A component coupling approach to dynamic analysis of a buckled,bistable vibration energy harvester structure

Nonlinear Dynamics - Over the past ten years, the energy harvesting community has focused on bistable structures as a means of broadening the working frequency range and, by extension, the...     

Finite element for the dynamic analysis of pipes subjected to water hammer

An axisymmetric finite element is developed for the dynamic analysis of pipes subjected to water hammer. The analysis seamlessly captures the pipe response due to water hammer by solving first the water hammer mass and momentum conservation equations, to recover the spatial–temporal distribution of the internal pressure, and then uses the predicted pressure history to form a time-dependent energy equivalent load vector within a finite element model. The study then determines the pipe response by solving the finite element discretized equations of motion. The formulation of the pipe response is based on Hamilton’s principle in conjunction with a thin shell theory formulation, and captures inertial and damping effects. The results predicted by the model are shown to be in agreement with those based on an axisymmetric shell model in Abaqus for static, free vibration and transient responses for benchmark problems. The water hammer and structural models are seamlessly integrated to enable advancing the transient solution well into the time domain to capture the effect of reflected pressure wave due to water hammer. The results indicate that the radial stress/displacement oscillations approach those of the quasi-steady response when the valve closure time exceeds eight times the period of radial vibrations obtained for the case of instantaneous valve closure.     

Analysis of nonlinear dynamic stability of liquid-converying pipes

Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson, Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different. Foundation items: the National Natural Science Foundation of China (50079007); the Hydraulic Science Foundation of China Hydraulic Ministry (SZ9830); the Natural Science Foundation of Yunnan Provicce (98E003G) Biographies: ZHANG Li-xiang (1959−) HUANG Wen-hu (1926−)     

Nonlinear frequency analysis of buckled nanobeams in the presence of longitudinal magnetic field

The nonlinear free vibration around the postbuckling configuration of nonlocal nanobeams with pinned–pinned boundary conditions are analytically investigated,considering the geometric nonlinearity arising from the mid-plane stretching and particularly the effect of a longitudinal magnetic field.When the applied axial force is small,the nanobeam is stable and its free vibration is around the straight equilibrium position.As the axial force becomes large and is beyond a certain critical value(critical axial force),however,either positive or negative non-trivial equilibrium configuration occurs and the free vibration is around the buckled configuration.The governing equation for the nanobeam before buckling exhibits a cubic nonlinearity while for a buckled nanobeam it contains both cubic and quadratic nonlinearities.Based on the nonlinear governing equations,approximate analytical solutions for the postbuckling configuration in terms of the applied axial force are evaluated,showing that the magnetic field parameter has a great effect on the critical axial force,buckled displacement and linear frequencies of the nanobeam system.More interestingly,the nonlinear frequency is found to be generally higher than the linear frequency in the case of prebuckling regime while it could be lower than the linear one in the case of postbuckling regime.The nonlinear frequency can be significantly influenced by the magnetic field,the nonlinear coefficient associated with the mid-plane stretching,and the initial vibration amplitude.     

温度场下岛-桥结构屈曲薄膜的动力学分析

基于岛-桥结构的柔性电子器件已被用于健康监测和皮肤电子等领域。但是柔性电子器件在工作中极易受工作温度变化等激励产生振动,进而影响器件的灵敏度与可靠性。因此本文研究在温度场作用下岛-桥结构屈曲薄膜的动力学问题。首先,基于Euler-Bernoulli梁理论,建立温度场作用下岛-桥结构屈曲薄膜的动力学控制方程。其次,通过引入新变量,将原动力学方程引入Hamilton体系中,得到相应的Hamilton正则方程。随后,采用辛Runge-Kutta方法求解该Hamilton正则方程,并与经典Runge-Kutta方法对比,数值结果显示了辛算法在求解非线性动力学方程时高精度、高数值稳定性的优势,进一步讨论了温度变化量、预应变、阻尼系数等对屈曲薄膜动力学响应的影响。本文研究为柔性电子器件动力学设计提供了理论参考。     

Nonlinear buckled states of rectangular plates

A constructive method is developed to establish the existence of buckled states of a thin, flat elastic plate that is rectangular in shape, simply supported along its edges, and subjected to a constant compressive thrust applied normal to its two short edges. Under the assumption that the stress function and the deformation of the plate are described by the nonlinear von Kármán equations, the approach used yields information regarding not only the number of buckled states near an eigenvalue of the linearized problem, but also the continuous dependence of such states on the load parameter and the possible selection of that buckled state “preferred” by the plate. In particular, the methods used provide a rigorous approach to studying the existence of buckled states near the first eigenvalue of the linearized problem (that is, near the “buckling load”) even when the first eigenvalue is not simple.     

