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In recent decades, quasi-zero stiffness (QZS) vibration isolation systems with nonlinear characteristics have aroused widespread attention and strong research interest due to their enormous potential in low-frequency vibration isolation. This work comprehensively reviews recent research on QZS vibration isolators with a focus on the principle, stru...
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Nowadays, thousands of studies have looked into the nonlinear vibration analysis of micro/nanostructures by solving nonlinear partial differential equations; however, there is almost no focus on the solution of the nonlinear boundary condition problems in the micro/nanoscale literature. This work presents the free vibration of a nonlocal functional...
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... Vibration isolation is still a recurrent problem in engineering; many mechanisms dedicated to passive vibration reduction (some of which can be tuned and/or optimized) are commercially available or under research [1][2][3]. ...
Even though the design of vibration isolators is well-established for many engineering applications, their efficiency in wide and multiple frequency ranges is still a challenge. In these cases, the use of Phononic-Based Vibration Isolators (PBVIs) may be advantageous as they present different Attenuation Regions (ARs) in which the elastic waves are strongly attenuated. Therefore, the present paper is devoted to the experimental evaluation, in terms of force transmissibility, of different types of supporting devices tested on a load mass and a motor of a Hermetic Compressor (HC). Those devices are the original Helical Coil Spring (HS) that equips the HC, the PBVI, and the Combined Structure (CS) which is composed of a PBVI combined in series with the HS. Results evidentiate the capability of the CSs to isolate vibrations, where the PBVI contributes with its ARs, thus operating as a “filter” in specific frequency ranges, while the HSs maintain the flexibility of the CSs, which is advantageous for impact-loads and/or transient-case scenarios. Hence, the capability, relevance and impact that these PBVIs present for force transmissibility reduction applications is highlighted here, which should capture the attention of and motivate the industry, e.g., producers of isolation systems, since it has wide-ranging engineering applications.
... This limitation arises from the interplay between the differing stiffness characteristics: positive stiffness elements, such as conventional springs, tend to exhibit a linear response, whereas negative stiffness mechanisms display fundamentally nonlinear behavior. However, the objective is not to achieve absolute zero stiffness across all displacements, since such a system would be inherently unstable [5,11]. Instead, QZS systems are designed to exploit their nonlinear nature, creating a state where zero stiffness is flanked by regions of positive stiffness, providing stability. ...
... The landscape of QZS system designs presents a variety of configurations [10,11], most of which exhibit resonance frequencies at or above 1 Hz, and this includes even the active systems. Despite the progression in QZS technology, these systems typically face limitations such as being restricted to small relative displacements and having a high degree of tuning specificity. ...
Modern aircraft designs with high aspect ratio wings pose challenges in accurately determining vibrational modes due to the increased flexibility of their wings. To accurately represent the large deformations occurring during flight in experimental modal analysis, actuators of low stiffness are needed, leading to the exploration of quasi-zero-stiffness vibration isolators. Such vibration isolators, combining positive and negative stiffness elements, lack the adaptability needed for varying wing load conditions. This study explores bellow-type soft pneumatic actuators, fabricated using 3D printing for iterative design and parameter studies, as a potential solution.
Initial experiments and simulations focused on the actuator stiffness for different geometric parameters and pressures. While simulations suggested that the occurrence of zero stiffness was primarily influenced by geometric parameters like the radius-to-height ratio, experimental results did not align with these findings, revealing discrepancies due to unmodeled boundary conditions. This misalignment highlighted the challenges in achieving the desired zero-stiffness characteristic in practical applications.
In conclusion, This study reveals that current bellow-type actuators fall short of the near-zero stiffness required for accurate modal analysis in flexible aircraft structures. Despite promising simulation results, experimental discrepancies highlight the need for improved designs and testing methods. Future research, potentially exploring rolling lobe actuators and refining 3D printing techniques, remains crucial in the ongoing quest for an ideal actuator in this domain.
... In other words, the vibration isolation of the QZS isolator is sensitive to load changes [5][6][7]. Thus, introducing active control into the QZS isolator [8][9][10] can not only compensate the load changes, but also improve the vibration isolation performance [11][12][13]. ...
Nonlinear vibraion isolation technique is widely employed for vibration suppression. An identification-control integrated method based on data-driven approaches is proposed for solving the optimal control law of a nonlinear time-continuous dynamic system. A dynamic surrogate model of the quasi-zero-stiffness (QZS) vibration isolation system is established by using an identification algorithm combined physical information neural network and Runge–Kutta method with the input and output signals of the original model. Two approximate optimal controllers are trained through the particle swarm optimization with ‘loser-out’ skill and the twin delayed deep deterministic policy gradient (TD3) in the sense of a self-defined objective function, where controllers communicate with the dynamic surrogate model during the training process. Then, the comprehensive performance in the condition of variable load and Gaussian noise excitation, and the displacement transmissibility are tested on the original model. The results show that the identified surrogate model can accurately reproduce the dynamic characteristics of the original model and the trained controllers are able to accomplish the control tasks successfully with a certain adaptability, further enhancing the low-frequency vibration isolation of the QZS isolator.
... As a result of study, it was observed that dual using of NSS provided better isolation performance. Ma et al. [22] conducted a comprehensive review study on the quasi-zero stiffness mechanism. Some studies were focused on the parameter's optimization of the NSS [23,24]. ...
In this study a narrow suspension seat with a negative stiffness structure (NSS) was investigated. First, this suspension seat's fundamental equations were detected, and then a simulation model was created using Altair Inspire software and validated by a literature study. Inspire software was used for the first time for suspension seats with NSS in the literature. Afterward, the case design was created via the Taguchi method to determine the parameter effects of NSS of the suspension seat. Signal-to-noise ratio (S/N) and ANOVA were used to examine simulation results, thus, parameter effects of NSS of suspension seat were examined comprehensively for the first time in the literature visa -vis the authors' literature search. Therefore, it was seen that the spring ratio is a much more effective parameter than the spring preload value for vibration isolation. In addition, optimal parameters of NSS were detected. Finally, with frequency response and road input results, it was observed that the suspension seat with NSS, which was created via optimal values, showed much better isolation performance than the other passive suspension seat.
... To optimize the vibration isolation band, engineers commonly adopt a strategy of reducing the stiffness of the supporting springs, thereby decreasing its resonant frequency [2]. Accordingly, the development of a vibration isolator with high static stiffness and low dynamic stiffness has become a prominent research focus [3]. A higher static stiffness results in an increased static load capacity, while a lower dynamic stiffness enhances the vibration isolation performance. ...
... With the study of single-degree-of-freedom (DOF) QZS systems, various types of QZS systems have been developed. Zhou and Ma et al. [3] provided a systematic summary of the research progress and future directions regarding QZS vibration isolators in recent years. The negative stiffness structure of QZS vibration isolators can be generally divided into three parts: the passive, semi-active, and active mechanisms. ...
... The negative stiffness structure of QZS vibration isolators can be generally divided into three parts: the passive, semi-active, and active mechanisms. Among these, the passive mechanism can be further classified into several types, including the mechanical springs, pre-buckled beams, geometrically nonlinear structures, magnetic structures, and composite structures [3]. Alabudzev et al. [4] theoretically studied different types of QZS isolators, including typical QZS systems with a combination of lateral and vertical springs and explored the feasibility of implementation of these systems. ...
