• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model?

    2021-09-28 02:17:28WeiZhang張偉MingYuanLi李明遠(yuǎn)QiLiangWu吳啟亮andAnXi襲安
    Chinese Physics B 2021年9期
    關(guān)鍵詞:張偉

    Wei Zhang(張偉),Ming-Yuan Li(李明遠(yuǎn)),Qi-Liang Wu(吳啟亮),and An Xi(襲安)

    1Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures,Beijing University of Technology,Beijing 100124,China

    2College of Mechanical Engineering,Beijing University of Technology,Beijing 100124,China

    3School of Artificial Intelligence,Tiangong University,Tianjin 300387,China

    4The Fifth Electronic Research Institute of MIIT,Guangzhou 510610,China

    Keywords:iced cable,wind excitation,galloping,chaotic motion

    1.Introduction

    The nonlinear statics,dynamics,and stability of cables have received considerable attention due to their extensive applications in the engineering field.High-voltage transmission lines are a flexible cable structure widely used in transmission engineering due to their ability to conduct power over long distances.Cable dynamics have a rich history,which has been summarized in the review articles by Irvine and Caughey,[1]Starossek,[2]and Rega and Ibrahim.[3–5]Among all the different types of cable structures,the suspended cable is a fundamental type used in theoretical studies,and exhibits various dynamic phenomena as a prototype model in applied mechanics.

    The nonlinear dynamic responses of elastic suspended cables due to finite vibration amplitudes have received considerable research attention,as suspended cables exhibit a variety of phenomena due to their high flexibility and low damping characteristics.Perkins[6]derived a continuum model that describes the nonlinear,three-dimensional response of an elastic cable to tangential oscillations of one support.A twodegree-of-freedom approximation was used to examine the coupled in-plane and out-of-plane response.Additionally,a four-degree-of-freedom model was developed from the continuum equations by Benedettini et al.,[7]and is able to capture the main phenomena that are likely to occur in the nonplanar finite dynamics of an elastic suspended cable subjected to external force and support motion.Gattulli et al.[8]used analytical and finite element models to study the modal interactions in both planar and spatial responses to harmonic in-plane and out-of-plane loads.Luongo et al.[9,10]derived a nonlinear model of a twisted cable and studied the effect of the twist angle on the nonlinear galloping of suspended cables.Luongo et al.[11]also established a nonlinear two-degree-of-freedom model to describe a flexible elastic suspended cable undergoing galloping oscillations.Kim and Perkins[12]investigated the resonant responses of suspended elastic cables driven by a steady current.Srinil and Rega[13]presented a model formulation capable of reflecting the large-amplitude free vibrations of a suspended cable in three dimensions.Based on a multidegree-of-freedom model,numerical procedures were implemented to solve both spatial and temporal problems.Zhao and Wang[14]investigated the nonlinear responses of suspended homogeneous elastic cables with low initial sag-to-span ratio in the case of 3:1 internal resonance by considering the vertical load.Casciati and Ubertini[15]considered the nonlinear vibration of shallow cables equipped with a semi-active control device.Abdel-Rohman and Spencer[16]studied the along-wind and across-wind responses of suspended cables.Zheng et al.[17]investigated the super-harmonic and internal resonance characteristics of a viscously damped cable with nearly commensurable natural frequencies via a novel method.Chang et al.[18]studied the nonlinear interaction of the first two inplane modes of a suspended cable with a moving fluid along the plane of the cable.Ouni and Kahla[19]investigated the nonlinear dynamics of a cable under first-and second-order parametric excitations.Zhao et al.[20,21]investigated the approximate series solutions of nonlinear free vibrations of suspended cables via the Lindstedt–Poincar′e method and the homotopy analysis method.

    Owing to the combination of quadratic and cubic nonlinearities,suspended cables exhibit various planar and nonplanar internal resonance conditions.Srinil et al.[22]and Srinil and Rega[23]conducted an analytical investigation of resonant multimodal dynamics resulting from 2:1 internal resonance in the finite-amplitude free vibrations of horizontal/inclined cables.Nayfeh et al.[24]investigated the nonlinear,nonplanar responses of suspended cables subjected to external excitation.Lacarbonara and Rega[25]investigated 1:1,2:1,3:1,and internal resonances in undamped,unforced,one-dimensional systems with arbitrary linear,quadratic,and cubic nonlinearities for a class of shallow symmetric structural systems.Kamel and Hamed[26]studied the nonlinear behavior of an elastic cable subjected to harmonic excitation.Rega et al.[27]studied an experimental model of an elastic cable carrying eight concentrated masses and hanging from in-phase or out-of-phase vertically-moving supports.Zhang and Tang[28]investigated the chaotic dynamics and global bifurcations[29–31]of a suspended elastic cable under combined parametric and external excitations.Considering 1:1 internal resonance,Abe[32]investigated the accuracy of nonlinear vibration analyses of suspended cables that possess quadratic nonlinearity and cubic nonlinearity,respectively.By the Galerkin method,Huang et al.[33]derived the governing equations describing the motion of a coupled suspended cable-stayed beam structure,and studied its 1:2 internal resonance.Taking into account the bending stiffness,Kang et al.[34,35]systematically investigated the linear and nonlinear dynamics of a suspended cable.