Multiple buckled states of rectangular plates

We consider the buckling of a simply supported plate subjected to a constant edge thrust λ. The aspect ratio l is such that the critical thrust (the first bifurcation point of the associated non-linear eigenvalue problem) is of multiplicity two. A study of the non-linear static problem indicates that there are nine possible equilibrium states. One of these corresponds to the unbuckled state while the remaining eight represent buckled states. A linear stability analysis and a calculation of the potential energy of each of the static solutions indicates that four of the solutions are stable and five are unstable.     

The buckled states of rectangular plates

In this paper, based on the generalized variational principle of plates, the buckled states of rectangular plates under uniaxial compression are studied by use of the finite element method and the numerical analysis results under various boundary conditions are obtained by using the continuation calculation method.     

Secondary buckled states of rectangular sandwich plates

In this paper, for a rectangular sandwich plate with edges simply supported and subjected to a constant compressive thrust λ along two opposite edges; the secondary bifurcation points and the secondary buckled states that bifurcate from the primary buckled states are determined by a perturbation method. These results are useful for their numerical calculation and can be used to explain the phenomenon of “mode-jumping”. Project Supported by National Natural Science Foundation of China.     

Stability analysis of viscoelastic curved pipes conveying fluid

Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.     

Modeling and analysis of water-hammer in coaxial pipes

The fluid-structure interaction is studied for a system composed of two coaxial pipes in an annular geometry, for both homogeneous isotropic metal pipes and fiber-reinforced (anisotropic) pipes. Multiple waves, traveling at different speeds and amplitudes, result when a projectile impacts on the water fillinhe annular space between the pipes. In the case of carbon fiber-reinforced plastic thin pipes we compute the wavespeeds, the fluid pressure and mechanical strains as functions of the fiber winding angle. This generalizes the single-pipe analysis of J. H. You, and K. Inaba, Fluid-structure interaction in water-filled pipes of anisotropic composite materials, J. Fl. Str. 36 (2013). Comparison with a set of experimental measurements seems to validate our models and predictions.     

The buckled states of annular sandwich plates

In this paper, the axisymmetric buckled states of an annular sandwich plate (Reissner- type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled states in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.     

开口型管道内瓦斯爆炸冲击波动压的数值模拟

为了研究瓦斯爆炸冲击波的动压演化规律,利用数值模拟软件模拟开口型管道内的爆炸。结果表明:动压与流速在时间上存在较好的对应关系,基本同时出现正向和反向的峰值;动压在3个方向上不仅伴随传播距离的增大而不断增大,也伴随传播时间的延长而增大;沿管道方向(火焰传播方向)上的最大动压值是其他2个方向(管道径向)上的数千倍;相比爆炸超压而言,管道径向上的动压对爆炸破坏效应的影响较小,而沿管道方向上的动压造成的破坏效应不能忽视;验证了动压与流速的平方呈正比关系,同时通过分析给出了动压基于管道几何尺寸和流速的经验公式。     

Distributed piezoelectric actuation of a bistable buckled beam

Bistable structures, such as buckled beams or plates, are characterized by a two-well potential. Their nonlinear properties are currently exploited in actuators design (e.g. MEMS micropumps, switches, memory cells) to produce relatively high displacements and forces with low actuation energies. We investigate the use of distributed multiparameter actuation to control the buckling and postbuckling behavior of a three-layer piezoelectric beam pinned at either end. A two-parameter bending actuation controls the transversal motion, whilst an axial actuation and a beam end-shortening modulate the tangent bending stiffness. The postbuckling behavior is studied by reducing to a 2 dof system a nonlinear extensible elastica model. When the bending actuation is spatially symmetric, the postbuckling phenomena are analogue to those obtained for a transversal midspan force, being characterized by a snap-through instability. The use of a two-parameter actuation opens new transition scenarios, where it is possible to get true quasi-static transitions between the two specular equilibria of the buckled beam, without any instability phenomenon. The efficiencies of these different transition paths are discussed in terms of energetic requirements and stability properties. A numerical example shows the technical feasibility of the proposed actuation technique.     

Nonlinear response of a parametrically excited buckled beam

A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented.