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In order to achieve low frequency vibration and noise reduction, researchers have found and explored many types of metamaterial structures. Based on this, an innovative multiphase metamaterial structure composed of hard materials and soft materials is proposed in this paper. According to Bloch's theorem, the band gap characteristics of the proposed structure are calculated using the finite element method, and the formation mechanism of the band gap is analyzed. In addition, the effects of the stiffness and density of the two materials on the band gap are studied in detail. Then, the phase velocity, group velocity and wave propagation direction are calculated according to a certain frequency of the specific dispersion curve, and the important information of wave propagation in the structure is obtained. Finally, according to the transmission characteristics of vibration in a finite periodic structure, it is verified that the existence of band gap can inhibit the vibration transmission, and it is further clarified that the proposed structure has a good performance in the design of low-frequency band gaps with large amplitude. [ABSTRACT FROM AUTHOR]

The suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch's theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure's two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure's excellent low-frequency vibration suppression capability. [ABSTRACT FROM AUTHOR]

This paper provides an extension to previous work on end-effector control of flexible space manipulators. Those works considered the use of a special output called the µ-tip rate for feedback control of desired end-effector trajectories with simultaneous vibration control. Implementation of this special output requires measurement of end-effector position or the use of flexible forward kinematics to determine it. For the latter, one requires measurements of the joint angles and flexible coordinates. The second of these is difficult to measure in space scenarios, so this paper looks at the use of an estimation scheme to approximate it and use it in a task-space control law. Multiple simulations are conducted to investigate the use of these approximated elastic coordinates in robustly controlling a one-link and two-link flexible manipulator with a payload mass. The error between desired and actual trajectory is calculated, and the results are juxtaposed with results from a joint-space feedback scheme. There is an emphasis on comparing the estimated elastic coordinates with the actual simulated coordinates. Using the estimated elastic coordinates to determine the end-effector location via forward kinematics, yielded similar results to when the actual elastic coordinates were used. Overall, the estimation equation used is shown to provide reasonable end-effector tracking results with the end-effector being able to track various types of trajectories. [ABSTRACT FROM AUTHOR]

In this study, we achieved energy localization and amplification of flexural vibrations by utilizing the defect mode of plate-attachable locally resonant metamaterials, thereby realizing compact and low-frequency vibration energy suppression and energy harvesting with enhanced output performance. We designed a cantilever-based metamaterial unit cell to induce local resonance inside a periodic supercell structure and form a bandgap within the targeted low-frequency range of 300–450 Hz. Subsequently, a defect area was created by removing some unit cells to break the periodicity inside the metamaterial, which led to the isolation and localization of the vibration energy. This localized vibration energy was simultaneously converted into electrical energy by a piezoelectric energy harvester coupled with a metamaterial inside the defect area. Consequently, a substantially enhanced energy harvesting output power was achieved at 360 Hz, which was 43-times higher than that of a bare plate without metamaterials. The proposed local resonant metamaterial offers a useful and multifunctional platform with the capability of vibration energy isolation and harvesting, while exhibiting easy handling via attachable designs that can be tailored in the low-frequency regime. Highlights: • Compact multifunctional vibration isolation-energy harvesting metastructures based on a low-frequency defect bandgap. • Enhanced harvesting power by a factor of 43 over a wide frequency range of 310-380 Hz • Easily mass-produced metamaterial unit cell via a laser-cutting process. • Multifunctionality, i.e., vibration isolation and harvesting, proved by a carefully-designed experiment. [ABSTRACT FROM AUTHOR]

This article studies the vibrational behavior of composite conical-cylindrical shells (CCSs) with functionally graded coatings (FGCs) in thermal environments using the first-order shear deformation theory. Firstly, the equivalent material parameters, fundamental frequency, and resonant displacement responses of the CCSs with FGCs are derived using the mixture principle, complex modulus method, and transfer function approach. Then, detailed thermal vibration tests are performed on CCS structures with and without coatings to assess the reliability of the proposed model, revealing that the current model accurately forecasts the thermal vibration behavior of the CCSs with FGCs. Finally, the effect of key parameters on the vibrational properties of the CCSs with FGCs is investigated. The results demonstrate that increasing the functionally graded index, coating thickness, and Young's modulus ratio can greatly enhance the vibration suppression capability of the structure. [ABSTRACT FROM AUTHOR]

This article presents a hybrid model to predict the positions of the ball screw drive system of machine tool and then modify the trajectory through constructing a pre-compensation method to reduce servo errors in machine motion axes. To achieve this objective, a flexible control model is initially developed to characterize the ball screw drive system, and by leveraging this model, a high-bandwidth controller is constructed, with its physical representation, i.e. the state-space equation, being derived. Subsequently, a data-driven hybrid model is proposed to predict the positions of the ball screw drive system concerning the next multiple time steps from the current time step, and then the predicted positions associated with these steps are utilized as initial conditions to adjust and compensate for the physical model's prediction errors corresponding to these multiple time steps. As a result, a compensated trajectory with high tracking accuracy is generated. Finally, experiments confirm that the proposed prediction method offers superior prediction accuracy and enhanced adaptability, and the pre-compensated trajectory leads to reduced tracking errors. [Display omitted] • A hybrid model is constructed to pre-compensate servo error in the ball screw system. • A high bandwidth controller is designed by incorporating the feedback of the velocity. • A compensated trajectory with high tracking accuracy is generated. • The method can achieve a nice tracking accuracy and improve the bandwidth. • A series of comparative experiments validate the proposed method. [ABSTRACT FROM AUTHOR]

