Wave energy is one of the most abundant renewable clean energy sources,and has been widely studied because of its advantages of continuity and low seasonal variation.However,its low capture efficiency and narrow captu...Wave energy is one of the most abundant renewable clean energy sources,and has been widely studied because of its advantages of continuity and low seasonal variation.However,its low capture efficiency and narrow capture frequency bandwidth are still technical bottlenecks that restrict the commercial application of wave energy converters(WECs).In recent years,using a nonlinear stiffness mechanism(NSM)for passive control has provided a new way to solve these technical bottlenecks.This literature review focuses on the research performed on the use of nonlinear mechanisms in wave energy device utilization,including the conceptual design of a mechanism,hydrodynamic models,dynamic characteristics,response mechanisms,and some examples of experimental verification.Finally,future research directions are discussed and recommended.展开更多
The small dimensions of microfabricated devices present challenges in applications such as inertial sensing,where a larger proofmass is necessary for enhanced sensitivity.An effective approach to addressing the limita...The small dimensions of microfabricated devices present challenges in applications such as inertial sensing,where a larger proofmass is necessary for enhanced sensitivity.An effective approach to addressing the limitations of linear sensing is to use nonlinear mechanisms that adapt the device’s response according to different operating conditions.This paper introduces a new nonlinear spring mechanism for use in microsensors that harnesses the buckling phenomenon to achieve stiffness softening.The proposed mechanism utilizes a micro-arm to apply an eccentric axial load to an inclined beam,causing it to buckle in a controlled manner under a specified load.Once buckled,linear springs dominate the response of the system.We demonstrate that this method results in a smaller bias displacement compared to previously reported techniques based on snap-through behaviour,leading to potential reductions in device size and improvements in operational range.The behaviour is analytically modelled and verified through simulations.A prototype device was designed and microfabricated to experimentally validate the design principles.Compared to pre-curved nonlinear springs,the proposed design results in an 11-fold reduction in bias force,a 100-fold reduction in bias displacement,and a reduction in mechanical stiffness by a factor of 520.These results were verified through experiments conducted on a microfabricated accelerometer with an on-chip optical interferometer.Test results reveal an extended linear range of better than 150mg,a bias force of 0.3 mN,and a bias displacement of 10μm,measured with an integrated optical interferometer with a displacement noise floor of 40 pm/√ Hz p at 2 Hz and sensitivity of 194°=mg.展开更多
The variation of the nonlinear contact stiffness induced by the elastic wheel-holding effect between the aircraft and tractor has an important effect on the vibration characteristics of an airfield towbarless traction...The variation of the nonlinear contact stiffness induced by the elastic wheel-holding effect between the aircraft and tractor has an important effect on the vibration characteristics of an airfield towbarless traction system,making it essential for ensuring the safety of this emerging towing-out mode.In this paper,the frequency evolutionary tendency of the traction system is studied and obtained considering the variation of nonlinear contact stiffness for the first time.A novel modal analysis method,based on a derived nonlinear contact relationship,is proposed to investigate the vibration characteristics for mechanical system.Frequency veering and mode exchange phenomena in the low-order modes are observed due to the variation of nonlinear contact stiffness.These findings are further validated by the experimental results of a scaled-down model.In addition,it is also found that the veering critical point will be shifted with the external loads.The study provides valuable insights into the vibration characteristics and frequency veering behavior of similar mechanism-based systems,such as towbarless traction system,and has important implications for improving their design and operational performance.展开更多
A nonlinear stiffness actuator(NSA)could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range,both of which are beneficial for physical interaction between a robot and...A nonlinear stiffness actuator(NSA)could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range,both of which are beneficial for physical interaction between a robot and the environment.Currently,most of NSAs are complex and hardly used for engineering.In this paper,oriented to engineering applications,a new simple NSA was proposed,mainly including leaf springs and especially designed cams,which could perform a predefined relationship between torque and deflection.The new NSA has a compact structure,and it is lightweight,both of which are also beneficial for its practical application.An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed.The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring.Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism,the sliding displacement between the cam and the leaf spring is very small,and consumption of sliding friction force is very low.Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles.Three kinds of prototype experiments,including verification experiment of the predefined torque‒deflection profile,torque tracking experiment,and position tracking experiment under different loads,were conducted.The results prove the accuracy of performing the predefined torque‒deflection profile,the tracking performance,and the interactive performance of the new NSA.展开更多
With numerous applications coilable masts in high-precision astronomical observations,such as X-ray source observations,it is important to investigate mast stiffness.To date,there have been many studies on the bending...With numerous applications coilable masts in high-precision astronomical observations,such as X-ray source observations,it is important to investigate mast stiffness.To date,there have been many studies on the bending stiffness of coilable masts,but few studies on their torsional stiffness,especially regarding the nonlinear characteristics of torsional stiffness of coilable masts under large torsional deformation.In this paper,a nonlinear analysis method is presented to examine the torsional stiffness of coilable masts with triangular sections.Based on the second-order bending buckling hypothesis of battens under large torsion deformation,the nonlinear relationship between torsional torque and torsional angle is obtained by analyzing torsional deformation and force of coilable masts.This method is used to analyze the torsional stiffness nonlinearity of a certain type of coilable mast which will be used in a practical application in the future and the results are verified by simulation and testing.The comparison results show that the error is within the acceptable range,which proves the effectiveness of the proposed method.展开更多
In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results ...In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.展开更多
Nonlinearity can take an important and critical role in engineering systems,and thus cannot be simply ignored in structural design,dynamic response analysis,and parameter selection.A key issue is how to analyze and de...Nonlinearity can take an important and critical role in engineering systems,and thus cannot be simply ignored in structural design,dynamic response analysis,and parameter selection.A key issue is how to analyze and design potential nonlinearities introduced to or inherent in a system under study.This is a must-do task in many practical applications involving vibration control,energy harvesting,sensor systems,robotic technology,etc.This paper presents an up-to-date review on a cutting-edge method for nonlinearity manipulation and employment developed in recent several years,named as the X-structure/mechanism approach.The method is inspired from animal leg/limb skeletons,and can provide passive low-cost high-efficiency adjustable and beneficial nonlinear stiffness(high static&ultra-low dynamic),nonlinear damping(dependent on resonant frequency and/or relative vibration displacement),and nonlinear inertia(low static&high dynamic)individually or simultaneously.The X-structure/mechanism is a generic and basic structure/mechanism,representing a class of structures/mechanisms which can achieve beneficial geometric nonlinearity during structural deflection or mechanism motion,can be flexibly realized through commonly-used mechanical components,and have many different forms(with a basic unit taking a shape like X/K/Z/S/V,quadrilateral,diamond,polygon,etc.).Importantly,all variant structures/mechanisms may share similar geometric nonlinearities and thus exhibit similar nonlinear stiffness/damping properties in vibration.Moreover,they are generally flexible in design and easy to implement.This paper systematically reviews the research background,motivation,essential bio-inspired ideas,advantages of this novel method,the beneficial nonlinear properties in stiffness,damping,and inertia,and the potential applications,and ends with some remarks and conclusions.展开更多
Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design ...Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.展开更多
The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches....The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.展开更多
Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-deg...Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-degree-of-freedom (DOF) nonlinear vibration model for such a system, deduced the differential equations of motion which govern its dynamics, and worked out the solutions for the governing equations by the principle of superposition of nonlinear normal modes (NLNM) based on Shaw’s theory of invariant manifolds. We conducted numerical simulations with the established model, using superposition of nonlinear normal modes and direct numerical methods, respectively. The obtained results demonstrate the feasibility of the proposed method in that its calculated data varies in a similar tendency to that of the direct numerical solutions.展开更多
This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The ...This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.展开更多
The goat’s hind limbs play an important role in dampening vibrations caused by ground impact during movement.Inspired by the unique structure of their hind limbs,a novel bionic limb vibration isolator has been develo...The goat’s hind limbs play an important role in dampening vibrations caused by ground impact during movement.Inspired by the unique structure of their hind limbs,a novel bionic limb vibration isolator has been developed to suppress low-frequency vibrations.It consists of the base,the carrying platform,four bionic legs and so on.The bionic legs are made up of rods of varying lengths and springs in different directions to imitate the various shapes of bones such as the femur and patella of the hind limbs of goats and developed muscles such as the biceps and quadriceps.The bionic device was found to have excellent nonlinear stiffness through statics analysis,and could be flexibly adjusted to the work range and load capacity.The bionic vibration isolator offers lower natural frequencies(2.3 Hz),better vibration isolation effect and a wider vibration isolation band than conventional linear vibration isolator.The bionic device can effectively suppress vibrations above 3.2 Hz and reduce the amplitude of random vibrations to more than 90%.In addition,compared to similar bionic vibration isolation devices,the bionic isolator achieves excellent load-bearing capacity in a smaller size,which facilitates its application in practical production.展开更多
In order to provide a theoretical guide for choosing the material for the hawsers for the FPSO side-by-side offloading system, which is moored by the yoke system, the 3D potential flow theory and full coupled time-dom...In order to provide a theoretical guide for choosing the material for the hawsers for the FPSO side-by-side offloading system, which is moored by the yoke system, the 3D potential flow theory and full coupled time-domain analysis are presented to study the dynamic response of the offloading system. The MingZhu FPSO offloading system in the field BZ25-1 is simulated here; and four different characteristic fiber ropes are used as the material for the hawsers. To acquire an accurate hawser line tension, the polynomial fitting method is used to calculate the nonlinear stiffness of the hawsers. By comparing the hawser lines＇ tension and the relative motion between the FPSO and the shuttle tanker, a suitable material for the hawser lines is chosen and discussed in this paper. The results indicate that the nonlinear stiffness characteristic of the fiber rope has a small effect on the relative motion of the vessels, but the hawser lines＇ tension is greatly influenced by the different characteristics of the fiber ropes. The hawser lines＇ tension with nonlinear stiffness is in accordance with the one with the upper and lower bound linear stiffness, which proves this method of fitting the fiber ropes＇ nonlinear stiffness is reasonable and reliable.展开更多
Considering the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force, a dynamical model of rub-impact rotor system is established, then the nonlinear dynamical behavior is studied by num...Considering the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force, a dynamical model of rub-impact rotor system is established, then the nonlinear dynamical behavior is studied by numerical analysis method. The effect of rotation speed, nonlinear stiffitess ratio and speed effect factor on brifurcation and chaotic behavior for rub-impact rotor system is comprehensively analyzed. The analysis results show that the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force on the dynamical behavior of the rotor system has close relation with rotation speed. The chaotic behavior exists in a wider parameter region, and the chaotic evolution rule is more complicated. The research provides a reliable theory basis and reference for diagnosing some faults of the rotor system.展开更多
The J-lay method is regarded as one of the most feasible methods to lay a pipeline in deep water and ultra-deep water. A numerical model that accounts for the nonlinear soil stiffness is developed in this study to eva...The J-lay method is regarded as one of the most feasible methods to lay a pipeline in deep water and ultra-deep water. A numerical model that accounts for the nonlinear soil stiffness is developed in this study to evaluate a J-lay pipeline. The pipeline considered in this model is divided into two parts： the part one is suspended in water, and the part two is laid on the seabed. In addition to the boundary conditions at the two end points of the pipeline, a special set of the boundary conditions is required at the touchdown point that connects the two parts of the pipeline. The two parts of the pipeline are solved by a numerical iterative method and the finite difference method, respectively. The proposed numerical model is validated for a special case using a catenary model and a numerical model with linear soil stiffness. A good agreement in the pipeline configuration, the tension force and the bending moment is obtained among these three models. Furthermore, the present model is used to study the importance of the nonlinear soil stiffness. Finally, the parametric study is performed to study the effect of the mudline shear strength, the gradient of the soil shear strength, and the outer diameter of the pipeline on the pipelaying solution.展开更多
