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1.
Second-order approximation of primary resonance of a disk-type piezoelectric stator for traveling wave vibration 总被引:1,自引:0,他引:1
Considering the quadratic nonlinear constitutive relations of piezoelectric materials, a traveling wave dynamic model for
a lead zirconate titanate stator of a traveling wave ultrasonic motor is established using Hamilton’s principle and the Rayleigh–Ritz
method. Applying the method of multiple scales, the second-order approximation of the primary resonance for traveling wave
vibration of the stator is investigated. The second harmonic component is found in the primary response of the stator, which
arises from the quadratic stiffness in the condition of weak excitation. In the region of the resonance, the two coupled modals
are split and the lower-order peak bends to the left, hence a jump and delay exist in the response. In this way numerical
results are given to verify the feasibility of the analytical approach. The results provide a theoretical foundation for further
nonlinear dynamic analysis and design of the traveling wave ultrasonic motor. 相似文献
2.
The present work targets shaft whirling motions induced by direct blade/casing unilateral contact occurrences in aircraft engine bladed-disk assemblies. These contact events are favored by increasingly reduced blade-tip clearances and potentially lead to harmful interactions that may threaten the engine structural integrity.A simplified 2D in-plane finite element model representative of the engine fan stage is built, accounting for the flexibility of the shaft through two linear springs attached to the disk center node and the structural coupling provided by the fan frame and the bearings, modeled by an array of linear springs. A linear stability analysis of the reduced-order coupled system reveals two unstable zones in a selected rotational speed range, emanating from the linearly predicted modal coincidence speeds.Through a time-marching strategy, two asymmetric contact initiation mechanisms are investigated: (1) a prescribed casing distortion and (2) a mass imbalance on the bladed-disk. It is shown how the 1-nodal diameter mode of the first modal family of the bladed-disk is dominant when a modal interaction arises from the transient casing distortion and leads to divergent regimes. The presence of the frame/bearings coupling induces a shift in the critical speeds detected, generally characterized by a backward traveling wave in the rotating frame and a forward traveling one in the fixed frame. Further, when a mass imbalance is the excitation source, the suspension modes appear to have a major role and a stable limit cycle is reached regardless of the coupling stiffness with much lower energy levels than in divergent regimes. 相似文献
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5.
C.C. Glynn 《International Journal of Non》1982,17(5-6):327-341
Large amplitude, traveling wave motion of an inextensible, linearly elastic, rotating ring is analyzed. Equations governing the planar dynamics of a thin rod, curved in its undeformed state and moving in a horizontal reference frame which rotates about a fixed axis, are obtained via Hamilton's extended principle. The equations are specialized to study the behavior of a rotating circular ring and approximate solutions are obtained near resonance utilizing a perturbation analysis. Undamped free and viscously damped forced traveling wave motion is considered. The motion is found to consist of a forward and a backward traveling wave which may be coupled due to the non-linear terms present in the equations of motion 相似文献
6.
Periodic Traveling Waves for Diffusion Equations with Time Delayed and Non-local Responding Reaction 总被引:6,自引:0,他引:6
We develop a singular perturbation technique to study the existence of periodic traveling wave solutions with large wave speed
for a class of reaction-diffusion equations with time delay and non-local response. Unlike the classical singular perturbation
method, our approach is based on a transformation of the differential equations to integral equations in a Banach space that
reduces the singular perturbation problem to a regular perturbation problem. The periodic traveling wave solutions then are
obtained by the use of Liapunov-Schmidt method and a generalized implicit function theorem. The general result obtained has
been applied to a non-local reaction-diffusion equation derived from an age-structured population model with a logistic type
of birth function. 相似文献
7.
The effects of elastic anisotropy in piping materials on fluid–structure interaction are studied for water-filled carbon-fiber reinforced thin plastic pipes. When an impact is introduced to water in a pipe, there are two waves traveling at different speeds. A primary wave corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of pipe travels fast. An anisotropic stress–strain relationship of piping materials has been taken into account to describe the propagation of primary and precursor waves in the carbon-fiber reinforced thin plastic pipes. The wave speeds and strains in the axial and hoop directions are calculated as a function of carbon-fiber winding angles and compared with the experimental data. As the winding angle increases, the primary wave speed increases due to the increased stiffness in the hoop direction, while the precursor wave speed decreases. The magnitudes of precursor waves are much smaller than those of primary waves so that the effect of precursor waves on the deformation of pipe is not significant. The primary wave generates the hoop strain accompanying the opposite-signed axial strain through the coupling compliance of pipe. The magnitude of hoop strain induced by the primary waves decreases with increasing the winding angle due to the increased hoop stiffness of pipe. The magnitude of axial strain is small at low and high winding angles where the coupling compliance is small. 相似文献
8.