Novel structures in vehicle control-by-wire chassis have re-emphasized the problem of wheel shimmy. Proper suppression of shimmy in the independent wheel subsystems would significantly improve the performance of the steer-by-wire control. In this paper, a wheel shimmy suppression method using a nonlinear energy sink (NES) is proposed. Compared with traditional methods of increasing steering damping, the NES seldom interferes with the designed steering dynamics of the vehicle due to its particularly small mass and volume, thus reserving availability for in-service or after-designed vehicles. By installing the NES in the wheel frame, a single towed wheel model with NES is constructed. Although the NES has almost no effect on the linear stability characteristics, an excellent effect on suppressing vibration amplitudes is explored where over 90% oscillation amplitude of shimmy is mitigated by the NES within a wide range of reasonable parameters. Parameter optimization for the NES global dynamics is performed to handle the speed-dependent nature of shimmy, and the result highlights its effectiveness and parameter robustness. Integration of the single-wheel model into the full vehicle with independent steering structures summarizes that the NES could be a favorable way to both suppress the existing shimmy phenomenon and control the coupled lateral oscillations of the vehicle body. [ABSTRACT FROM AUTHOR]

Nonlinear elastic metamaterials are attracting increasing attention owing their unusual properties of wave manipulation. However, the robustness of these benefits under varying amplitude should be increased and the challenge lies in the design. Here, we demonstrate a robust design strategy of nonlinear metamaterial via combining collision and damping. The damping will not interfere but enhance the nonlinear effects for broadband vibration reduction. The design presents low-frequency, broadband, efficient vibration reduction under varying amplitude. The effect can be activated by a small input amplitude. The performance remains high in a large amplitude range, i.e., high robustness is achieved. This property is systematically demonstrated with simulations and experiments on a nonlinear metamaterial beam. This article can offer an effective method to realize robust vibration suppression. [ABSTRACT FROM AUTHOR]

The shell composed of large-scale parts is the essential component of mechanical structures in the aerospace, shipping, and railway industries. These workpieces are characterized by thin walls and weak rigidity, thus requiring an effective technology for high-performance machining. Accordingly, an embedded locally resonant metamaterial with double resonators is proposed and combined with the magnetic follow-up support technology to attenuate the vibration of thin-walled parts for the first time. The band structures and parametric adjustment laws are systematically investigated and validated by analytical calculation and finite element method, which proves the proposed model is broadband, lightweight, and flexible in low frequencies. Its characteristics, as well as the relatively simple structure, are unique advantages for thin-walled structure milling. Finally, mirror milling experiments have been performed to assess the slave module with the proposed substructure. From the results, the root mean square amplitude of the thin-walled workpiece with the combined device decreases by nearly 9%, which means that the performance has been improved by the combined device. Furthermore, this work provides an integrated and efficient solution for vibration suppression in thin-walled parts milling, which extends locally resonant metamaterials to practical engineering fields and helps to improve the status quo of mirror milling from the perspective of metamaterials. [ABSTRACT FROM AUTHOR]

This study investigates the vibration energy flow transmission behavior of laminated composite plate structures coupled with a line hinge. The time-averaged vibration energy transfer is determined using the substructure-based power flow analysis (SPFA) method. The effects of the fiber orientation, boundary conditions and the position of the coupling hinge on the vibration transmission path and its level are examined. It is demonstrated that the fiber orientations can be used to modify substantially the power flow transmission path and locations of energy sinks. Enhancement of vibration suppression of the coupled structure can be achieved by tailor designing the fiber angles. [ABSTRACT FROM AUTHOR]

An innovative structural system of magnetic-hydraulic double-floating journal bearing is designed to improve the ability to resist offset loads. By considering the magnetic force to the water-lubricated journal bearing and the magnetic structure design, a force model of the innovative bearing is proposed. The magnetic force and water film force for the bearing are simulated by comparing the load-carry capacity of only water film force. Experimental results showed the load-carry capacity and stability test of the innovative bearing. The design of innovative bearing with the upper suction and lower magnetic repulsion based on the Halbach array can provide a larger supporting magnetic force. The axially non-uniform magnetic structure deployment can manipulate the changes of the magnetic force in the axial direction to hold the offset load. The test found that by comparing the traditional water-lubricated bearing, the bearing has a certain vibration suppression ability in the vertical direction. Under the test speed, the bearing stiffness hardly changes with the change of the speed, which also shows a slightly decreasing trend with the increase of the excitation frequency. [ABSTRACT FROM AUTHOR]