In this work, a semi-active quasi-zero-stiffness (QZS) vibration isolation system with controllable lateral springs was proposed and its practical vibration isolation effectiveness was demonstrated through theoretical and experimental studies. A semi-active control strategy was developed to allow for the regulation of the lateral spring length to address the large resonant responses in the low-frequency range of the QZS system, while maintaining QZS benefits of increasing the control bandwidth with sufficiently low transmissibility and satisfactory static stiffness. The effect of the length of the lateral springs on the negative stiffness of the system under static conditions was investigated, and the stability of the system was analyzed to ensure the system’s stability during its operation. Moreover, by employing the semi-active control strategy with the resonance-detuning approach, the dynamic characteristics of the QZS system could be altered from linear to nonlinear through the highly-responsive adjustment of the lateral spring stiffness. As a result, the excitation of low-frequency resonance could be avoided while simultaneously obtaining an increase of control bandwidth with low transmissibility. Specifically, experimental results showed that the developed QZS vibration isolation system could achieve a reduction of transmissibility peaks by 9.68 dB and 15.59 dB, compared to the linear isolation system and the QZS vibration isolation system without control, respectively. The QZS vibration isolation system also achieved an overall reduction in vibration transmissibility with its low-frequency 0-dB bandwidth reduced by 11.8% (from 3.64 to 3.21 Hz) when compared to the linear system, demonstrating an improved vibration isolation effectiveness.
... While decreasing stiffness can extend the isolation frequency range, it negatively impacts stability and loading capability, and can also result in vibration isolation system failure. Researchers have addressed this inherent tradeoff between load bearing capability and isolation range by incorporating nonlinearity into the vibration system [4]. These nonlinearities reduce resonance and enable enhanced isolation performance at low frequencies. ...
The dynamic response of high-static-low-dynamic-stiffness (HSLDS) isolators often exhibits a pronounced rightward bend under large excitation and low damping, significantly reducing the effective isolation region. Aiming at such a problem, a novel isolator is proposed in this study by combining the HSLDS characteristic with the sliding mass inertia (SMI). The isolator comprises a negative stiffness structure and two specially introduced masses that can move freely in the horizontal direction. The working principle of the newly proposed isolator is introduced, and the nonlinear dynamic equation of motion of the corresponding system is derived using the Lagrange principle. A Taylor series expansion is then conducted to derive an approximated equation of motion, and the effect of the SMI and HSLDS are clarified through a parametric study in terms of the equivalent mass, equivalent stiffness force and resonance frequency. The harmonic balance method is employed to the approximated equation for the steady-state displacement transmissibility in the frequency domain under base excitation. The isolation performance and the effects of design parameters are evaluated, and validated through simulations in ADAMS along with comparisons to two counterparts. The results reveal that the coupling between the sliding mass and the HSLDS mechanism significantly shifts the transmissibility peak towards the lower left region. This coupling can completely eliminate the hardening in the dynamic response under low damping and high amplitude of excitations, and thus increase the stability of the overall system. Moreover, the anti-resonance induced by the sliding mass enhances the vibration isolation effect in the low-frequency region. These advantages imply potential application to vibration isolation in various engineering.
... The QZS feature can be realized by connecting the positive-stiffness element and the negative-stiffness one in parallel [18,19]. As a key part, the negative-stiffness element can be achieved by a variety of mechanisms, such as oblique springs [20][21][22], elastic beams [23][24][25], cam-roller-spring mechanisms [26][27][28], origami structures [29][30][31], X-shaped mechanisms [32,33], magnets [34][35][36] and bio-inspired structures [37,38]. ...
... NS can be physically achieved by pre-compressed spring mechanisms ( [116], [117]), convex-interface pendulum [118], magnetic mechanism [119], curved or buckled beams ( [120], [121]), bio-inspired structures ( [122], [123]), etc. The NS device is widely used on vibration isolators to achieve a high-static-low-dynamic stiffness property, known as quasi-zero stiffness ([124]- [128]), thus exhibiting an excellent vibration isolation performance. NS can also be combined with dashpots, forming Negative Stiffness Amplifying Dampers (NSADs) ( [115], [129]- [132]). ...