We study traveling wavefront solutions for two reaction–diffusion systems, which are derived respectively as diffusion approximations to two nonlocal spatial SIRS models. These solutions characterize the propagating progress and speed of the spatial spread of underlying epidemic waves. For the first diffusion system, we find a lower bound for wave speeds and prove that the traveling waves exist for all speeds bigger than this bound. For the second diffusion system, we find the minimal wave speed and show that the traveling waves exist for all speeds bigger than or equal to the minimal speed. We further prove the uniqueness (up to translation) of these solutions for sufficiently large wave speeds. The existence of these solutions are proved by a shooting argument combining with LaSalle’s invariance principle, and their uniqueness by a geometric singular perturbation argument. 相似文献
9.
摩擦材料是超声波电机的关键零件,其应用方式直接影响超声波电机的驱动特性.以行波超声波电机为研究对象,将摩擦材料分别应用到转子和定子上,与相应的定子和转子组合,模拟超声波电机的接触方式,研究了超声波电机的负载和磨损特性随摩擦材料应用方式的变化规律.借助于阻抗仪测试了摩擦材料应用到定子齿面前后的阻抗特性,采用精密粗糙度仪和金相显微镜评价了超声波电机定子和转子接触界面磨损前后的形貌变化及其磨损模式.结果表明:当摩擦材料应用到定子齿面时,定子的谐振频率略微降低;当2台超声波电机空载转速相同时,摩擦材料应用到定子齿面与金属转子配副时可获得较大的堵转力矩,定子摩擦材料表面呈现抛光的磨损特征,而当摩擦材料应用到转子表面与金属定子配副时,转子摩擦材料表面呈现较严重的犁沟磨损. 相似文献
10.
The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation. 相似文献
11.
This paper presents theoretical analyses and experimental investigations of a mechanical seal subjected to axial impulses of one of its mating rings (stator). The amplitude of oscillations of stator depends on the pressure of sealed fluid. The frequency of oscillations is influenced by the geometry of frontal faces of the seal rings and depends on the rotational speed of rotor. The analytical models include the analyses of the static equilibrium of the investigated mechanical seal and the dynamic response of stator. The experimental analysis implies the conception of the testing system, the experimental estimation of the leakage and the measurements of amplitude and frequency of oscillations. During operating time, the experimental variations of leakage of a mechanical seal with oscillating stator are monitored for different rotational speed of rotor. Finite element analysis is used to visualize the stress distribution of stator as a function of the applied forces. 相似文献
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Blade vibration may trigger a self-induced aeroelastic instability (flutter). In turbomachinery choke flutter appears when a strong shock-wave chokes the blade passage. The aim of this study is to identify mechanisms responsible for the instability. An innovative methodology relying on the splitting of the emitter and receiver role of the blade is presented. It is successfully applied to 2D linearized RANS computations of choke flutter. The emission splitting shows that the vibration of the blades downstream of the shock-wave generates a backward traveling pressure wave triggering the aeroelastic instability. The reception splitting demonstrates the destabilising contribution of the shock-wave / separated boundary layer interaction. The source of flutter is finally a combination of inviscid (regressive waves) and viscous (unsteady separation) mechanisms. 相似文献
14.
弹性波在岩体中传播时与岩体缺陷相互作用形成复杂的传播图案。为研究缺陷对弹性波多次散射作用的影响,建立了双椭圆缺陷模型,基于Green函数基本解,采用边界积分的计算方法,得到了反映缺陷界面条件的刚度矩阵,分析了弹性波在双椭圆缺陷间的多次散射效应。结果表明:与单椭圆缺陷模型相比,双缺陷的相互作用使得弹性波频散和衰减效应增强,定量给出了缺陷的影响区域,从而明确了多次散射效应的尺度界限。进一步探讨了弹性波传播的多尺度效应,结果表明频散的Rayleigh峰、Mie峰和衰减的峰值频率同椭圆长轴和入射波波长两个尺度密切相关,存在明确的定量关系。相应的数值模拟结果表明,弹性波和缺陷相互作用在缺陷界面上诱发界面波,该界面波也存在频率相关性,影响了弹性波宏观传播的频散和衰减特征。 相似文献
15.