This study delves into the nonlinear dynamics of metamaterials, exploring the dual objective of enhancing power output and achieving vibration suppression through piezoelectric energy harvesters (PEHs). Our approach is structured into a sequence of increasingly complex models that bridge mechanical resonators with their electromechanical counterparts. We initiate with (1) modeling mechanical resonators, incorporating nonlinear behaviors that are often overlooked in the linear domain. This lays the groundwork for understanding the fundamental mechanisms of vibration within metamaterials. Subsequently, we progress to (2) electromechanical resonators, where piezoelectric components are integrated, revealing a richer dynamic landscape that is influenced by the interplay of mechanical and electrical energies. The latter sections of our investigation introduce and examine (3) mechanical and (4) electromechanical internally coupled resonators. These segments unveil the role of internal couplings in steering the metamaterial's energy harvesting capabilities and its resilience to vibrational disturbances. Through meticulous simulations and analysis, the research brings to light the significant influence of specific PEH nonlinear parameters on the system's efficiency, offering insights for the optimization of PEHs in practical applications. [ABSTRACT FROM AUTHOR]

Nonlinear energy sink (NES) is a passive control device that can absorb a wide band, and it has the advantages of lightweight and strong robustness, which can play a very important role in vibration suppression. In this paper, the dynamic modeling and research on vibration suppression of NES with linear damping and geometrically nonlinear damping are carried out, and the effects of NES parameters on the vibration reduction effect are investigated. For the study of dynamic bifurcation, the slowly varying equation of the system is obtained by using the complex variable average method, and the effects of NES parameters on the number of fixed points and stability of the system are analyzed according to the slowly varying equation. At the same time, the effects of excitation amplitude and excitation frequency on the system response amplitude are also investigated. For the study of strongly modulated response (SMR), the slowly varying equation is further analyzed by using the multi-scale method, and the conditions for SMR phenomenon in the system are described by slow invariant manifold and phase portraits. By studying the slow manifold, the detuned parameter interval for the system to appear SMR is derived. For vibration reduction performance analysis, the effects of NES parameters on vibration reduction performance are analyzed from the perspectives of energy and amplitude-frequency response, and the influence laws of various parameters on vibration suppression are revealed. The vibration reduction performance of different NES is compared and analyzed, and it is concluded that the new NES proposed in this paper has better vibration reduction performance. [ABSTRACT FROM AUTHOR]

Vibration problems have become one of the most important factors affecting robot performance. To this end, a terminal residual vibration suppression method based on joint trajectory optimization is proposed to improve the accuracy and stability of robot motion. Firstly, based on the characteristics of the friction nonlinearity due to joint coupling and physical feasibility of dynamic parameters, a semidefinite programming method is used to identify dynamic parameters with actual physical meaning, thereby obtaining an accurate dynamic model. Then, based on the result of the residual vibration time domain analysis, a joint trajectory optimization model with the goal of minimizing joint tracking error is established. The Chebyshev collocation method is used to discretize the optimization model. The dynamic model is used as the optimization constraint, and barycentric interpolation is used to obtain the optimized joint motion trajectory. Finally, industrial robot experiments prove that the vibration suppression method proposed in this article can reduce the maximum acceleration amplitude of residual vibration by 62% and the vibration duration by 71%. Compared with the input shaping method, the method proposed in this paper can reduce the terminal residual vibration more effectively and ensure the consistency of running time and trajectory. [ABSTRACT FROM AUTHOR]

Phononic crystals based on lattice structures provide important wave dispersion characteristics as band structures, showing excellent compatibility with additive manufacturing. Although the lattice structures have shown the potential for vibration suppression, a design guideline to control the frequency range of the bandgap has not been well established. This paper studies the dispersion characteristics of plane wave propagation in lattice-based mechanical metamaterials to realize effective vibration suppression for potential aerospace applications. Triangular and hexagonal periodic lattice structures are mainly studied in this paper. The influence of different geometric parameters on the bandgap characteristics is investigated. A finite element approach with Floquet–Bloch's principles is implemented to effectively evaluate the dispersion characteristics of waves in lattice structures, which is validated numerically and experimentally with a 3D-printed lattice plate. Based on numerical studies with the developed analysis framework, the influences of the geometric parameters of lattice plate structures on dispersion characteristics can mainly be categorized into three patterns: change in specific branches related to in-plane or out-of-plane vibrations, upward/downward shift in frequency range, and drastic change in dispersion characteristics. The results obtained from the study provide insight into the design of band structures to realize vibration suppression at specific frequencies for engineering applications. [ABSTRACT FROM AUTHOR]

Abstract In this study, we achieved energy localization and amplification of flexural vibrations by utilizing the defect mode of plate-attachable locally resonant metamaterials, thereby realizing compact and low-frequency vibration energy suppression and energy harvesting with enhanced output performance. We designed a cantilever-based metamaterial unit cell to induce local resonance inside a periodic supercell structure and form a bandgap within the targeted low-frequency range of 300–450 Hz. Subsequently, a defect area was created by removing some unit cells to break the periodicity inside the metamaterial, which led to the isolation and localization of the vibration energy. This localized vibration energy was simultaneously converted into electrical energy by a piezoelectric energy harvester coupled with a metamaterial inside the defect area. Consequently, a substantially enhanced energy harvesting output power was achieved at 360 Hz, which was 43-times higher than that of a bare plate without metamaterials. The proposed local resonant metamaterial offers a useful and multifunctional platform with the capability of vibration energy isolation and harvesting, while exhibiting easy handling via attachable designs that can be tailored in the low-frequency regime.

Purpose – This paper aims to design an active shock absorber scheme for use in conjunction with a passive shock absorber to suppress the horizontal vibration of elevator cars in a smaller range and shorter time. The developed active shock absorber will also improve the safety and comfort of passengers driving in ultra-high-speed elevators. Design/methodology/approach – A six-degree of freedom dynamic model is established according to the position and condition of the car. Then the active shock absorber and disturbance compensation-based adaptive control scheme are designed and simulated in MATLAB/Simulink. The results are analysed and compared with the traditional shock absorber. Findings – The results show that, compared with traditional spring-based passive damping systems, the designed active shock absorber can reduce vibration displacement by 60%, peak acceleration by 50% and oscillation time by 2/3 and is more robust to different spring stiffness, damping coefficient and load. Originality/value – The developed active shock absorber and its control algorithm can significantly reduce vibration amplitude and converged time. It can also adjust the damping strength according to the actual load of the elevator car, which is more suitable for high-speed elevators.

This paper presents a novel Flexnertia metastructure concept to perform vibration suppression through coupling rotational inertia to structural flexural motion. Theoretical analysis and experimental test of the proposed metastructure with emphasis on dissipating structural flexural motion is exhibited, showing vibration control performance. The experimental and numerical results are in good agreement, both confirming that the average overall response of the metastructure is significantly reduced. The attenuation becomes most pronounced in the low-frequency range where structures tend to suffer most due to high response around the regime of the first flexural modes. [ABSTRACT FROM AUTHOR]

In order to achieve low-frequency vibration and noise reduction, this paper proposes an innovative structure based on the four-ligament chiral structure. The band gap characteristics and the principle of band gap generation are numerically analyzed by using the finite element method. By optimizing the proposed structure, the band gap is obviously transferred to the low frequency. The propagation characteristics of elastic waves with a specific frequency on the passband in the proposed structure are studied. Finally, the calculated band gap frequency range is compared with the finite element simulation results, and the two correspond perfectly. The research shows that the proposed structure has a good bandgap frequency range, which can play a good role in suppressing vibration transmission, and by improving the chiral structure of the basic four ligaments, the bandgap frequency range of the structure can be transferred from a high frequency to low frequency, which provides ideological guidance and scheme for the structural design of metamaterial that suppress low-frequency waves. [ABSTRACT FROM AUTHOR]

Sandwich structures possess a high stiffness-to-mass ratio, which facilitates flexural wave propagation at lower frequencies and enhances their vibration isolation and sound insulation capabilities, therefore, sandwich-like metamaterial plates with the nonlinear local oscillator is constructed in this paper to obtain adjustable bandgap in low-frequency. The buckling beam oscillator consists of a small mass, linear support spring, and buckling elastic elements for nonlinear stiffness. First, governing equations of flexural vibrations of plates are deduced based on the Hamilton principle. By utilizing the harmonic balance method (HBM), the dispersion relation of a sandwich-like plate can be determined. Theoretical analysis reveals the presence of structural bandgap ranges at lower frequencies, which are subject to the excitation amplitudes. And in order to validate the theoretical findings, the finite element method (FEM) is employed. Moreover, the influence of structural parameters, including oscillator mass, linear spring stiffness, buckling beam angle, and Young's modulus, are conducted to enhance the vibration control in the low-frequency. Interestingly, it is observed that the effectiveness of low-frequency suppression in the nonlinear metamaterial plate varies significantly across different boundary conditions. Therefore, the sandwich structures with nonlinear local oscillators can provide an effective way to suppress low-frequency vibration and maintain dynamic stability. [ABSTRACT FROM AUTHOR]

Acoustic black hole (ABH), as a new wave manipulation technique, shows excellent applications in vibration and noise reduction of structures. Nowadays, most ABHs use materials with a fixed elastic modulus, limiting their low-frequency performance. Herein ABH plates with variable elastic modulus (VM-ABH) is designed, and its vibration and acoustic radiation characteristics are investigated by using numerical analysis. The results show that the vibration response of VM-ABH has a decrease of 5–13.2 dB relative to that of the uniform texture ABH (UT-ABH) in the frequency range of 10–5000 Hz, and the degree of energy aggregation is significantly improved. Moreover, the sound pressure level was reduced by 3.6 dB. Meanwhile, by linearly varying the elastic modulus in the center region of the VM-ABH, the effects of gradient index and terminal elastic modulus on the damping characteristics and dynamic response are revealed. The research results provide new objects for the study of vibration and noise reduction of ABH. [ABSTRACT FROM AUTHOR]

