Mechanical snap-through instability of bi-stable structures may find many practical applications such as state switching and energy transforming.Although there exist diverse bi-stable structures capable of snap-throug...Mechanical snap-through instability of bi-stable structures may find many practical applications such as state switching and energy transforming.Although there exist diverse bi-stable structures capable of snap-through instability,it is still difficult for a structure with high slenderness to undergo the axial snap-through instability with a large stroke.Here,an elastic structure with high slenderness is simply constructed by a finite number of identical,conventional bi-stable units with relatively low slenderness in series connection.For realizing the axial snap-through instability with a large stroke,common scissors mechanisms are further introduced as rigid constraints to guarantee the synchronous snap-through instability of these bi-stable units.The global feature of the large-stroke snap-through instability realized here is robust and even insusceptible to the local out-of-synchronization of individual units.The present design provides a simple and feasible way to achieve the large-stroke snap-through instability of slender structures,which is expected to be particularly useful for state switching and energy transforming in narrow spaces.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
The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relations...The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.展开更多
A modified snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises three springs that are configured so that the potential energy of the system has two s...A modified snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises three springs that are configured so that the potential energy of the system has two stable equilibrium points. In particular, the small vibration behavior of the harvester around one of the equilibriums is of interest. A multi-scale method(MSM) is used to analyze the frequency response curve. Two snap-through mechanisms are considered. One has both horizontal and vertical springs. The other has only horizontal springs. The frequency response curves of these two classes are compared under the same excitation and electric loading conditions. The latter exhibits more bending of the frequency response curve than the former one. The results are also validated by some numerical work. The averaged power subject to the Gaussian white noise is calculated numerically, and the results demonstrate that bi-stable energy harvesting with only horizontal springs can outperform the mechanism with both horizontal and vertical springs for the same distance between two equilibriums.展开更多
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor...Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.展开更多
Snap-through phenomenon widely occurs for elastic systems,where the systems lose stability at critical points.Here snapthrough of an elastica under bilateral displacement control at a material point is studied,by rega...Snap-through phenomenon widely occurs for elastic systems,where the systems lose stability at critical points.Here snapthrough of an elastica under bilateral displacement control at a material point is studied,by regarding the whole elastica as two components,i.e.,pinned-clamped elasticas.Specifically,stiffness-curvature curves of two pinned-clamped elasticas are firstly efficiently located based on the second-order mode,which are used to determine the shapes of two components.Similar transformations are used to assemble two components together to form the whole elastica,which reveals four kinds of shapes.One advantage of this way compared with other methods such as the shooting method is that multiple coexisting solutions can be located accurately.O n the load-deflection curves,four branches correspond to four kinds of shapes and first two branches are symmetrical to the last two branches relative to the original point.For the bilateral displacement control,the critical points can only appear at saddle-node bifurcations,which is different to that for the unilateral displacement control.Specifically,one critical point is found on the first branch and two critical points are found on the secondary branch.In addition,the snap-through among different branches can be well explained with these critical points.展开更多
The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to es...The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to estimate the influence of the dynamic effects on the response. A table tennis ball is considered as an example of a thin-walled elastic shell. It is shown that the increase of the impact velocity leads to a variation of the deformed shape thus resulting in larger de- formation energy. The increase of the contact force is caused by both the increased contribution of the inertia forces and contribution of the increased deformation energy. The contact force resulted from deformation/inertia of the ball and the shape of the deformed region are calcu- lated by the proposed theoretical models and compared with the results from both the finite element analysis and some previously obtained experimental data. Good agreement is demonstrated.展开更多
Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent ...Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent decades.The reported research presents the double snap-through mechanism applied to a hemispheric point absorber type wave energy converter(WEC)to improve the energy absorption perfomance.The double snap-through mechanism comprises four oblique springs mounted in an X-configuration.This provides the WEC with different dynamic stability behaviors depending on the particular geometric and physical parameters employed.The efficiency of these different WEC behaviors(linear,bistable,and tristable)was initially evaluated under the action of regular waves.The results for bistable or tristable responses indicated significant improvements in the WEC's energy capture efficiency.Furthermore,the WEC frequency bandwidth was shown to be significantly enlarged when the tristable mode was in operation.However,the corresponding tristable trajectory showed intra-well behavior in the middle potential well,which induced a more severe low-energy absorption when a small wave amplitude acted on the WEC compared to when the bistable WEC was employed.Nevertheless,positive effects were observed when appropriate initial conditions were imposed.The results also showed that for bistable or tristable responses,a suitable spring stiffness may cause the buoy to oscillate in high energy modes.展开更多
Three-dimensional(3D)mesostructures with distinct compressive deformation behaviors and tunable mechanical responses have gained increasing interest in recent years.3D cage-shaped mesostructures are representative fra...Three-dimensional(3D)mesostructures with distinct compressive deformation behaviors and tunable mechanical responses have gained increasing interest in recent years.3D cage-shaped mesostructures are representative framework structures widely exploited in 3D flexible electronics,owing to their unique cellular geometry and unusual mechanical responses.The snap-through behavior of cage-shaped mesostructures could potentially result in the performance degradation of electronics,while it could also be harnessed to design reconfigurable electronics.Due to the complicated deformation modes and random characteristics in experiments,the snap-through behavior of cage-shaped mesostructures remains largely unexplored,espe-cially in terms of probability-based analyses.In this work,we present a systematic study on the configuration evolution and snap-through of 3D cage-shaped mesostructures under out-of-plane compressions.Experimental and computational studies show the existence of two distinct deformation modes associated with the snap-through,which is controlled by the energy barrier based on the energetic analyses.Phase diagrams of the deformation modes decode how key geometric parameters and assembly strain affect the snap-through.Compressive experiments based on periodic arrays(10 × 10)of mesostructures provided a large amount of deformation data,allowing for statistical analyses of the snap-through behavior.These results provide new insights and useful guidelines for the design of 3D reconfigurable devices and multistable metamaterials based on 3D cage-shaped mesostructures.展开更多
We have examined the elastic snap-through behaviors of single crystal copper strips numerically and theoretically to investigate factors that influence the characteristic snap-through time scale.The strip is simply su...We have examined the elastic snap-through behaviors of single crystal copper strips numerically and theoretically to investigate factors that influence the characteristic snap-through time scale.The strip is simply supported on both ends,and the snap-through is launched by suddenly removing the concentrated forces that have already been statically applied to produce an initial bending configuration.On the one hand,the process is implemented in the molecular dynamics(MD)simulator LAMMPS.On the other hand,a theoretical formulation is provided with the consideration of surface tension.Increasing surface tension is found to increase the snap-through time.The results show that the snap-through behavior is further closely related to the magnitude of the initially stored deformation and the strip thickness.Finally,snap-through times provided by the above numerical and theoretical analyses are on the same order of magnitude.This is an interesting agreement,especially considering that the huge gap of time scales between MD simulations and experiments has been a well-known fundamental issue.We believe that the present study about spontaneous processes such as snap-through has cast some light on the fbndamental issue that deformation in MD simulations generally happens much faster than in physical experiments.展开更多
The dielectric elastomer(DE)has attracted significant attention due to its desired features,including large deformation,fast response,and high energy density.However,for a DE actuator(DEA)utilizing a snap-through defo...The dielectric elastomer(DE)has attracted significant attention due to its desired features,including large deformation,fast response,and high energy density.However,for a DE actuator(DEA)utilizing a snap-through deformation mode,most existing theoretical models fail to predict its deformation path.This paper develops a new finite element method(FEM)based on the three-parameter Gent-Gent model suitable for capturing strain-stiffening behaviors.The simulation results are verified by experiments,indicating that the FEM can accurately characterize the snap-through path of a DE.The method proposed in this paper provides theoretical guidance and inspiration for designing and applying DEs and bistable electroactive actuators.展开更多
Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications.Enhancing the performance of a vibration energy harvester(VEH)incorporating nonlinear techniques,for example...Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications.Enhancing the performance of a vibration energy harvester(VEH)incorporating nonlinear techniques,for example,the snap-through VEH with geometric non-linearity,has gained attention in recent years.A conventional snap-through VEH is a bi-stable system with a time-invariant potential function,which was investigated extensively in the past.In this work,a modified snap-through VEH with a time-varying potential function subject to harmonic and random base excitations is investigated.Modified snap-through VEHs,such as the one considered in this study,are used in wave energy harvesters.However,the studies on their dynamics and energy harvesting under harmonic and random excitations are limited.The dynamics of the modified snap-through VEH is represented by a system of differential algebraic equations(DAEs),and the numerical schemes are proposed for its solutions.Under a harmonic excitation,the system exhibits periodic and chaotic motions,and the energy harvesting is superior compared with the conventional counterpart.The dynamics under a random excitation is investigated by the moment differential method and the numerical scheme based on the modified Euler-Maruyama method.The Fokker-Planck equation representing the dynamics is derived,and the marginal and joint probability density functions(PDFs)are obtained by the Monte Carlo simulation.The study shows that the modified snap-through oscillator based VEH performs better under both harmonic and random excitations.The dynamics of the system under stochastic resonance(SR)is investigated,and performance enhancement is observed.The results from this study will help in the development of adaptive VEH techniques in the future.展开更多
Photo-responsive nematic polymers can transduce light into mechanical work,but the rate is limited by the quasi-static deformation.To enhance the work output,a strat・egy of exploiting photo-triggered snap-through of g...Photo-responsive nematic polymers can transduce light into mechanical work,but the rate is limited by the quasi-static deformation.To enhance the work output,a strat・egy of exploiting photo-triggered snap-through of glassy nematic shallow spherical shells with hemeotropic director alignment is examined here.The criterion for the nonlinear instability is derived analytically by using the modified iteration method.It is shown that,for thin shells of small height and large basal radius,snap-through can be caused by an incident light with moderate irradiation intensity.The phenomenon may inspire some new designs of contactless and ultra-fast actuation devices with high-rate output of mechanical work.展开更多
This study applies a double snap-through mechanism on a box-type oscillating buoy(OB)wave energy converter(WEC)-floating breakwater integrated system(OB WEC-FB)to simultaneously achieve efficient wave energy conversio...This study applies a double snap-through mechanism on a box-type oscillating buoy(OB)wave energy converter(WEC)-floating breakwater integrated system(OB WEC-FB)to simultaneously achieve efficient wave energy conversion and nearshore protection within a low-frequency bandwidth.This mechanism consists of four oblique springs and can operate in mono-stable,bi-stable,and tri-stable modes.A viscous-flow-based numerical model is established to investigate the hydrodynamic performance and dynamic behavior of the proposed multi-stable breakwater.The operational performance of the breakwater at different dynamic modes is first compared.The effects of the springs’original length and stiffness coefficient are then analyzed.The results show that the tri-stable breakwater has a wider resonance frequency tuning range than the bi-stable one,both of which outperform the mono-stable and linear ones in shifting the effective bandwidth to a lower frequency range.For a tri-stable breakwater,a large distance between outermost potential wells is conducive to tuning resonance frequency,whereas shallow potential wells limit this effect.The increase in spring stiffness distinctly causes a higher potential barrier and thus constrains the motion response of the breakwater.A well-designed double snap-through mechanism can excite large-amplitude inter-well motion,tune the resonance frequency of breakwater from 3.98 to 1.96 rad/s,and decrease the lower limit of the effective transmission bandwidth from 3.75 to 3.00 rad/s.It is crucial for improving the power absorption and wave attenuation capabilities of multi-stable OB WEC-FB.This study contributes to the limited research on the implementation of a double snap-through mechanism on multifunctional marine structures.It establishes the underlying connection between nonlinear dynamic behaviors and hydrodynamic coefficients.展开更多
Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;...Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.展开更多
The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and ...The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11972027,12472093,and 11772272)the New Interdisciplinary Cultivation Fund of Southwest Jiaotong University(Grant No.2682022JX001)+1 种基金the Frontier Science and Technology Cultivation Project of Southwest Jiaotong University(Grant No.2682022KJ048)the Laboratory of Flexible Electronics Technology at Tsinghua University.