The suspension of electrodynamic loudspeakers includes a surround of the cone and a spider, and it is characterized by the mechanic stiffness in the lumped-parameter model. By solving the nonlinear differential equati...The suspension of electrodynamic loudspeakers includes a surround of the cone and a spider, and it is characterized by the mechanic stiffness in the lumped-parameter model. By solving the nonlinear differential equation of motion which considers the nonlinearity of suspension at low frequencies numerically and measuring different kinds of surrounds and spiders, the nonlinear behavior of suspension is theoretically and experimentally studied. Since the nonlinear stiffness of spiders and surrounds can be measured and fitted respectively before assembled into loudspeakers, which spider works best with which surround is studied. The performance of loudspeakers such as harmonic distortion based on the nonlinear parameters can be predicted.展开更多
A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further c...A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical experiments.Especially, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.展开更多
Inspired by the safe landing of a cat falling from a high altitude,a bio-inspired polygonal skeleton(BIPS) structure is proposed,and its nonlinear characteristics are systematically studied to explore its potential ap...Inspired by the safe landing of a cat falling from a high altitude,a bio-inspired polygonal skeleton(BIPS) structure is proposed,and its nonlinear characteristics are systematically studied to explore its potential application in the suppression of vibration. The polygon is formed by the skeleton structure of the cat’s entire body and the ground. The BIPS system consists of two symmetrical bionic legs with three robs(as skeleton) and four horizontal springs(as muscle). Two bionic legs are connected through the bearing platform(as spine),which could adjust the distance between the two bionic legs. A theoretical model is developed to characterize its stiffness nonlinearity through geometrical and mechanical analysis. Parameter analysis reveals that the BIPS structure has diverse stiffness,including nonlinear positive stiffness and negative stiffness. By imitating adjustment of leg posture and telescopic function of the spine(control the distance between legs),these flexible stiffness properties can be adjusted by structure parameters. In addition,the load capacity and working range can also be designed by the length of the bars,the initial angle,the mounting position,and the spring stiffness. The experimental setup is established,and the vibration isolation performance under various excitation is tested. The experimental results verify the accuracy of the dynamic model and also show that the proposed BIPS structure can suppress the vibration effectively under a variety of excitations. These peculiarities may provide potential possibility of an innovative approach to passive vibration control and isolation.展开更多
In the preliminary design stage of high-speed train smart suspension,a simple,yet accurate magnetorheological(MR)damper model whose parameters have clear physical meaning is needed.Based on the working mechanism analy...In the preliminary design stage of high-speed train smart suspension,a simple,yet accurate magnetorheological(MR)damper model whose parameters have clear physical meaning is needed.Based on the working mechanism analysis and the dynamic behavior study of the MR damper,a new consecutive viscoelastic plastics(VEP)model is proposed.A methodology to find the parameters of the proposed model directly has been proposed.The comparison with experimental results indicates that the proposed model could adequately characterize the intrinsic nonlinear behavior of the MR damper,including the hysteretic behavior,roll-off phenomenon,and the variation of the hysteresis width in terms of the frequency and magnitude of excitation.The results of experimental testing prove that the accuracy of the proposed model is higher than that of the phenomenological model while only containing four undetermined parameters with clear physical meaning.Moreover,based on the proposed VEP model,a nonlinear stiffness VEP(nkVEP)model is developed with higher precision in the hysteretic region.The nkVEP model,which can reproduce the behavior of the damper with fluctuating input current,is developed.The proposed model could predict accurately the response of the MR damper in a wide range of frequency and displacement.展开更多
基金the State Key Laboratory of Coastal and Offshore Engineering of China(No.LP2019)the 2020 Research Program of Sanya Yazhou Bay Science and Technology City of China(No.SKJC-2020-01-006)+1 种基金the Hainan Provincial Natural Science Foundation of China(No.520QN290)the High-tech Ship Research Projects Sponsored by MIIT of China(No.[2019]357)。
文摘Wave energy is one of the most abundant renewable clean energy sources,and has been widely studied because of its advantages of continuity and low seasonal variation.However,its low capture efficiency and narrow capture frequency bandwidth are still technical bottlenecks that restrict the commercial application of wave energy converters(WECs).In recent years,using a nonlinear stiffness mechanism(NSM)for passive control has provided a new way to solve these technical bottlenecks.This literature review focuses on the research performed on the use of nonlinear mechanisms in wave energy device utilization,including the conceptual design of a mechanism,hydrodynamic models,dynamic characteristics,response mechanisms,and some examples of experimental verification.Finally,future research directions are discussed and recommended.
基金financially supported by the Canadian Space Agency(CSA)CMC Microsystems,the manager of the FABrIC project,which is funded by the Government of Canada,for providing CAD tools and test equipment that facilitated this research+2 种基金the 4D LABS core facility at Simon Fraser University,supported by the Canada Foundation for Innovation(CFI)British Columbia Knowledge Development Fund(BCKDF)Pacific Economic Development Canada(PacifiCan).
文摘The small dimensions of microfabricated devices present challenges in applications such as inertial sensing,where a larger proofmass is necessary for enhanced sensitivity.An effective approach to addressing the limitations of linear sensing is to use nonlinear mechanisms that adapt the device’s response according to different operating conditions.This paper introduces a new nonlinear spring mechanism for use in microsensors that harnesses the buckling phenomenon to achieve stiffness softening.The proposed mechanism utilizes a micro-arm to apply an eccentric axial load to an inclined beam,causing it to buckle in a controlled manner under a specified load.Once buckled,linear springs dominate the response of the system.We demonstrate that this method results in a smaller bias displacement compared to previously reported techniques based on snap-through behaviour,leading to potential reductions in device size and improvements in operational range.The behaviour is analytically modelled and verified through simulations.A prototype device was designed and microfabricated to experimentally validate the design principles.Compared to pre-curved nonlinear springs,the proposed design results in an 11-fold reduction in bias force,a 100-fold reduction in bias displacement,and a reduction in mechanical stiffness by a factor of 520.These results were verified through experiments conducted on a microfabricated accelerometer with an on-chip optical interferometer.Test results reveal an extended linear range of better than 150mg,a bias force of 0.3 mN,and a bias displacement of 10μm,measured with an integrated optical interferometer with a displacement noise floor of 40 pm/√ Hz p at 2 Hz and sensitivity of 194°=mg.
基金co-supported by the Key Projects of the Civil Aviation Joint Fund of the National Natural Science Foundation of China(No.U2033208)。
文摘The variation of the nonlinear contact stiffness induced by the elastic wheel-holding effect between the aircraft and tractor has an important effect on the vibration characteristics of an airfield towbarless traction system,making it essential for ensuring the safety of this emerging towing-out mode.In this paper,the frequency evolutionary tendency of the traction system is studied and obtained considering the variation of nonlinear contact stiffness for the first time.A novel modal analysis method,based on a derived nonlinear contact relationship,is proposed to investigate the vibration characteristics for mechanical system.Frequency veering and mode exchange phenomena in the low-order modes are observed due to the variation of nonlinear contact stiffness.These findings are further validated by the experimental results of a scaled-down model.In addition,it is also found that the veering critical point will be shifted with the external loads.The study provides valuable insights into the vibration characteristics and frequency veering behavior of similar mechanism-based systems,such as towbarless traction system,and has important implications for improving their design and operational performance.
基金supported by the National Key R&D Program of China (Grant No.2019YFB1312404)the National Natural Science Foundation of China (Grant Nos.51975401 and 51875393).
文摘A nonlinear stiffness actuator(NSA)could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range,both of which are beneficial for physical interaction between a robot and the environment.Currently,most of NSAs are complex and hardly used for engineering.In this paper,oriented to engineering applications,a new simple NSA was proposed,mainly including leaf springs and especially designed cams,which could perform a predefined relationship between torque and deflection.The new NSA has a compact structure,and it is lightweight,both of which are also beneficial for its practical application.An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed.The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring.Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism,the sliding displacement between the cam and the leaf spring is very small,and consumption of sliding friction force is very low.Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles.Three kinds of prototype experiments,including verification experiment of the predefined torque‒deflection profile,torque tracking experiment,and position tracking experiment under different loads,were conducted.The results prove the accuracy of performing the predefined torque‒deflection profile,the tracking performance,and the interactive performance of the new NSA.
