper evaluated the energy characteristic and decarbonization potential of the system using four evaluation indices: the Self-Satisfy Ratio, Self-Consumption Ratio, Net Present Value, and Levelized Cost of Carbon Abatement. The results showed that the adaptive control system could effectively adjust the compressor speed based on the difference between the PV generation and AC power. The dynamic performance of the adaptive control was investigated experimentally. The compressor operated at maximal speed when the PV generation was higher than AC maximal power. When the PV generation fluctuated, the compressor speed was adjusted accordingly. The simulation results presented that a proper configuration of PV and AC capacities could reach a fundamental energy match, while excess photovoltaic energy was supplied back to the grid, contributing to carbon neutrality. Carbon neutrality could be achieved by installing a large PV capacity. However, increasing the PV capacity could impact the performance of the PVAC system. The indoor temperature was lower with a larger PV capacity, and thus the COP of the AC was lower. The study proved the feasibility of the adaptive control strategy and the potential of carbon neutrality of PVAC systems.