文摘Mechanical snap-through instability of bi-stable structures may find many practical applications such as state switching and energy transforming.Although there exist diverse bi-stable structures capable of snap-through instability,it is still difficult for a structure with high slenderness to undergo the axial snap-through instability with a large stroke.Here,an elastic structure with high slenderness is simply constructed by a finite number of identical,conventional bi-stable units with relatively low slenderness in series connection.For realizing the axial snap-through instability with a large stroke,common scissors mechanisms are further introduced as rigid constraints to guarantee the synchronous snap-through instability of these bi-stable units.The global feature of the large-stroke snap-through instability realized here is robust and even insusceptible to the local out-of-synchronization of individual units.The present design provides a simple and feasible way to achieve the large-stroke snap-through instability of slender structures,which is expected to be particularly useful for state switching and energy transforming in narrow spaces.
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Project supported by the National Natural Science Foundation of China(Nos.12293000,12293001,11988102,12172006,and 12202011)。
文摘The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.
基金Project supported by the State Key Program of National Natural Science of China(No.11232009)the National Natural Science Foundation of China(Nos.11502135 and 11572182)the Innovation Program of Shanghai Municipal Education Commission(No.2017-01-07-00-09-E00019)
文摘A modified snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises three springs that are configured so that the potential energy of the system has two stable equilibrium points. In particular, the small vibration behavior of the harvester around one of the equilibriums is of interest. A multi-scale method(MSM) is used to analyze the frequency response curve. Two snap-through mechanisms are considered. One has both horizontal and vertical springs. The other has only horizontal springs. The frequency response curves of these two classes are compared under the same excitation and electric loading conditions. The latter exhibits more bending of the frequency response curve than the former one. The results are also validated by some numerical work. The averaged power subject to the Gaussian white noise is calculated numerically, and the results demonstrate that bi-stable energy harvesting with only horizontal springs can outperform the mechanism with both horizontal and vertical springs for the same distance between two equilibriums.
基金financially supported by the National Natural Science Foundation of China(Grant No.51239007)the Independent Research Project of State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University(Grant No.GKZD010023)
文摘Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
基金supported by the National Natural Science Foundation of China(Grants 91648101 and 11972290)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(Grant CX201811)the Fundamental Research Funds for the Central Universities(Grant 3102018zy012).
文摘Snap-through phenomenon widely occurs for elastic systems,where the systems lose stability at critical points.Here snapthrough of an elastica under bilateral displacement control at a material point is studied,by regarding the whole elastica as two components,i.e.,pinned-clamped elasticas.Specifically,stiffness-curvature curves of two pinned-clamped elasticas are firstly efficiently located based on the second-order mode,which are used to determine the shapes of two components.Similar transformations are used to assemble two components together to form the whole elastica,which reveals four kinds of shapes.One advantage of this way compared with other methods such as the shooting method is that multiple coexisting solutions can be located accurately.O n the load-deflection curves,four branches correspond to four kinds of shapes and first two branches are symmetrical to the last two branches relative to the original point.For the bilateral displacement control,the critical points can only appear at saddle-node bifurcations,which is different to that for the unilateral displacement control.Specifically,one critical point is found on the first branch and two critical points are found on the secondary branch.In addition,the snap-through among different branches can be well explained with these critical points.
基金supported by the National Natural Science Foundation of China (11032001)
文摘The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to estimate the influence of the dynamic effects on the response. A table tennis ball is considered as an example of a thin-walled elastic shell. It is shown that the increase of the impact velocity leads to a variation of the deformed shape thus resulting in larger de- formation energy. The increase of the contact force is caused by both the increased contribution of the inertia forces and contribution of the increased deformation energy. The contact force resulted from deformation/inertia of the ball and the shape of the deformed region are calcu- lated by the proposed theoretical models and compared with the results from both the finite element analysis and some previously obtained experimental data. Good agreement is demonstrated.
基金supported by the China Scholarship Council under Grant No.201600090258the National Key Research and Development Program of China under Grant No.2016YFC0303700the 111 Project under Grant No.B18054。
文摘Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent decades.The reported research presents the double snap-through mechanism applied to a hemispheric point absorber type wave energy converter(WEC)to improve the energy absorption perfomance.The double snap-through mechanism comprises four oblique springs mounted in an X-configuration.This provides the WEC with different dynamic stability behaviors depending on the particular geometric and physical parameters employed.The efficiency of these different WEC behaviors(linear,bistable,and tristable)was initially evaluated under the action of regular waves.The results for bistable or tristable responses indicated significant improvements in the WEC's energy capture efficiency.Furthermore,the WEC frequency bandwidth was shown to be significantly enlarged when the tristable mode was in operation.However,the corresponding tristable trajectory showed intra-well behavior in the middle potential well,which induced a more severe low-energy absorption when a small wave amplitude acted on the WEC compared to when the bistable WEC was employed.Nevertheless,positive effects were observed when appropriate initial conditions were imposed.The results also showed that for bistable or tristable responses,a suitable spring stiffness may cause the buoy to oscillate in high energy modes.
基金National Natural Science Foundation of China,12225206,Yihui Zhang,12050004,Yihui Zhang,11921002,Yihui Zhangthe Tsinghua National Laboratory for Information Science and Technology,the Henry Fok Education Foundation,171003,Yihui Zhangthe Institute for Guo Qiang,Tsinghua University,2019GQG1012,Yihui Zhang.
文摘Three-dimensional(3D)mesostructures with distinct compressive deformation behaviors and tunable mechanical responses have gained increasing interest in recent years.3D cage-shaped mesostructures are representative framework structures widely exploited in 3D flexible electronics,owing to their unique cellular geometry and unusual mechanical responses.The snap-through behavior of cage-shaped mesostructures could potentially result in the performance degradation of electronics,while it could also be harnessed to design reconfigurable electronics.Due to the complicated deformation modes and random characteristics in experiments,the snap-through behavior of cage-shaped mesostructures remains largely unexplored,espe-cially in terms of probability-based analyses.In this work,we present a systematic study on the configuration evolution and snap-through of 3D cage-shaped mesostructures under out-of-plane compressions.Experimental and computational studies show the existence of two distinct deformation modes associated with the snap-through,which is controlled by the energy barrier based on the energetic analyses.Phase diagrams of the deformation modes decode how key geometric parameters and assembly strain affect the snap-through.Compressive experiments based on periodic arrays(10 × 10)of mesostructures provided a large amount of deformation data,allowing for statistical analyses of the snap-through behavior.These results provide new insights and useful guidelines for the design of 3D reconfigurable devices and multistable metamaterials based on 3D cage-shaped mesostructures.
基金the National Natural Science Foundation of China(Grant Nos.11672119 and 11972174).
文摘We have examined the elastic snap-through behaviors of single crystal copper strips numerically and theoretically to investigate factors that influence the characteristic snap-through time scale.The strip is simply supported on both ends,and the snap-through is launched by suddenly removing the concentrated forces that have already been statically applied to produce an initial bending configuration.On the one hand,the process is implemented in the molecular dynamics(MD)simulator LAMMPS.On the other hand,a theoretical formulation is provided with the consideration of surface tension.Increasing surface tension is found to increase the snap-through time.The results show that the snap-through behavior is further closely related to the magnitude of the initially stored deformation and the strip thickness.Finally,snap-through times provided by the above numerical and theoretical analyses are on the same order of magnitude.This is an interesting agreement,especially considering that the huge gap of time scales between MD simulations and experiments has been a well-known fundamental issue.We believe that the present study about spontaneous processes such as snap-through has cast some light on the fbndamental issue that deformation in MD simulations generally happens much faster than in physical experiments.
基金Project supported by the National Key Research and Development Program of China(No.2019YFB1311600)the National Natural Science Foundation of China(Nos.11902248 and 52075411)+1 种基金the Shaanxi Key Research and Development Program of China(No.2020ZDLGY06-11)the State Key Laboratory for Strength and Vibration of Mechanical Structures of China(No.SV2018-KF-08)。
文摘The dielectric elastomer(DE)has attracted significant attention due to its desired features,including large deformation,fast response,and high energy density.However,for a DE actuator(DEA)utilizing a snap-through deformation mode,most existing theoretical models fail to predict its deformation path.This paper develops a new finite element method(FEM)based on the three-parameter Gent-Gent model suitable for capturing strain-stiffening behaviors.The simulation results are verified by experiments,indicating that the FEM can accurately characterize the snap-through path of a DE.The method proposed in this paper provides theoretical guidance and inspiration for designing and applying DEs and bistable electroactive actuators.
文摘Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications.Enhancing the performance of a vibration energy harvester(VEH)incorporating nonlinear techniques,for example,the snap-through VEH with geometric non-linearity,has gained attention in recent years.A conventional snap-through VEH is a bi-stable system with a time-invariant potential function,which was investigated extensively in the past.In this work,a modified snap-through VEH with a time-varying potential function subject to harmonic and random base excitations is investigated.Modified snap-through VEHs,such as the one considered in this study,are used in wave energy harvesters.However,the studies on their dynamics and energy harvesting under harmonic and random excitations are limited.The dynamics of the modified snap-through VEH is represented by a system of differential algebraic equations(DAEs),and the numerical schemes are proposed for its solutions.Under a harmonic excitation,the system exhibits periodic and chaotic motions,and the energy harvesting is superior compared with the conventional counterpart.The dynamics under a random excitation is investigated by the moment differential method and the numerical scheme based on the modified Euler-Maruyama method.The Fokker-Planck equation representing the dynamics is derived,and the marginal and joint probability density functions(PDFs)are obtained by the Monte Carlo simulation.The study shows that the modified snap-through oscillator based VEH performs better under both harmonic and random excitations.The dynamics of the system under stochastic resonance(SR)is investigated,and performance enhancement is observed.The results from this study will help in the development of adaptive VEH techniques in the future.
基金This work is supported by the National Natural Science Foundation of China(Grant No.11572308).
文摘Photo-responsive nematic polymers can transduce light into mechanical work,but the rate is limited by the quasi-static deformation.To enhance the work output,a strat・egy of exploiting photo-triggered snap-through of glassy nematic shallow spherical shells with hemeotropic director alignment is examined here.The criterion for the nonlinear instability is derived analytically by using the modified iteration method.It is shown that,for thin shells of small height and large basal radius,snap-through can be caused by an incident light with moderate irradiation intensity.The phenomenon may inspire some new designs of contactless and ultra-fast actuation devices with high-rate output of mechanical work.
基金supported by the National Natural Science Foundation of China Program(No.51739010).
文摘This study applies a double snap-through mechanism on a box-type oscillating buoy(OB)wave energy converter(WEC)-floating breakwater integrated system(OB WEC-FB)to simultaneously achieve efficient wave energy conversion and nearshore protection within a low-frequency bandwidth.This mechanism consists of four oblique springs and can operate in mono-stable,bi-stable,and tri-stable modes.A viscous-flow-based numerical model is established to investigate the hydrodynamic performance and dynamic behavior of the proposed multi-stable breakwater.The operational performance of the breakwater at different dynamic modes is first compared.The effects of the springs’original length and stiffness coefficient are then analyzed.The results show that the tri-stable breakwater has a wider resonance frequency tuning range than the bi-stable one,both of which outperform the mono-stable and linear ones in shifting the effective bandwidth to a lower frequency range.For a tri-stable breakwater,a large distance between outermost potential wells is conducive to tuning resonance frequency,whereas shallow potential wells limit this effect.The increase in spring stiffness distinctly causes a higher potential barrier and thus constrains the motion response of the breakwater.A well-designed double snap-through mechanism can excite large-amplitude inter-well motion,tune the resonance frequency of breakwater from 3.98 to 1.96 rad/s,and decrease the lower limit of the effective transmission bandwidth from 3.75 to 3.00 rad/s.It is crucial for improving the power absorption and wave attenuation capabilities of multi-stable OB WEC-FB.This study contributes to the limited research on the implementation of a double snap-through mechanism on multifunctional marine structures.It establishes the underlying connection between nonlinear dynamic behaviors and hydrodynamic coefficients.
文摘Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.
基金Project supported by the National Natural Science Foundation of China(Nos.11832002 and 12072201)。
文摘The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.