文摘With numerous applications coilable masts in high-precision astronomical observations,such as X-ray source observations,it is important to investigate mast stiffness.To date,there have been many studies on the bending stiffness of coilable masts,but few studies on their torsional stiffness,especially regarding the nonlinear characteristics of torsional stiffness of coilable masts under large torsional deformation.In this paper,a nonlinear analysis method is presented to examine the torsional stiffness of coilable masts with triangular sections.Based on the second-order bending buckling hypothesis of battens under large torsion deformation,the nonlinear relationship between torsional torque and torsional angle is obtained by analyzing torsional deformation and force of coilable masts.This method is used to analyze the torsional stiffness nonlinearity of a certain type of coilable mast which will be used in a practical application in the future and the results are verified by simulation and testing.The comparison results show that the error is within the acceptable range,which proves the effectiveness of the proposed method.
文摘In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.
基金the Hong Kong Construction Industry Council R&D Fund of China(No.EPS 202017)the Innovation and Technology Fund of Hong Kong Innovation and Technology Commission of China(No.ITP/020/19AP)。
文摘Nonlinearity can take an important and critical role in engineering systems,and thus cannot be simply ignored in structural design,dynamic response analysis,and parameter selection.A key issue is how to analyze and design potential nonlinearities introduced to or inherent in a system under study.This is a must-do task in many practical applications involving vibration control,energy harvesting,sensor systems,robotic technology,etc.This paper presents an up-to-date review on a cutting-edge method for nonlinearity manipulation and employment developed in recent several years,named as the X-structure/mechanism approach.The method is inspired from animal leg/limb skeletons,and can provide passive low-cost high-efficiency adjustable and beneficial nonlinear stiffness(high static&ultra-low dynamic),nonlinear damping(dependent on resonant frequency and/or relative vibration displacement),and nonlinear inertia(low static&high dynamic)individually or simultaneously.The X-structure/mechanism is a generic and basic structure/mechanism,representing a class of structures/mechanisms which can achieve beneficial geometric nonlinearity during structural deflection or mechanism motion,can be flexibly realized through commonly-used mechanical components,and have many different forms(with a basic unit taking a shape like X/K/Z/S/V,quadrilateral,diamond,polygon,etc.).Importantly,all variant structures/mechanisms may share similar geometric nonlinearities and thus exhibit similar nonlinear stiffness/damping properties in vibration.Moreover,they are generally flexible in design and easy to implement.This paper systematically reviews the research background,motivation,essential bio-inspired ideas,advantages of this novel method,the beneficial nonlinear properties in stiffness,damping,and inertia,and the potential applications,and ends with some remarks and conclusions.
基金the China National Funds for Distinguished Young Scholars(No.12025204)。
文摘Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.
基金Project supported by the National Natural Science Foundation of China(Nos.11832002 and 12072201)。
文摘The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
基金Funded by the National Science Foundation of China (No. 50075029).
文摘Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-degree-of-freedom (DOF) nonlinear vibration model for such a system, deduced the differential equations of motion which govern its dynamics, and worked out the solutions for the governing equations by the principle of superposition of nonlinear normal modes (NLNM) based on Shaw’s theory of invariant manifolds. We conducted numerical simulations with the established model, using superposition of nonlinear normal modes and direct numerical methods, respectively. The obtained results demonstrate the feasibility of the proposed method in that its calculated data varies in a similar tendency to that of the direct numerical solutions.
基金supported by Yangtze River Delta HIT Robot Technology Research Institute(No.HIT-CXY-CMP2-VSEA-21-01)the Open Project Program(No.WDZL-202103)。
文摘This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.
基金This research was funded by the the Science and Technology Development Program of Jilin Province,China(Grant No.20230101117JC)National Natural Science Foundation of China(Grant No.51775234,91748211,51305157)the Science and Technology Development Program of Jilin Province,China(Grant No.20190302101GX,20180101090JC).
文摘The goat’s hind limbs play an important role in dampening vibrations caused by ground impact during movement.Inspired by the unique structure of their hind limbs,a novel bionic limb vibration isolator has been developed to suppress low-frequency vibrations.It consists of the base,the carrying platform,four bionic legs and so on.The bionic legs are made up of rods of varying lengths and springs in different directions to imitate the various shapes of bones such as the femur and patella of the hind limbs of goats and developed muscles such as the biceps and quadriceps.The bionic device was found to have excellent nonlinear stiffness through statics analysis,and could be flexibly adjusted to the work range and load capacity.The bionic vibration isolator offers lower natural frequencies(2.3 Hz),better vibration isolation effect and a wider vibration isolation band than conventional linear vibration isolator.The bionic device can effectively suppress vibrations above 3.2 Hz and reduce the amplitude of random vibrations to more than 90%.In addition,compared to similar bionic vibration isolation devices,the bionic isolator achieves excellent load-bearing capacity in a smaller size,which facilitates its application in practical production.
基金Supported by the National 111 Project of China under Grant No.B07019Important National Science & Technology Specific Project:Numerical Simulation and Experimental Investigation of FPSO and Offloading System,No.2011ZX05030-006-002
文摘In order to provide a theoretical guide for choosing the material for the hawsers for the FPSO side-by-side offloading system, which is moored by the yoke system, the 3D potential flow theory and full coupled time-domain analysis are presented to study the dynamic response of the offloading system. The MingZhu FPSO offloading system in the field BZ25-1 is simulated here; and four different characteristic fiber ropes are used as the material for the hawsers. To acquire an accurate hawser line tension, the polynomial fitting method is used to calculate the nonlinear stiffness of the hawsers. By comparing the hawser lines＇ tension and the relative motion between the FPSO and the shuttle tanker, a suitable material for the hawser lines is chosen and discussed in this paper. The results indicate that the nonlinear stiffness characteristic of the fiber rope has a small effect on the relative motion of the vessels, but the hawser lines＇ tension is greatly influenced by the different characteristics of the fiber ropes. The hawser lines＇ tension with nonlinear stiffness is in accordance with the one with the upper and lower bound linear stiffness, which proves this method of fitting the fiber ropes＇ nonlinear stiffness is reasonable and reliable.
文摘Considering the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force, a dynamical model of rub-impact rotor system is established, then the nonlinear dynamical behavior is studied by numerical analysis method. The effect of rotation speed, nonlinear stiffitess ratio and speed effect factor on brifurcation and chaotic behavior for rub-impact rotor system is comprehensively analyzed. The analysis results show that the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force on the dynamical behavior of the rotor system has close relation with rotation speed. The chaotic behavior exists in a wider parameter region, and the chaotic evolution rule is more complicated. The research provides a reliable theory basis and reference for diagnosing some faults of the rotor system.
基金supported by the China Scholarship Council,the Technology Major Project of China(Grant No.2011ZX05027-002)the National Natural Science Foundation of China(Grant No.51409128)the University Natural Science Research Project of Jiangsu Province(Grant No.14KJB570001)
文摘The J-lay method is regarded as one of the most feasible methods to lay a pipeline in deep water and ultra-deep water. A numerical model that accounts for the nonlinear soil stiffness is developed in this study to evaluate a J-lay pipeline. The pipeline considered in this model is divided into two parts： the part one is suspended in water, and the part two is laid on the seabed. In addition to the boundary conditions at the two end points of the pipeline, a special set of the boundary conditions is required at the touchdown point that connects the two parts of the pipeline. The two parts of the pipeline are solved by a numerical iterative method and the finite difference method, respectively. The proposed numerical model is validated for a special case using a catenary model and a numerical model with linear soil stiffness. A good agreement in the pipeline configuration, the tension force and the bending moment is obtained among these three models. Furthermore, the present model is used to study the importance of the nonlinear soil stiffness. Finally, the parametric study is performed to study the effect of the mudline shear strength, the gradient of the soil shear strength, and the outer diameter of the pipeline on the pipelaying solution.
基金supported by the National Natural Science Foundation of China(Grant No. 11274172)
文摘The suspension of electrodynamic loudspeakers includes a surround of the cone and a spider, and it is characterized by the mechanic stiffness in the lumped-parameter model. By solving the nonlinear differential equation of motion which considers the nonlinearity of suspension at low frequencies numerically and measuring different kinds of surrounds and spiders, the nonlinear behavior of suspension is theoretically and experimentally studied. Since the nonlinear stiffness of spiders and surrounds can be measured and fitted respectively before assembled into loudspeakers, which spider works best with which surround is studied. The performance of loudspeakers such as harmonic distortion based on the nonlinear parameters can be predicted.
基金National Natural Science Foundation of China(Grant No.11971412)Key Project of Education Department of Hunan Province(Grant No.20A484)Project of Hunan National Center for Applied Mathematics(Grant No.2020ZYT003).
文摘A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical experiments.Especially, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.
基金This work was supported by the National Science Fund for Distinguished Young Scholars(Grant No.11625208)the Innovation Program of Shanghai Municipal Education Commission(Grant No.2019-01-07-00-02-E00030)the Program of Shanghai Academic/Technology Research Leader(Grant No.19XD1421600)。
文摘Inspired by the safe landing of a cat falling from a high altitude,a bio-inspired polygonal skeleton(BIPS) structure is proposed,and its nonlinear characteristics are systematically studied to explore its potential application in the suppression of vibration. The polygon is formed by the skeleton structure of the cat’s entire body and the ground. The BIPS system consists of two symmetrical bionic legs with three robs(as skeleton) and four horizontal springs(as muscle). Two bionic legs are connected through the bearing platform(as spine),which could adjust the distance between the two bionic legs. A theoretical model is developed to characterize its stiffness nonlinearity through geometrical and mechanical analysis. Parameter analysis reveals that the BIPS structure has diverse stiffness,including nonlinear positive stiffness and negative stiffness. By imitating adjustment of leg posture and telescopic function of the spine(control the distance between legs),these flexible stiffness properties can be adjusted by structure parameters. In addition,the load capacity and working range can also be designed by the length of the bars,the initial angle,the mounting position,and the spring stiffness. The experimental setup is established,and the vibration isolation performance under various excitation is tested. The experimental results verify the accuracy of the dynamic model and also show that the proposed BIPS structure can suppress the vibration effectively under a variety of excitations. These peculiarities may provide potential possibility of an innovative approach to passive vibration control and isolation.
基金supported by grant from the Innovation and Technology Support Program of the Hong Kong Special Administrative Region,China(Project No.ITS/241/11)the National Natural Science Foundation of China(Grant No.61134002)the National Basic Research Program of China("973" Program)(Grant No.2011CB711106)
文摘In the preliminary design stage of high-speed train smart suspension,a simple,yet accurate magnetorheological(MR)damper model whose parameters have clear physical meaning is needed.Based on the working mechanism analysis and the dynamic behavior study of the MR damper,a new consecutive viscoelastic plastics(VEP)model is proposed.A methodology to find the parameters of the proposed model directly has been proposed.The comparison with experimental results indicates that the proposed model could adequately characterize the intrinsic nonlinear behavior of the MR damper,including the hysteretic behavior,roll-off phenomenon,and the variation of the hysteresis width in terms of the frequency and magnitude of excitation.The results of experimental testing prove that the accuracy of the proposed model is higher than that of the phenomenological model while only containing four undetermined parameters with clear physical meaning.Moreover,based on the proposed VEP model,a nonlinear stiffness VEP(nkVEP)model is developed with higher precision in the hysteretic region.The nkVEP model,which can reproduce the behavior of the damper with fluctuating input current,is developed.The proposed model could predict accurately the response of the MR damper in a wide range of frequency and displacement.