Bridge cranes used for vertical lifting and horizontal transportation of heavy objects are widely used in engineering. Based on the Hamilton principle, a dynamic model of a bridge crane system in planar space is established for the first time in this paper, and the movement of the main beam and trolley in planar space is considered at the same time. This paper introduces an adaptive fault-tolerant boundary control scheme, grounded in the Nussbaum function, to address the challenges posed by time-varying actuator faults and uncertain control directions. Ultimately, the control scheme can effectively suppress cable vibrations and achieve position tracking for both the main beam and the trolley, so as to provide a strong safety guarantee for the workers operating the bridge crane. The Lyapunov method is utilized to demonstrate the uniform ultimate boundedness of the closed-loop system. Furthermore, the effectiveness of the proposed control method is corroborated by simulation results. [ABSTRACT FROM AUTHOR]

Marine structures are supposed to simultaneously possess high stiffness bearing high loadings and large damping dissipating dynamic energy. Structural impact protection and stiffening approach is achieved via assembling a pre-compressed negative stiffness component and linear members, which not only exhibits high initial stiffness but also dissipation capacity approaching the theoretical limit under small deformation. The effects of design parameters on the energy dissipation characteristics are investigated by the combination of quasi-static, dynamic and finite element analysis. For potential applications, the dynamic responses and vibration suppression of a representative grille structure optimized by the novel design are studied via FE simulations. [ABSTRACT FROM AUTHOR]

Flexible manipulators have been widely used in industrial production. However, due to the poor rigidity of the flexible manipulator, it is easy to generate vibration. This will reduce the working accuracy and service life of the flexible manipulator. It is necessary to suppress vibration during the operation of the flexible manipulator. Based on the energy method and the Hamilton principle, the partial differential equations of the manipulator were established. Secondly, an improved radial basis function (RBF) neural network was combined with the fuzzy backstepping method to identify and suppress random vibration during the operation of the flexible manipulator, and the Lyapunov function and control law were designed. Finally, Simulink was used to build a simulation platform, three different external disturbances were set up, and the effect of vibration suppression was observed through the change curves of the final velocity error and displacement error. Compared with the RBF neural network boundary control method and the RBF neural network inversion method, the simulation results show that the effect of the RBF neural network fuzzy inversion method is better than the previous two control methods, the system convergence is faster, and the equilibrium position error is smaller. [ABSTRACT FROM AUTHOR]

This paper presents coupled structures based on a nonlinear hysteresis friction damper subjected to harmonic forces for vibration suppression. The steady-state responses of the structures are obtained by the Runge–Kutta method and the harmonic balance method, which describe the hysteretic nonlinearity of friction dampers and exhibit their attenuation performance. The forced response is well controlled by the normal force applied to the friction damper, and the amplitude and frequency of the resonance peaks can be varied within a certain range by changing force magnitude. The time-averaged vibrational power is calculated to show the total input power and power dissipated by each element. The results indicate that the friction damper participates in the energy dissipation in the frequency band around the resonance frequency, thereby enabling high-amplitude vibration filtering. The vibration power flow analysis shows that the normal force for the friction element can be designed to reduce vibration transfer. These results confirm that such friction dampers have the potential to be designed to be adjustable and meet different vibration control objectives. [ABSTRACT FROM AUTHOR]

The nonlinear energy sink (NES) system mainly dissipates energy through damping elements, and changing the position of the damping element will also change the performance of the NES. In this paper, a grounded damping NES is proposed by grounding the damping element of the traditional cubic stiffness NES. The complex dynamics of this two-degree-of-freedom system are investigated. The slow-varying equations of the system under 1:1 internal resonance are derived by using the complexification-averaging (C×A) method, based on which the influence of the primary structure’s damping on a bifurcation is analyzed. The conditions for the existence of strongly modulated response (SMR) are studied, and the accuracy of the results is verified using the slow invariant manifold (SIM), Poincare mapping, and time-history diagrams. This provides a means of verifying the analytical findings. The vibration suppression effects of the grounded damping NES, as compared to the cubic stiffness NES, are thoroughly studied under both pulse and harmonic excitations. The results indicate that the main structure damping affects the stability of the system and the occurrence of the SMR. Most previous studies of the NESs have overlooked the effect of main structure damping, which may influence the selection of structural parameters. Moreover, under relatively large pulse or harmonic excitations, the vibration suppression effectiveness of the grounded damping NES surpasses that of traditional cubic stiffness NES. This finding has important practical significance for improving the vibration suppression effect and robustness of the NES, and provides a reference for the structural design of the NES. [ABSTRACT FROM AUTHOR]