Conventionally, single-targeted H∞ or H2 optimization methods are adopted to determine the optimal parameters of different Dynamic Vibration Absorbers (DVAs) individually. A generic analytical framework for various DVAs considering a dual-target of H∞ and H2 norms is lacking. Addressing these issues, a hybrid analytical H∞-H2 optimization approach is proposed, leading to closed-form optimal solutions characterized by equal-height fixed points and conditional minimum H2-norms, combining the advantages of H∞ and H2 solutions. The proposed method is completely based on arbitrary filter coefficients of the targeted transfer function. Therefore, it can be generically applied for various DVAs. With the proposed method, the analytical optimal parameters of Negative-Stiffness Inerter-based Tuned Mass Systems (NS-ITMSs) are obtained based on an extended generic representation model considering multiple parameters. In extension, the method is illustratively applied on three complicated DVAs, including a Lever-type Inerter-based Vibration Absorber with Negative Stiffness (NS-LIVA) considering a leverage effect, a Piezoelectric Shunt Damping System (PSDS) considering an electro-mechanical coupling effect, and a Negative-Stiffness Tuned Viscous Mass Damper (NS-TVMD) for vibration isolator considering a transmissibility target. The closed-form solutions for these advanced DVAs are obtained for engineering reference. Furthermore, this method can be extended for more complicated energy dissipation or harvesting techniques.
... This nonlinear characteristic of low dynamic stiffness and high static stiffness can greatly reduce the "natural frequency" of the system while maintaining a high load bearing capacity, thereby extending the vibration isolation frequency band to low frequency region. The general principle for achieving the QZS property is to connect the positive stiffness element and the negative stiffness element in parallel with well-chosen system parameters [8], as shown in Fig. 1, and the key is to design an appropriate negative stiffness mechanism. The positive stiffness element plays the role of not only providing positive stiffness but also bearing the weight of the isolation object, and the negative stiffness element plays the role of counteracting the positive stiffness around the static equilibrium position, thus producing quasi-zero stiffness for the whole system. ...
Most of the engineering vibrations are harmful, due to many unfavorable consequences caused by them, such as structural damage, poor working accuracy, etc., making it necessary to implement vibration isolation measures. Traditional linear vibration isolation methods have significant deficiencies regarding isolating low-frequency vibrations, in which the stiffness of the isolation system becomes a dominant factor. The quasi-zero-stiffness (QZS) vibration isolation technology, developed in recent decades, can greatly reduce the dynamic stiffness without reducing the static stiffness and thus extend the vibration isolation frequency band to low frequency region. A variety of approaches for constructing QZS isolators have been proposed based on geometric nonlinearity, magnetic nonlinearity, deformable components and so on. With higher demands and more complex operating conditions, many improvement strategies have been proposed to further enhance the overall performance of QZS isolators from various aspects. To date, a small portion of theoretical achievements in QZS vibration isolation have been applied in engineering fields, showing great advantages over linear vibration isolation methods. In these contexts, a comprehensive review of the QZS vibration isolation technology is essential. This paper is devoted to summarize the main research progress of QZS vibration isolation in terms of designs, improvement strategies and applications, to provide a general overview of the QZS vibration isolation technology for researchers in related fields.
... One effective approach is passive energy dissipation, which involves using friction-based, impact-based, oil/waterbased, or air-based systems. Elastic materials are utilized in these systems to dissipate energy (Katsamakas et al. 2021;Ma et al. 2022). ...
This paper presents an experimental and simulation-based investigation into the force characteristics of rubber ball-based energy dissipaters. The study focuses on exploring the dimensional considerations in energy dissipation, where rubber balls serve as a medium to control vibrations. The paper scrutinizes the force properties through various approaches, including filling ratio, rotor speed, dissipater dimensions, and ball size. The results indicate that the size of the rubber balls significantly improves the performance of the energy dissipater, suggesting that larger balls enhance their effectiveness. Additionally, enhancing the filling ratio and the dimensions of the energy dissipater results in greater force. A numerical simulation technique based on the discrete element analysis method is employed to supplement the experimental findings for an exhaustive quantitative and qualitative analysis of the energy dissipater. The close correlation between the experimental and simulation results confirms the accuracy of the proposed model, especially for large-scale energy dissipation systems.
