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81.
82.
83.
84.
Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures 总被引:1,自引:0,他引:1
Slava Krylov 《International Journal of Non》2007,42(4):626-642
The dynamic pull-in instability of double clamped microscale beams actuated by a suddenly applied distributed electrostatic force and subjected to non-linear squeeze film damping is investigated. A reduced order model is built using the Galerkin decomposition with undamped linear modes as base functions and verified through comparison with numerical finite differences solution. The stability analysis of a beam actuated by one and two electrodes symmetrically located at two sides of the beam and operated by a step-input voltage is performed by evaluating the largest Lyapunov exponent, the sign of which defines the character of the response. It is shown that this approach provides an efficient quantitative criterion for the evaluation of dynamic pull-in instability, especially when combined with compact reduced order models. Based on the Lyapunov exponent criterion, the influence of various parameters on the beam dynamic stability is investigated. 相似文献
85.
Variable Order and Distributed Order Fractional Operators 总被引:1,自引:0,他引:1
Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m
2) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m
2 memory may be chosen for a particular application. Memory retentiveness (m
2) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined. 相似文献
86.
F. Fang C. C. Pain I. M. Navon M. D. Piggott G. J. Gorman P. A. Allison A. J. H. Goddard 《国际流体数值方法杂志》2009,59(8):827-851
A novel proper orthogonal decomposition (POD) model has been developed for use with an advanced unstructured mesh finite‐element ocean model, the Imperial College Ocean Model (ICOM, described in detail below), which includes many recent developments in ocean modelling and numerical analysis. The advantages of the POD model developed here over existing POD approaches are the ability:
- 1. To increase accuracy when representing geostrophic balance (the balance between the Coriolis terms and the pressure gradient). This is achieved through the use of two sets of geostrophic basis functions where each one is calculated by basis functions for velocities u and v.
- 2. To speed up the POD simulation. To achieve this a new numerical technique is introduced, whereby a time‐dependent matrix in the discretized equation is rapidly constructed from a series of time‐independent matrices. This development imparts considerable efficiency gains over the often‐used alternative of calculating each finite element over the computational domain at each time level.
- 3. To use dynamically adaptive meshes in the above POD model.
87.
Professor A. Siginer 《Rheologica Acta》1991,30(5):447-473
Superposition of oscillatory shear imposed from the boundary and through pressure gradient oscillations and simple shear is investigated. The integral fluid with fading memory shows flow enhancement effects due to the nonlinear structure. Closed-form expressions for the change in the mass transport rate are given at the lowest significant order in the perturbation algorithm. The elasticity of the liquid plays as important a role in determining the enhancement as does the shear dependent viscosity. Coupling of shear thinning and elasticity may produce sharp increases in the flow rate. The interaction of oscillatory shear components may generate a steady flow, either longitudinal or orthogonal, resulting in increases in flow rates akin to resonance, and due to frequency cancellation, even in the absence of a mean gradient. An algorithm to determine the constitutive functions of the integral fluid of order three is outlined.Nomenclature
A
n
Rivlin-Ericksen tensor of order .
-
A
k
Non-oscillatory component of the first order linear viscoelastic oscillatory velocity field induced by the kth wave in the pressure gradient
-
d
Half the gap between the plates
-
e
x, e
z
Unit vectors in the longitudinal and orthogonal directions, respectively
-
G(s)
Relaxation modulus
-
G
History of the deformation
-
Stress response functional
-
I()
Enhancement defined as the ratio of the frequency dependent part of the discharge to the frequencyindependent part of it at the third order
-
I
*()
Enhancement defined as the ratio of the increase in discharge due to oscillations to the total discharge without the oscillations
-
k
Power index in the relaxation modulus G(s)
-
k
i
–1
Relaxation times in the Maxwell representation of the quadratic shear relaxation modulus (s
1, s
2)
-
m
i
–1, n
i
–1
Relaxation times in the Maxwell representations of the constitutive functions 1(s
1,s
2,s
3) and 4 (s
1, s
2,s
3), respectively
-
P
Constant longitudinal pressure gradient
-
p
Pressure field
-
mx
,(3)
nz
,(3)
Mean volume transport rates at the third order in the longitudinal and orthogonal directions, respectively
- 0,(3), 1,(3)
Frequency independent and dependent volume transport rates, respectively, at the third order
-
s = t-
Difference between present and past times t and 相似文献
88.
复合随机振动分析的扩阶系统方法 总被引:6,自引:2,他引:6
提出了随机结构系统反应的子空间次序正交分解的思想.基于这一思想,文中导出了一类用于考虑随机激励的随机结构复合随机振动分析的扩阶系统方法,从而可以应用传统的确定性结构随机振动各种分析方法求解复合随机振动问题.作为特例,本文给出了使用模态分析法求解的过程.将文中算例与随机模拟结果相比较,证实了本文思想与方法的实用性. 相似文献
89.
A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-I quasi-static steady crack growth in
the incompressible (v=1/2) elastic perfectly-plastic media. The results show that the near-tip stress and strain are fully continuous, and the
strain possesses In (A/r) singularity at the crack tip. The expressions of the stress, strain and velocity in each region are also given.
The project supported by National Natural Science Foundation of China 相似文献
90.
Higher order elements were first design for linear problems where, in certain situations, they present advantages over the lower order elements. A method to efficiently extend their use to geometrical nonlinear problems as panel flutter and postbuckling behavior is presented. The chaotic and limit-cycle oscillations of an isotropic plate are obtained based on direct integration of the discretized equation of motion. The plate is modeled using the von Karman theory and the geometrical nonlinearities are separated in a nonlinear term of the first kind which manifests especially in the prebuckling and buckling regimes, and a nonlinear term of the second kind which is responsible for the postbuckling behavior. A fifth order, fully compatible element has been used to model thin plates while the inplane loads where introduced through a membrane element. The aerodynamics was modeled using the first order 'piston theory. The method introduces the concept of a deteriorated form of the second geometric matrix which is equivalent to neglecting higher order terms in the strain energy of the plate. This allows for a drastic reduction in the computational effort with no observable loss of accuracy. Well established results in the literature are used to validate the method. 相似文献