Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

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.

Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

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.

Nonlinear energy harvesting based on a modified snap-through mechanism

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.

An Oscillating Wave Energy Converter with Nonlinear Snap-Through Power-Take-Off Systems in Regular Waves

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.

Static and dynamic snap-through behaviour of an elastic spherical shell

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.

Evaluation of the Double Snap-Through Mechanism on the Wave Energy Converter’s Performance

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.

Snap-through path in a bistable dielectric elastomer actuator

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.

Nonlinear dynamics and performance analysis of modified snap-through vibration energy harvester with time-varying potential function

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.

Probability-Based Analyses of the Snap-Through in Cage-Shaped Mesostructures Under Out-of-Plane Compressions

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.

Inter-well internal resonance analysis of rectangular asymmetric cross-ply bistable composite laminated cantilever shell under transverse foundation excitation

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.

多层级曲梁多稳态超材料的可重用性研究

多稳态超材料凭借其出色的力学性能而广受关注和应用.然而,现有研究主要集中在单曲梁结构,对于由多层级曲梁单胞构建的复杂拓扑结构的可重复吸能特性缺乏深入探讨.此外,与传统材料相比,多稳态超材料在循环加载下的疲劳性能也鲜有研究.文章以两端固支直梁一阶屈曲模态为初始构型构造曲梁单胞,并通过3D打印技术制备双材料双稳态单元.进而建立多层级曲梁结构,并给出预测多层级曲梁正则化的力和势能随位移变化的5次、6次多项式经验公式,相比于以往3次、4次多项式结果更为准确.以双曲梁单胞为基本单元,通过中心旋转的方式设计三维点状多稳态超材料,研究其稳态性能和力学特性.并通过参数化分析研究单元几何参数和模块化拓扑构型对结构力学响应的影响,最后通过疲劳实验验证了该类多稳态超材料的疲劳寿命.该结构能够在小变形和大变形范围内实现正负刚度的转变,同时变形是弹性稳定的,即杨氏模量基本保持不变,且具有多稳态和可重复吸能特性.随着双曲梁几何参数Q(高厚比)的增大,其有效压溃距离和能量吸收效率随之增加.提出的设计策略为制造多稳态多步可逆变形的力学超材料开辟了新路径,并为设计材料-结构-功能一体化的工程材料提供了一种新思路.

Snap-through of an elastica under bilateral displacement control at a material point

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.

非对称铺设双稳态正交复合材料层合方形板的静力学与动力学分析

建立了非对称铺设双稳态正交复合材料层合方形板的静力学和动力学模型。通过固化分析确定了三个平衡状态,展示了以温差绝对值为控制参数的超临界叉形分岔。通过稳定性分析确定了三个平衡状态为两个稳定平衡状态和一个不稳定平衡状态。通过静力学分析确定了双势阱势能曲线,这有助于对动态跳跃现象的研究。通过在动力学分析中引入阻尼,分析了平衡点的动态分岔。通过数值模拟讨论了基础激励频率对动力学特性的影响。当激励频率处于一定范围内时,系统会发生双势阱大振幅动态跳跃和非线性振动,此频率范围可以被设定为特定频率带宽。双稳态系统的主要动力学特性表现为周期振动、概周期振动和混沌振动。

热冲击下四边简支浅壳的动态突跳行为

准确地分析和预测浅壳结构在热冲击下的动态稳定性和结构完整性,对于工程中普遍使用的壳结构的设计和优化具有重要意义。利用非线性浅壳理论,并使用Ritz法和Newmark直接积分法研究了内表面受热冲击作用的四边简支各向同性浅壳的动态突跳(snap-through)行为。分析结果表明:浅壳在足够强的热冲击下会发生动态突跳,而在突跳前后都会发生较剧烈的热振动;Budiansky-Hutchinson准则可用于判定发生动态突跳的临界热冲击条件。

On the snap-through time of a nanoscale elastic strip

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.

Photo-Activated Snap-Through of Nematic Shallow Spherical Shells

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.

基于多稳态的智能可调表面设计及仿真分析

结合多稳态结构的跳变特性和形状记忆智能材料,提出了一种基于多稳态结构的智能可调表面设计。首先,研究了双稳态余弦梁单胞的机械驱动跳变行为;其次,将形状记忆聚合物材料引入余弦梁单胞,实现了智能驱动双稳态结构的跳变,并研究了余弦梁支座厚度对结构跳变行为的影响;基于余弦梁单胞设计了马鞍形余弦梁单胞,通过调控支座厚度,影响单胞的形状记忆跳变成功与否;基于“像素成像”思想,结合马鞍形余弦梁结构单胞的可调形状记忆跳变特性,实现了可定制表面的设计策略;最后,通过有限元仿真分析验证了“HIT”和“力”智能可调表面的设计有效性。

混凝土密肋式锥面网壳的几何非线性分析

混凝土密肋式锥面网壳是通过将圆锥面等分成密肋平板后,再由其在谷(脊)线处交汇形成的新型空间结构。为掌握该类结构的稳定性,在弹性稳定分析的基础上,采用弧长法进行几何非线性分析。并讨论矢跨比、边梁刚度、初始几何缺陷等因素对结构承载力的影响。结果表明:结构薄弱部位主要为谷线跨中与密肋平板交汇处;屈曲失稳具有壳体结构的特征,在跳跃失稳后承载力急剧下降;矢跨比的增大会降低结构极限承载力;因边梁作为主要传力构件在增大其刚度时,能有效提高结构整体刚度;脊(谷)线梁刚度和屋面板板厚的变化对提高结构整体稳定贡献较小;增大密肋梁刚度会有效增强结构抵抗失稳能力;初始几何缺陷对结构极限承载力影响较小,将幅值L/300作为结构可接受的最大初始缺陷。对此类结构进行稳定承载力公式的拟合,发现其误差在工程精度可接受的范围之内。

热声载荷下C/SiC薄壁层合板结构动力学响应计算与寿命分析

高超音速飞行器薄壁结构在工作环境下承受着复杂的高温强噪声载荷,高温会使材料性能发生变化,导致局部区域出现热声疲劳破坏,影响结构的耐久性和完整性。针对此类问题,基于薄壁结构大挠度非线性振动理论,构建热声载荷下四边固支C/SiC薄壁层合板结构的数值仿真模型,并对其进行了动力学响应计算,研究了不同热声载荷组合下的振动响应规律,并采用线性累计损伤理论对结构进行疲劳寿命的预估和分析。结果表明,热声载荷对碳/碳化硅薄壁层合板的非线性响应影响不同,热载荷通过改变结构基频来影响结构非线性响应。四边固支C/SiC薄壁层合板在热声载荷作用下表现出非线性随机振动特性,并且呈现在平衡位置随机振动、随机跳变等多种运动状态,跳变运动给结构造成更大的的损伤更大。

考虑二阶效应的拱结构面内弹性屈曲

对拱结构的极值点屈曲及分支点屈曲进行了详细阐述。利用有限元分析程序ANSYS对拱进行非线性分析,考虑结构屈曲前变形对临界力的影响。选取线性屈曲前几阶模态作为扰动位移,对拱的整个受载过程进行跟踪分析,得到拱的屈曲临界力。将矢跨比、跨径及矢高与截面回转半径的比值作为影响参数,分析竖向均布力及径向均布力作用下,无铰拱和两铰拱的屈曲性能。分析表明,屈曲前变形降低了坦拱的屈曲临界力,考虑二阶效应后拱的屈曲临界力与线性屈曲临界力的比值,随矢跨比的减小而减小,随跨径的增大而增大;对于矢跨比较小的坦拱,矢高与截面回转半径的比值将决定拱的屈曲形式。