Distributed dynamic absorbers have many advantages such as wide frequency bandwidth for vibration suppression, strong detuning adaptability, and high system stability, making them very suitable for the vibration and noise control of continuous structures. Therefore, they have broad application prospects in various fields such as transportation, aviation, and aerospace. However, there are still many challenges in the engineering applications of distributed dynamic absorbers for vibration suppression, including the engineering realization of the optimal damping of traditional optimal coherence dynamic absorbers, and the engineering applicability of the finite periodic array dynamic absorbers. Based on the damping material properties obtained by the dynamic mechanical analyzer tests, this paper establishes the finite element model of the cantilever-beam-type dynamic absorber with constrained damping layers, aiming to realize the accurate determination of the optimal damping. Experiments are conducted by attaching the traditional dynamic absorbers with the optimal damping to a thin-walled panel with four clamped edges. Results show that the vibration of the panel is well suppressed, with the reduction of the frequency response peak larger than 14 dB and the reduction ratio of RMS larger than 58% within 500 Hz. Afterwards, the periodically arrayed dynamic absorbers are designed according to the bandgap regulation method. The tuning behavior of the arrayed dynamic absorbers by changing designing parameters is investigated. The vibration reduction effect of arrayed dynamic absorbers is compared with that of the traditional dynamic absorbers under the same mass ratio through experiments. Results indicate that the arrayed dynamic absorbers are easier to design, and have a similar reduction effect on the modal vibration of the thin panel as the traditional dynamic absorbers within a narrow frequency range near the natural frequency, while they perform unsatisfactory in a broad band. Significantly, if the appropriate frequency and damping of the arrayed absorbers are chosen, a relatively wide bandgap can also be generated, which shows high engineering applicability. The research work in this paper provides beneficial reference for the design of distributed dynamic absorbers suitable for vibration suppression of thin-walled panel structures. [ABSTRACT FROM AUTHOR]

A novel hollow star-shaped chiral metamaterial (SCM) is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial, exhibiting a wide band gap over 1 500 Hz. To broaden the band gap, solid single-phase and two-phase SCMs are designed and simulated, which produce two ultra-wide band gaps (approximately 5 116 Hz and 6 027 Hz, respectively). The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave. The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied. Decreasing the concave angle leads to an increase in the width of the widest band gap, and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases. Additionally, the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces, wave propagation directions, group velocities, and phase velocities. Ultimately, the analysis focuses on the transmission properties of finite periodic structures. The solid single-phase SCM achieves a maximum vibration attenuation over 800, while the width of the band gap is smaller than that of the two-phase SCM. Both metamaterials exhibit high vibration attenuation capabilities, which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies. [ABSTRACT FROM AUTHOR]

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper deals with the problem of obtaining a given dynamic behavior of simply supported bridge beams from the impact of rolling stock. Resonant vibrations of beams become a reality at high speeds if the train is formed of identical cars, which is typical for passenger trains. The phenomenon of suppression of beam vibrations by a train, known from publications, is possible only with an exact ratio of the length of the car and the beam. This significantly reduces the possibilities of choosing the necessary spans of beams. Consideration of issues of interaction in the "bridge–track—train" system for security purposes requires the involvement of a rather complex mathematical apparatus and appropriate software. The paper proposes a new method for determining the specified dynamic behavior of bridge beams, suitable for any spans and available to engineers at the stage of pre-design assignment of dynamic parameters of beams. The requirements that are necessary and sufficient conditions for preventing the resonance of bridge beams on the HSR are determined. At the same time, it does not require the involvement of software based on a complex mathematical technique. [ABSTRACT FROM AUTHOR]

The working mechanism of an acoustic metamaterial (AM) for broadband elastic vibration suppression with non-independent local resonators is presented in this paper along with the general formulas for the effective mass (EM), dispersion relation, and transmission spectrum (TR) of this metamaterial unit. A kind of flexible metamaterial sticker that is lightweight and skillfully uses flexible materials is proposed based on a theoretical approach. The flexible metamaterial sticker has a surface density of only 2.22 kg/m² and an overall thickness of only 3 mm. It is made by depositing the flexible cylindrical supports in a square lattice pattern on the surface of the flexible plate. The finite element method (FEM) was used to systematically investigate the band structures, frequency response function (FRF), dynamic effective mass density (EMD), as well as the formation mechanisms of the flexural vibration bandgaps (FVBGs) of the metamaterial plates (composite structure after applying the metamaterial sticker). Additionally, a thorough analysis was conducted on the impacts of geometrical parameters (the rubber cylinder thickness, the flexible material plate thickness, the lattice constant, and the rubber cylinder radius) on the FVBGs. Finally, an overall vibration attenuation for the proposed metamaterials was estimated by using the spatial quadratic velocity and experiment. The findings confirmed that the AM caused multi-frequency negative EM, while the overall bandgap width was substantially wider than that of conventional metamaterials. Due to the numerous vibration modes of the flexible metamaterial, the suggested flexible lightweight metamaterial sticker can generate several observable local resonance FVBGs in the low-frequency range. Significantly broadening the bandwidth of FVBGs can be achieved by varying the rubber cylinder radius and thickness, as well as by adjusting the lattice constant and flexible material plate thickness. Within the FVBGs, the proposed lightweight flexible metamaterial sticker shows a good vibration-suppression performance, when compared with the traditional damping structure or metamaterials. [ABSTRACT FROM AUTHOR]

The lubricating medium of the aerostatic spindle is gas, with relatively low rigidity, which is easy to cause rotor offset and additional vibration under the action of external load, thus affecting the processing accuracy of the spindle. To solve the problem of unbalanced vibration of the spindle, a new type of controllable radial aerostatic bearing is designed by combining piezoelectric ceramics, which use the inverse piezoelectric effect of piezoelectric ceramics to squeeze the air film to produce corresponding control force, and the radial unbalanced vibration of the spindle is suppressed. A bearing–rotor–piezoelectric ceramic coupling model was established, and the control method of feedforward combined with feedback was used to reduce the hysteresis characteristics of piezoelectric ceramics. On this basis, the sliding mode controller of the entire system, and through research, it is found that the sliding mode controller based on the extended observer has the best vibration suppression effect compared with other sliding mode controllers in the article; this research results can improve the rotation accuracy of the spindle system and the machining accuracy of ultra-precision machine tools. [ABSTRACT FROM AUTHOR]

Automated assembly tasks require industrial robots to improve the efficiency of the manufacturing process. Most rigid or flexible objects handled by robots vibrate due to motion and transient disturbance. This work proposes an active vision-based vibration suppression strategy for flexible beams by providing motion to the wrist of a robot during robotic assembly process, which reduces the time to suppress vibration. The proposed method uses a cheap monocular camera to identify objects through a virtual marker and measure their dimensions. Subsequently, finite element method based mathematical model of a flexible beam predicts the maximum error. The proposed second stage controller determines the controller input in terms of wrist motion based on the predicted maximum error. The performance of the controller is assessed through simulations and experiments on metallic beams with different material characteristics and dimensions. The controller suppresses vibration amplitude within a safe limit so that object is inserted into the slot. It was observed from experiments that the controller can reduce vibration amplitude by ~96% in less than 2 s and decrease suppression time up to ~97%. These improvements were achieved without disturbing the internal robot controller. [ABSTRACT FROM AUTHOR]

A novel tuned vibration absorber with frictional interfaces (FTVA) is proposed in this study, combining the benefits of a tuned absorber and nonlinear dry friction damping to dissipate energy. Firstly, the mechanism of the nonlinear dry friction damper is revealed using a simplified model with a one-degree-of-freedom tuned mass absorber and a hysteresis friction contact element. Then, a practical configuration for the FTVA is proposed, employing a metal strip to tune the absorber and incorporating frictional interfaces with adjustable normal loads. Numerical simulations and experimental investigations have been conducted, demonstrating the effectiveness of the innovative FTVA design. When the absorber is well-tuned and the frictional interfaces are properly designed, a significant reduction in vibration amplitude can be achieved, along with an expanded frequency range where vibration amplitudes are constrained. The nonlinear contact element plays a crucial role in mitigating the occurrence of additional peak vibrations, as the friction damping is activated once the system response surpasses a certain threshold. Furthermore, the effects of contact parameters, such as the normal load of the interface and the forcing level, have been extensively examined, highlighting its potential to suppress vibrations in engineering. [ABSTRACT FROM AUTHOR]

Optimal control of nonlinear vibration requires precise knowledge of the system and the solution to Hamilton–Jacobi–Bellman (HJB) equation. However, in practical engineering applications, acquiring precise system parameters poses challenges, and the analytical solutions for the HJB equation are difficult to obtain. In this paper, two reinforcement learning algorithms, Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and Soft Actor-Critic (SAC) algorithm, are employed to train neural network-based optimal controllers for the van der Pol vibration system in the presence of unknown system parameters. To validate their performance, the controllers undergo testing in a series of experiments, including assessments of free vibration, frequency sweep excitation, and Gaussian noise excitation. The results indicate that both the TD3-trained and SAC-trained neural network-based controller are capable of proficiently suppress the vibration of the van der Pol oscillator. Additionally, these two model-free controllers can approximate the optimal control law which solved based on the dynamic model of the nonlinear system. [ABSTRACT FROM AUTHOR]

AbstractThe propulsion system of mine boring machines often experiences severe vibration during mining. To suppress the vibration of the main beam system of roadheader and prevent the excessive fatigue of propulsion system, a magnetic nonlinear energy sink (MNES) is designed to suppress vibration. In this paper, firstly, the structure and design principle of MNES are introduced, and the dynamic equations of the main beam-MNES system are established. On this basis, the genetic algorithm is applied to optimize the vibration suppression of MNES, and the optimal parameters are determined. In results, the accumulative energy dissipation rate of optimal MNES in transient vibration can reach 90.2% and the vibration reduction effect of the optimal MNES in steady-state vibration is about 82.2%. [ABSTRACT FROM AUTHOR]

A contact-force control and vibration suppression problem for a constrained one-link flexible manipulator with unknown control direction and time-varying actuator fault is discussed in this paper. The manipulator is described by a Partial Differential Equation model. The Nussbaum function is used to solve the unknown control direction and time-varying actuator fault problems. A Nussbaum function provides an adaptive boundary controller constructed to control the contact force to a target and simultaneously eliminate the vibration of the flexible manipulator. The Variable Separation Technique is used along with system boundary conditions to prove the necessary existence and uniqueness of the system solution more concisely than using the common C 0 -semigroup contractions method. Because force sensors are not necessary, the noise caused by a force sensor can be avoided. Numerical simulations verify the effectiveness of the proposed controller-based solution. [ABSTRACT FROM AUTHOR]