Anna Ghazaryan Peter Gordon Christopher K. R. T. Jones 《Journal of Dynamics and Differential Equations》2007,19(4):951-966
We study traveling wave solutions arising in Sivashinsky’s model of subsonic detonation which describes combustion processes
in inert porous media. Subsonic (shockless) detonation waves tend to assume the form of a reaction front propagating with
a well defined speed. It is known that traveling waves exist for any value of thermal diffusivity [5]. Moreover, it has been
shown that, when the thermal diffusivity is neglected, the traveling wave is unique. The question of whether the wave is unique
in the presence of thermal diffusivity has remained open. For the subsonic regime, the underlying physics might suggest that
the effect of small thermal diffusivity is insignificant. We analytically prove the uniqueness of the wave in the presence
of non-zero diffusivity through applying geometric singular perturbation theory.
Dedicated to Mr. Brunovsky in honor of his 70th birthday. 相似文献
16.
V. A. Saraikin 《Journal of Applied Mechanics and Technical Physics》2009,50(6):1063-1070
This paper studies the properties of a model of a block medium consisting of absolutely rigid blocks separated by deformable
layers. The model is proposed to describe the low-frequency spectral region of a perturbation wave propagating in the medium
of this structure. The model is based on the assumption that the low-frequency part of the wave train provides the least distorted
information on the average characteristics of the structure of the medium on the wave pathway. Calculation of waves in a one-dimensional
assembly of blocks (rods) and deformable layers show that the model ignoring the deformation of the blocks is applicable only
in the case where the stiffness of the layer is low compared to the stiffness of the rod. A correction is applied to eliminate
this restriction in the case of a long-wave approximation. 相似文献
17.
超声马达转子摩擦材料厚度对驱动性能的影响研究 总被引:5,自引:0,他引:5
制备了一系列不同厚度的摩擦材料 ,利用超声马达摩擦特性模拟试验装置 ,研究了摩擦材料厚度对超声马达空载转速和堵转力矩的影响 .基于一个简化的行波超声马达定子和转子接触模型 ,用有限元法计算了定子和转子接触变形随摩擦材料厚度的变化规律 ,提出了定子和转子具有合理接触变形的摩擦材料厚度范围 .根据试验和理论计算结果确定了摩擦材料最佳厚度 ,为超声马达摩擦材料厚度设计提供了理论依据 相似文献
18.
Wenxian Shen 《Journal of Dynamics and Differential Equations》2004,16(4):1011-1060
The current paper is devoted to the study of traveling waves in diffusive random media, including time and/or space recurrent, almost periodic, quasiperiodic, periodic ones as special cases. It first introduces a notion of traveling waves in general random media, which is a natural extension of the classical notion of traveling waves. Roughly speaking, a solution to a diffusive random equation is a traveling wave solution if both its propagating profile and its propagating speed are random variables. Then by adopting such a point of view that traveling wave solutions are limits of certain wave-like solutions, a general existence theory of traveling waves is established. It shows that the existence of a wave-like solution implies the existence of a critical traveling wave solution, which is the traveling wave solution with minimal propagating speed in many cases. When the media is ergodic, some deterministic \hbox{properties} of average propagating profile and average propagating speed of a traveling wave solution are derived. When the media is compact, certain continuity of the propagating profile of a critical traveling wave solution is obtained. Moreover, if the media is almost periodic, then a critical traveling wave solution is almost automorphic and if the media is periodic, then so is a critical traveling wave solution. Applications of the general theory to a bistable media are discussed. The results obtained in the paper generalize many existing ones on traveling waves. AMS Subject Classification: 35K55, 35K57, 35B50 相似文献
19.
The impact of passage rotation on the gasdynamic wave processes is analyzed through a numerical simulation of ideal shock-tube flow in a closed rotating-channel containing a gas in an initial state of homentropic solid-body rotation. Relevant parameters of the problem such as wheel Mach number, hub-to-tip radius ratio, length-to-tip radius ratio, diaphragm temperature ratio, and diaphragm pressure ratio are varied. It is shown that for a fixed geometry and initial conditions, the contact interface acquires a distorted three-dimensional time-dependent orientation at non-zero wheel Mach numbers. At a fixed wheel Mach number, the level of distortion depends primarily on the density ratio across the interface and also the hub-to-tip radius ratio. The nature of the rarefaction and shock wave propagation is one-dimensional, although the acoustic waves are diffracted due to the radially varying propagation speed. Under conditions of initially homentropic solid-body rotation, a degree of similarity exists between rotating and stationary shock-tube flows. This similarity is exploited to arrive at an approximate analytical solution to the Riemann problem in a rotating shock-tube. 相似文献