Sinusoidal Excitation Research Articles

Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force

This paper delves into the dynamical, chaotic, and stability aspects of the Duffing oscillator (DO) under sinusoidal external excitation, underscoring its relevance in various scientific and engineering applications. The DO, with its complex behavior, poses a significant challenge to our understanding. A unique perturbation technique, the multiple-scales (MS), is harnessed to tackle this challenge and enrich our knowledge. The analysis entails determining third-order expansions, exploring resonant cases, and factoring in the influence of viscous damping. The accuracy of the analytical solution is cross-validated with numerical results using the Runge–Kutta fourth-order (RK4). The paper also employs effective methods to assess the obtained results qualitatively. As a result, Visual figures, such as bifurcation diagrams and Lyapunov exponents’ spectra (LES), have been presented to illustrate diverse system motions and demonstrate Poincaré diagrams. Moreover, stability analysis has been investigated via resonance curves showing the stable and unstable regions. These aids facilitate our comprehension of the system’s complex behavior and its variations under different conditions. The results are elucidated through displayed curves, offering insights into the dynamics of the DO under sinusoidal excitation and damping effects. The influence of excitation and the quadratic parameter on bifurcation diagrams, LES, and Poincaré maps helps us understand the intricate behavior of nonlinear oscillatory systems, such as DO. The presented oscillator is a compelling example of elucidating the nonlinear behavior observed in numerous engineering and physics phenomena.

A fast-aware multi-target response prediction approach and its application in aeronautical engineering

Response prediction is a fundamental yet challenging task in aeronautical engineering, requiring an accurate selection of sensor positions correlated with the target responses to achieve precise predictions. Unfortunately, in large-scale structures, the rigorous selection of reliable sensor candidates for multi-target responses remains largely unexplored. In this paper, we propose a flexible and generalized framework for selecting the most relevant sensors to the multi-target response and predicting the target response, referred to as the Fast-aware Multi-Target Response Prediction (FMTRP) approach in the spirit of divide-and-conquer. Specifically, first, a multi-task learning module is designed to predict multi-point response tasks at the same time. Simultaneously, we meticulously devise adaptive mechanisms to facilitate loss-term reweighting and encourage prioritization of challenging tasks in multiple prediction tasks. Second, to ensure ease of interpretation, we introduce a hybrid penalty to select sensors at the group-sparsity, individual-sparsity and element-sparsity levels. Finally, due to the substantial number of candidate sensors posing a significant computational burden, we develop a more efficient search strategy and support computation to make the proposed approach applicable in practice, leading to substantial runtime improvements. Extensive experiments on aircraft standard model response datasets and large airliner test flight datasets validate the effectiveness of the proposed approach in identifying sensor locations and simultaneously predicting responses at multiple points. Compared to state-of-the-art methods, the proposed approach achieves an accuracy of over 99% in sinusoidal excitation and exhibits the shortest runtime (3.514 s).

Measurement and Modeling of Self-Directed Channel (SDC) Memristors: An Extensive Study

This study systematically addresses the challenge of accurately modeling memristors, focusing on four distinct types doped with tungsten, tin, chromium, and carbon, fabricated by Knowm Inc. A comprehensive characterization is performed by subjecting the devices to sinusoidal excitations with varying frequencies and amplitudes, followed by data averaging and high-frequency filtering. The resulting measurements are fitted using three prominent memristor models: VTEAM, MMS, and Yakopcic. Additional bespoke modifications are assessed. These models, typically formulated as coupled algebraic differential equations integrating electrical quantities (voltage and current) with internal state variables governing device dynamics, are optimized using two robust approaches: (1) interior-point optimization with gradient-based search, and (2) Nelder–Mead gradient-free optimization, both with box constraints applied. A thorough comparison and discussion of the optimized model parameters ensue, accompanied by an examination of the sensitivity to diverse frequency and amplitude ranges. The findings inform conclusions and provide a foundation for future refinements, underscoring the importance of multi-model evaluation and advanced optimization strategies in precise memristor modeling. The presented methodology offers a valuable framework for elucidating optimal modeling paradigms tailored to specific memristor architectures and operating regimes, ultimately enhancing their integration in emerging neuromorphic and computational applications.

A nonlinear and asymmetric monostable compliant ortho-planar spring piezoelectric vibrational energy harvester using a H-I structure

This paper proposes a compliant ortho-planar spring piezoelectric vibrational energy harvester (COPS-PVEH) using a H-I structure that exploits a nonlinearity and an asymmetric mono-stability to enhance the bandwidth of the device. The main structure is based on a double clamped beam (I-structure) coupled with four cantilever beams (H-structure) and an ortho-planar spring in the centre of the I-structure. Finite element analysis (FEA), analytical modelling, and experimentation were performed to analyse the dynamical and electrical behaviour of the harvester. The device was fabricated using polylactide (PLA). Six bimorph PZT-5H piezoelectric materials, electrically connected in parallel, were used as piezoelectric generators. The device was tested using an optimum load resistor of 90 kΩ under sinusoidal and sine sweep excitation in the gravity (vertical) direction. The pre-load (due to gravitation) causes a softening nonlinearity and an asymmetric mono-stability in the potential energy function. The results show that multiple peaks are observed in the output voltage of the harvester in the FEA, analytical modelling, and experimentation under harmonic excitation in the sub 15 Hz frequency range. Furthermore, analytical modelling and experimentation exhibit softening nonlinearity and chaotic behaviour, reaching a maximum amplitude power of 1.01 mW (at 8.3 Hz) and 1.07 mW (at 9.5 Hz) respectively under sine sweep excitation (amplitude of 0.6 g (g = 9.81 m/s2)). Experimentally, the harvester also generates an average power greater than 46 µW with a 6.8 Hz bandwidth under the same excitation. The softening nonlinearity and asymmetric mono-stability enhance the bandwidth of the harvester in the low frequency region where most broadband ambient vibrations are available in practical environments.

Smart whole-body vibration attenuation, cushion for heavy equipment seating: Model and simulation

Off-road mobile machine operators are exposed to whole-body vibration (WBV) which can result in adverse health effects. Seat suspensions are used to reduce WBV exposure, but typical passive seats cannot attenuate frequencies below 1.13 Hz. The proposed device is designed to minimize transmissibility from 0 to 20 Hz because this bandwidth contains the dominant frequency for most off-road vehicles. The semi-active smart device uses bang-bang control and is designed to be installed in place of the seat-pan cushion in OEM passive seats. Modelled as a two degree of freedom system, simulations were performed using a lumped mass model (ωn = 3 Hz; sinusoidal base excitation 0-20 Hz). Using a hexapod robot, a prototype reduced transmissibility compared to a passive OEM seat. The device was up to 5 times more effective than a passive seat in reducing vibration transmissibility. Simulations revealed that operator mass and seat stiffness variations have little effect on device WBV attenuation performance.

Highly dynamic force control for experimental vibration analysis with an electrodynamic shaker

A new control method aims at the precise high dynamic control of the force signal for experimental vibration analysis, which is generated by an electrodynamic shaker. A bending beam is used as a nonlinear test object. A design and a surrogate model of the test rig are shown and parameterized based on test rig measurements. The force control algorithm using input/output linearisation is described and implemented in Matlab/Simulink for simulative validation studies. Conclusions drawn from the mathematical description of the problem as well as simulation results show that the design of the contact between shaker and test object is crucial to achieve a high control bandwidth and at the same time reduce the energy consumption of the shaker. This leads to the practical application using a novel damping contact element. Finally, experimental test rig results are presented which show a closed loop bandwidth of at least 250 Hz for sinusoidal excitation signals.

Research on the Performance and Control Strategy of Electro-Hydraulic Servo System for Selective Hole Digging Tree Planter

Compared to agricultural environments, afforestation sites are more complex, often presenting issues such as undulating and uneven terrain. These conditions lead to instability in hole digging depth and plant spacing during continuous movement, and the hole shape may not meet expectations. Additionally, the hydraulic system exhibits slow response speed and long steady-state time, affecting the quality of sapling planting. To address these issues, this paper designs an intelligent planting control system for intermittent hole digging under continuous dynamic movement, based on a large tree planter. The focus is on studying the dynamic accuracy of the hole digging cylinder to resolve the instability of plant spacing and planting depth in actual planting processes. Firstly, a motion trajectory model of the intermittent hole digging mechanism is established to obtain the relationship between the displacement trajectory of the rotating cutter and the displacements of the floating cylinder and the hole digging cylinder. Secondly, a mathematical model of the electro-hydraulic servo system is established to control the dynamic accuracy of the hole digging operation. Finally, a Simulink simulation model of the system is established to analyze the performance indicators of the hydraulic system during operation using step and sinusoidal excitation signals. The test results show that the displacement of the hydraulic piston rod can ensure a linear extension trend within the range of 0 to 0.4 m, and the extension distance of the hole digging cylinder in the planting system is 0 to 0.35 m, ensuring linear change within this stroke. When the system’s extension command is 1 V, the actual output is 0.6 m, with a relative error of less than 10% compared to the simulation value, indicating that the control strategy can effectively improve the dynamic performance of the system. When the hydraulic system is in a steady-state extension state at 50 to 58.6 s, the relative error with the simulation value is 7.3%, meeting the “double ten indicators” requirement. The research results clearly verify the superior performance of the proposed intelligent control system, and the proposed control strategy has great potential in practical applications, promising to improve afforestation quality by stabilizing planting spacing and planting depth.

Achieving smooth motion in displacement amplification piezoelectric stick-slip actuator.

Traditional piezoelectric stick-slip actuators often suffer from significant backward motion phenomena, which greatly impact their output performance. To overcome this issue, a novel displacement amplification piezoelectric stick-slip actuator was meticulously designed. It integrates an L-shaped displacement amplification mechanism with a parallelogram-compliant mechanism. By dynamically adjusting the compressive force between the stator and the mover, this actuator effectively increases the single-step displacement, resulting in smooth and stable motion output. The design process involved thorough structural feasibility validation and core dimension optimization, utilizing Castigliano's second theorem and finite element simulation analysis. These efforts successfully yielded a substantial increase in the single-step output displacement. Experimental results demonstrate the actuator's capability to achieve smooth and stable motion output, even under challenging conditions, such as symmetric excitation signals and horizontal loading. Under specific operating parameters-preloading force of 3 N, input voltage of 100VP-P, and driving frequency of 625Hz sinusoidal excitation signal, the actuator achieves an impressive maximum driving speed of 25.22 mm/s, with a substantial maximum load capacity of 2.1 N. Compared to previous studies, the designed actuator exhibits superior adaptability to various excitation signals, offering significant potential for enhancing the performance and expanding the applications of piezoelectric stick-slip actuators.

Design and analysis of a piezoelectric energy harvesting shock absorber for light truck applications

Vehicle suspension vibration is a prevalent form of oscillation, with approximately 22.5 % of automobile energy dissipated through suspension-induced vibration. This phenomenon suggests that recovering the energy dissipated by the suspension system holds significant potential. This paper introduces a novel piezoelectric energy harvesting shock absorber (EHSA) based on non-contact magnetic force for light truck applications. The vibration of the vehicle suspension system is transformed into the rotation of a ball screw, enabling the one-way high-speed output of the rotor through a one-way bearing and planetary gear mechanism. Based on the non-contact magnetic force, the piezoelectric patches generate frequent oscillations, and a novel energy harvesting circuit is designed that efficiently converts the output of multiple piezoelectric units into usable electricity. The damping and energy harvesting characteristics of the EHSA with different external and internal variables are explored. Under sinusoidal excitation of 40 mm amplitude and 0.4 Hz frequency, the EHSA achieves a maximum output power of 7.51 W, with an average output power of 1.89 W. Furthermore, under random action, the EHSA can successfully illuminate 824 LED lights, enabling the temperature and humidity sensor to function normally. These findings indicate that the proposed EHSA can effectively harness vehicle suspension vibration to power onboard self-powered appliances while offering a new design idea for integrating vibration energy harvesters into vehicles.

Detecting the Sigma Phase in Duplex Stainless Steel by Magnetic Noise and First Harmonic Analysis.

Non-destructive electromagnetic tests based on magnetic noise analysis have been developed to study, among others, residual stress, heat treatment outcomes, and harmful microstructures in terms of toughness. When subjected to thermal cycles above 550 °C, duplex stainless steels form an extremely hard and chromium-rich constituent that, if it is superior to 5%, compromises the steel's corrosion resistance and toughness. In the present work, a study was carried out concerning the interaction of excitation waves with duplex stainless steel. Hence, by analyzing the magnetic noise and variations in the amplitude of the first harmonic of the excitation waves, the detection of the deleterious sigma phase in SAF 2205 steel is studied. To simplify the test, a Hall effect sensor replaced the pick-up coil placed on the opposite surface of the excitation coil. Sinusoidal excitation waves of 5 Hz and 25 Hz with amplitudes ranging from 0.25 V to 9 V were applied to samples with different amounts of the sigma phase, and the microstructures were characterized by scanning electron microscopy. The results show that the best testing condition consists of applying waves with amplitudes from 1 V to 2 V and using the first harmonic amplitude. Thus, the test proved effective for detecting the formation of the deleterious sigma phase and can follow the ability to absorb energy by impact and, thus, the material embrittlement.

Picking up railway track vibration energy using a novel doughnut-shaped piezoelectric energy harvester

Railway transportation is essential for modern infrastructure, and ensuring safety through real-time monitoring of track conditions is critical. However, providing cost-effective and stable power for sensors in remote areas remains a challenge. This paper presents a novel doughnut-shaped piezoelectric energy harvester designed to address this issue. Under a sinusoidal excitation of 50N and 110Hz, the harvester achieves an output power of 0.047 mW, which increases linearly with load. At optimal resistance (230 kΩ) and a load of 3 kN at 7Hz, the output voltage reaches 37.61V, resulting in an output power of 7.23 mW. In track vibration conditions, the harvester produces an output power of 207.67 mW, making it suitable for Internet of Things (IoT) applications, such as powering acceleration and speed sensors to monitor train operations and ensure track safety.

Design and evaluation of self-tuning optimal control for vibration suppression of magnetorheological semi-active suspension

The objective of this paper is to enhance the vibration damping capabilities of magnetorheological (MR) semi-active suspension by utilizing a self-tuning LQG control method. Firstly, to determine the mechanical model of MR damper using the hyperbolic tangent model, mechanical experiments were performed with a damping force test machine under various input excitations. Experimental and simulation data were compared to confirm the accuracy of the mechanical model for MR damper. The MR damper is then incorporated into the vehicle’s semi-active suspension system to create a quarter-car suspension model. In order to tackle the problems associated with low control accuracy and poor dynamic adjustment in traditional LQG controllers where the weighting matrix coefficients are difficult to determine, a self-tuning LQG controller based on gravity search algorithm (GSA-LQG) was designed. Finally, the designed controller performance was evaluated by the simulation and experimental results obtained from the random and sinusoidal excitation roads. Experimental data reveal that when subjected to GSA-LQG control, the suspension control performance is considerably enhanced compared to the passive control, PID control and conventional LQG control suspension. Based on these outcome, it can be concluded that the proposed algorithm is effective and the experimental platform is feasible.

Effect of anteroposterior vibration frequency on the risk of lumbar injury in seated individuals

Few studies investigate the impact of anterior-posterior excitation frequency on the time-domain vibrational response and injury risk of the lumbar spine in seated individuals. Firstly, this study utilised a previously developed finite element model of an upright seated human body on a rigid chair without a backrest to investigate the modes that affect the anterior-posterior vibrations of the seated body. Subsequently, transient dynamic analysis was employed to calculate the lumbar spine’s time-domain responses (displacement, stress, and pressure) and risk factors under anteroposterior sinusoidal excitation at varying frequencies (1–8 Hz). Modal analysis suggested the frequencies significantly affecting the lumbar spine’s vibration were notably at 4.7 Hz and 5.5 Hz. The transient analysis results and risk factor assessment indicated that the lumbar responses were most pronounced at 5 Hz. In addition, risk factor assessment showed that long-term exposure to 8 Hz vibration was associated with a greater risk of lumbar injury.

Explaining the correlation between subharmonic amplitude and ambient pressure for subharmonic-aided pressure estimation (SHAPE)

BackgroundSubharmonic aided pressure estimation (SHAPE) is an innovative non-invasive technique that leverages ultrasound subharmonic imaging to estimate pressure. This method exploits the “negative correlation between subharmonic amplitude and ambient pressure” observed in experimental settings. Despite extensive experimental validation and some promising results in clinical studies, the underlying mechanism of SHAPE remains incompletely understood. Although some studies have attempted to provide theoretical explanations, definitive conclusions have yet to be reached. In addition, theoretical investigations have mainly focused on the steady oscillation of bubbles under long pulse excitation, which contrasts with the short pulse excitation required for clinical SHAPE applications. An understanding of the SHAPE principle under short pulse excitation is needed. MethodsThe exponential elasticity model (EEM) was used to simulate Sonazoid bubbles, and a probe-to-probe acoustic propagation model was introduced to mimic a practical SHAPE scenario. The simulated acoustic signals in response to three-cycle sinusoidal pulse excitations were analyzed for spectral composition. The relationship between microbubble oscillation patterns and subharmonic characteristics was identified through detailed investigation. ResultsFor the excitation pulse of 2.5 MHz frequency and 350 kPa magnitude, bubbles larger than the resonance radius (2.29 μm) exhibited significant subharmonics in the magnitude spectrum, while bubbles smaller than the subharmonic resonance radius (3.85 μm) showed the activity of scattering subharmonic energy and the sensitivity to ambient pressure. The emergence of subharmonics when increasing excitation power was related to the increasing amplification of the bubble self-oscillation and the period-doubling features in the acoustically forced oscillation. The negative correlation between subharmonic amplitude and ambient pressure was attributed to the reduced self-oscillation caused by increasing ambient pressure and hence bubble size reduction. Microbubbles falling between 2 and 3 μm showed the desired subharmonic sensitivity to ambient pressure under the specified excitation conditions. ConclusionThe transient oscillatory behavior of microbubbles in response to short pulse excitation, characterized by a ringing down self-oscillation after the acoustic forcing effect has ceased, is crucial for understanding the subharmonic emergence and the observed negative correlation between subharmonic amplitude and ambient pressure. The proposed concepts of subharmonic resonance radius, subharmonic-significant bubbles, and subharmonic-active bubbles provide valuable insights into the diverse subharmonic behavior of microbubbles. The theoretical explanation of this negative correlation highlights the importance of using subharmonic-significant-and-active bubbles for SHAPE applications.

A multi-stable rotational energy harvester for arbitrary bi-directional horizontal excitation at ultra-low frequencies for self-powered sensing

A rotational multi-stable energy harvester has been presented in this paper for harnessing broadband ultra-low frequency vibrations. The novel design adopts a toroidal-shaped housing to contain a rolling sphere magnet which absorbs mechanical energy from bidirectional base excitations and performs continuous rotational movement to transfer the energy using electromagnetic transduction. Eight alternating tethering magnets are placed underneath its rolling path to induce multi-stable nonlinearity in the system, to capture low-frequency broadband vibrations. Electromagnetic transduction mechanism has been employed by mounting eight series connected coils aligned with the stable regions in the rolling path of the sphere magnet, aiming to achieve greater power generation due to optimized rate of change of magnetic flux. A theoretical model has been established to explore the multi-stable dynamics under varying low-frequency excitation up to 5 Hz and 3 g acceleration amplitudes. An experimental prototype has been fabricated and tested under low frequency excitation conditions. The harvester is capable of operating in intra-well, cross-well, and continuous rotation mode depending on the input excitation, and the validated physical device can generate a peak power of 5.78 mW with 1.4 Hz and 0.8 g sinusoidal base excitation when connected to a 405 Ω external load. The physical prototype is also employed as a part of a self-powered sensing node and it can power a temperature sensor to get readings every 13 s on average from human motion, successfully demonstrating its effectiveness in practical wireless sensing applications.

Pulsed MPI Relaxometry of Brownian and Néel Field-Dependent Relaxation in Superparamagnetic Magnetite Nanoparticles Confirm Theory and Simulations.

Superparamagnetic iron oxide nanoparticles (SPIOs) are used as tracers in Magnetic Particle Imaging (MPI). It is crucial to understand the magnetic properties of SPIOs for optimizing MPI imaging contrast, resolution, and sensitivity. Brownian and Néel relaxation theory developed in the early 1950s posits that relaxation times can vary with particle size, shell thickness, medium viscosity, and the applied field strength. Magnetic relaxation can soon provide a unique imaging capability, the ability to distinguish bound from unbound MPI tracers in vivo. Yet experimental validation of these theories has not been completed. In this paper, a novel method of pulsed magnetic field relaxometry is used to directly probe the relaxation behavior of superparamagnetic magnetite nanoparticles over a spectrum of magnetic field amplitudes, providing the first experimental validation of theoretical relaxation models. It is also shown that closed-form approximations generated in the early 1970s accurately match both data and numerical Fokker Planck computational models, which are computationally burdensome. This means researchers can trust these approximations for future modeling. All the findings can be translated to sinusoidal excitations used in conventional MPI scanningtrajectories.

Engineering model for seismic analysis of flexible rail‐bound structures with uplift

AbstractIn this paper, a highly simplified two‐dimensional three‐mass oscillator model is presented, which reproduces the typical behaviour of flexible structures of large mobile equipment transverse to the rail under seismic excitation. The typical rocking motion of the machine found in previous investigations, which is reproduced in the simplified analytical model, is taken into account together with the characteristic properties of the load‐bearing structure of the complete model. The three‐mass oscillator model is designed in such a way that it is able to provide information about uplift, rocking and tilting as a function of the model parameters and the excitation. A novel approach for the coefficient of restitution is derived, which takes into account the impact of wheel on rail and at the same time includes the stiffness of the subsoil. Also, a non‐linear ground stiffness could be captured with this approach, and thus the influence of the ground could be investigated. This approach is of generic character, so it may be useful to a wide range of other engineering fields than mobile equipment as well. Structural parameters are determined for a range of bucket wheel machines and stackers, producing rocking and tilting spectra under sinusoidal excitations and generating tilting delimitations under seismic excitations. Using a numerical beam‐mass model corresponding to the engineering model, the simplified multi‐mass model can be validated.

Frequency-Dependent Bouc–Wen Modeling of Magnetorheological Damper Using Harmonic Balance Approach

Magnetorheological dampers (MRDs) are of great interest in engineering due to their continuously adjustable damping characteristics. Accurate models are essential for optimizing MRDs and analyzing system dynamics. However, conventional methods widely overlook the impact of excitation frequency and amplitude. To address this issue, this work proposes a modified Bouc–Wen model that can be adapted to various excitation conditions. The model’s parameters depend on the current, excitation frequency, and amplitude. The mechanical characteristics of the MRD were analyzed by the tests. The parameters in the Bouc–Wen model were identified by combining the harmonic balance method and the genetic algorithm. The modified Bouc–Wen model was established by analyzing the variation of each parameter with current, excitation frequency, and amplitude. Finally, the agreement between the modified prediction model and the test results was verified under sinusoidal excitation of 80 mm and 1 Hz. The average relative errors were 3.87%, 2.82%, 2.45%, 2.19%, and 3.27% for current excitations of 0 A, 0.5 A, 1 A, 1.5 A, and 2.0 A, respectively. Since the MRD in this paper operates from 0.5 Hz to 2 Hz, the modified model was validated in the same range. Experiments demonstrate that the modified Bouc–Wen model efficiently and accurately describes the mechanical properties of the MRD under various excitation conditions.

Generation of uniform micro-textured structures by two-dimensional modulation fly-cutting

Micro-textured structures are widely applied in the fields of aerospace, military and medical etc. because of their unique properties such as self-cleaning, structural color and antibacterial effects. The traditional fast tool servo technology is believed to be an ideal machining method for the fabrication of micro-textured structures, however, its frequency response is limited by the varied linear velocity along the radial direction of workpieces, which make it difficult to machine uniform micro-textured structures. In this paper, a novel two-dimensional modulation fly-cutting system is developed to machine uniform micro-textured structures. In the machining system, the principal cutting motion is generated by a fly-cutting while a sinusoidal excitation motion as the assistive modulation is generated by a two-dimensional vibration platform. The two-dimensional vibration platform can apply excitation both in the x- and z-directions to the workpiece. By changing the excitation frequency, tool rotation radius and feed rate in X-axis, the corresponding optimal offset angle, length-width ratio and density of micro-textured structures can be obtained. Also, uniform concave-convex micro-textured structures are fabricated further by two-dimensional modulation of the principal cutting motion. According to the experimental results, uniform concave-convex micro-textured structures have good quality, which proves that the present machining method is effective. The present study provides an effective machining method for fabrication of micro-textured structures, and also serves as a reference for the fabrication of other similar micro-textured structures.

A study on maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolator.

This paper aims to study the maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolators (CMIs). The maglev force and stiffness of CMIs were analytically computed based on equivalent charge theory, and the transfer function of the system was conducted. The effects of magnet geometry parameters and air gap on the maglev force, stiffness, and vibration transmission characteristics of the CMI system were revealed through parametric analyses. With the increase in magnet length and width, the maximum value of maglev force increases, but the displacement range of near-zero stiffness, amplitude, and phase of the system gradually decrease. With the increase in magnet height, the displacement range of near-zero stiffness increases, while the variation in the amplitude and phase of the system has minimal impact. Meanwhile, in the Halbach array, the height variation of the magnet at different positions has different impacts on the magnetic force. As the air gap increases, the maximum value of maglev force decreases, but the amplitude and phase gradually increase, and the displacement range of near-zero stiffness first rises and then decreases. Finally, an experimental study was carried out to test the vibration attenuation characteristics of CMIs, in which sinusoidal excitation, hammer strike excitation, and random excitation were applied.