In this study, a novel composite control scheme for the vehicle-guideway coupling systems is proposed, consisting of FTDOs and a FTC, aiming to address the challenges of unknown disturbances and vibration suppression. Specifically, this method adopts a single magnet-track coupling model and introduces a finite-time disturbance observer (FTDO) that utilizes only measured electromagnet-side signals to estimate unmeasurable states and unknown disturbances. Based on the estimated information provided by the FTDO, a finite-time control (FTC) scheme is developed, which simultaneously handles the problems of disturbance compensation and finite-time tracking control. Additionally, the finite-time stability of the levitation system is analyzed and proven. Finally, simulation and experimental results are given to demonstrate the feasibility and superiority of the proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, a boundary control scheme based on the partial differential equation (PDE) model is proposed for the vibration control problem of the flexible manipulator with input constraints and external disturbances. Based on the backstepping method, two boundary controllers are designed to stabilize the position loop subsystem and the attitude loop subsystem, respectively, and auxiliary systems based on the smooth hyperbolic tangent function and Nussbaum function are designed in the controllers to deal with the input saturation and external disturbances. The Nussbaum function can overcome the difficulties in controller design and stability analysis caused by the derivatives of smooth hyperbolic tangent functions. The well‐posedness of the closed‐loop system is proven by employing the semigroup theory, and the uniformly bounded stability is proved by Lyapunov direct method. Finally, the performance of the proposed control laws is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

The nonlinear energy sink (NES) and Galfenol material can achieve vibration suppression and energy harvesting of the structure, respectively. Compared with a linear structure, the geometric nonlinearity can affect the output performances of the cantilever beam structure. This investigation aims to present a coupled system consisting of a nonlinear energy sink (NES) and a cantilever Galfenol energy harvesting beam with geometric nonlinearity. Based on Hamilton's principle, linear constitutive equations of magnetostrictive material, and Faraday's law of electromagnetic induction, the theoretical dynamic model of the coupled system is proposed. Utilizing the Galliakin decomposition method and Runge–Kutta method, the harvested power of the external load resistance, and tip vibration displacements of the Galfenol energy harvesting model are analyzed. The influences of the external excitation, external resistance, and NES parameters on the output characteristic of the proposed coupling system have been investigated. Results reveal that introducing NES can reduce the cantilever beam's vibration while considering the geometric nonlinearity of the cantilever beam can induce a nonlinear softening phenomenon for the output behaviors. Compared to the linear system without NES, the coupling model proposed in this work can achieve dual efficacy goals over a wide range of excitation frequencies when selecting appropriate parameters. In general, large excitation amplitude and NES stiffness, small external resistance, and small or large NES damping values can achieve the effect of broadband energy harvesting. [ABSTRACT FROM AUTHOR]

This paper provides an extension to previous work on end-effector control of flexible space manipulators. Those works considered the use of a special output called the μ-tip rate for feedback control of desired end-effector trajectories with simultaneous vibration control. Implementation of this special output requires measurement of end-effector position or the use of flexible forward kinematics to determine it. For the latter, one requires measurements of the joint angles and flexible coordinates. The second of these is difficult to measure in space scenarios, so this paper looks at the use of an estimation scheme to approximate it and use it in a task-space control law. Multiple simulations are conducted to investigate the use of these approximated elastic coordinates in robustly controlling a one-link and two-link flexible manipulator with a payload mass. The error between desired and actual trajectory is calculated, and the results are juxtaposed with results from a joint-space feedback scheme. There is an emphasis on comparing the estimated elastic coordinates with the actual simulated coordinates. Using the estimated elastic coordinates to determine the end-effector location via forward kinematics, yielded similar results to when the actual elastic coordinates were used. Overall, the estimation equation used is shown to provide reasonable end-effector tracking results with the end-effector being able to track various types of trajectories.

Vibration reduction strategies based on wave propagation phenomena, such as generating band gaps in periodic structures, are attracting attention in the field of mechanical engineering. This paper investigates how the structural and material compositions influence band gap characteristics (band gap frequencies and width) of composite beams of metallic materials with flat surfaces. The composite beams in this study are composed of the periodic structure of the "unit cell," and a unit cell consists of two different parts (called cells a and b). Numerical analysis to obtain a dispersion curve by applying the wave finite element method (WFEM) was first carried out to check band gap generation in the metallic composite beams. The relationship between structural characteristics (bending rigidity ratio, mass ratio, or length of the two parts of the unit cell) and the band gap characteristics was investigated numerically using the WFEM. Some composite beams with a band gap lower than 1 kHz with a broad frequency band were designed. Then, their frequency response characteristics were calculated using a commercial FEM software Ansys to confirm the vibration reduction (or suppression) effect in the specified frequency band. Actual metallic composite beams were created using a metal 3D printer, and excitation tests were conducted to verify the numerical results. As a result, band gap generation was demonstrated experimentally. Numerical investigations were also carried out to design composite beams of two different metals to have a wider band gap.