    Considering the effect of the geometric nonlinearity of the cable on the coupled behavior between the modes of the beam and cable,Wei et al.[36]developed and investigated a model of the cable-stayed beam system.Wu and Qi studied the dynamic responses of an iced suspended cable were investigated[37]by the finite element method.Jing et al.[38]proposed a numerical model of a wind-loaded two-dimensional(2D)cable,and analyzed the vibration responses induced by rain-wind.The bases of the flow behavior and phenomena existing during 2D airflow were explained by Gorski et al.[39]to analyze the motions of an ice-accreted bridge cable.Via the use of the optimal equivalent control algorithm,Zhao et al.[40]studied a method of controlling the vibration responses of a stay cable.Chang et al.[41]reported experimental results of the mechanism and mitigation of the vibrations of stay cables under rainwind load.Electromagnetic inertial mass dampers were considered by Li et al.[42]to experimentally and analytically study the vibration mitigation of stay cables.

    In recent years,some investigations of suspended cable models and research methods have been updated.Using the method of multiple scales,Huang et al.[43]developed a new nonlinear partial differential equation to investigate a suspended cable-stayed beam structure by considering the finite deformations of the structure and the initial configuration of the main cable.Ahmad et al.[44]established an analytical model of a hybrid system composed of two parallel taut cables interconnected by a transverse linear flexible cross-tie.Ishihara and Oka[45]studied the aerodynamic coefficients of a single bundled iced suspension cable and four bundled iced suspension cables for comparison with the results of a wind tunnel test.Akkaya and Horssen[46]described a model of the rain-wind-induced oscillations of an inclined cable.Based on the mode superposition method with enhanced shape functions,Javanbakht et al.[47]proposed a control-oriented numerical model to evaluate the dynamic response of a stay cable.Li et al.[48]established a generalized gust loading model for predicting the buffeting response,which is applicable to both small-aspect-ratio and long-span,line-like bridges.Guo et al.[49]proposed an elastic cable-rigid body coupled model to investigate the dynamic interaction between the torsional dynamics of the boundary tower and the nonlinear transversal vibrations of the cables.According to catenary theory,Mansour et al.[50]studied the free undamped vibration of a suspension cable with arbitrary sag and inclination.Zhao et al.[51,52]investigated the influence of the temperature on the vibration characteristics of suspension cables related to the excitation amplitude and sag-to-span ratio,and the results revealed that temperature variation gave rise to qualitative and/or quantitative changes of the nonlinear vibration properties.

    The present study focuses on the complex nonlinear vibrations of a three-degree-of-freedom iced cable.The influences of the support displacement and wind excitation on the nonlinear dynamic responses of the system are analyzed.Considering the galloping of the suspended structure under transverse wind,a nonlinear dynamic model of the three-degree-offreedom iced cable is established.The nonlinear partial differential equations of motion for the iced cable are established via Hamilton’s principle.Additionally,the dimensionless differential equations of motion are obtained and reduced into a set of nonlinear ordinary differential equations by the Galerkin method.[53,54]With the assistance of the method of multiple scales,the averaged equations of the system in the presence of principal parametric resonance?1/2 subharmonic resonance and 2:1 internal resonance are obtained.According to the averaged equations,the numerical results including bifurcation diagrams,waveforms,phase plots,and frequency spectrum are obtained to investigate the intrinsically nonlinear behaviors of the iced cable.It is demonstrated that the iced cable exhibits alternating periodic and chaotic motions according to the influences of the nonlinear factors.

    2.Theory and formulation

    Fig.1.Model of iced cable.

    Considering the interception of a small section of the iced cable for centralized mass,the center of mass of the line lies on the origin O.In the Cartesian coordinate(oxy)system,the vertical coordinate of the center of mass is y.For a wind speed Vm,the relative velocity is Vr=Vw?

    then the angle of attackαwill be

    Because the cross-section of the iced cable is a non-circular irregular shape,the gust of the suspension produces not only a resistance Fdin the Vrdirection,but also a lift FLand a torsional force Fwthat are perpendicular to it.According to the aerodynamic principle,the following equations can be obtained:

    The tangential force and normal force of the cable are respectively

    Because the model considers low-frequency vibration,the value ofαis very small;thus,the following approximate expressions can be held:

    By substituting Eqs.(2),(3),and(5)into Eq.(4),the effects of the wind along the cable in the tangential,normal,and rotational directions of the component can be calculated,respectively,as

    where d is the maximum dimension of the aerial surface of the cable,and CL,CD,and CMare respectively the lift,drag,and torsional coefficients,which are the functions of the crosssectional shape and the angle of attack.

    According to Hamilton’s principle,

    whereΠT,ΠS,andΠWare the kinetic energy,strain energy,and external force work,respectively.The equations of motion can be obtained by applying Hamilton’s principle as follows:

    The boundary conditions of the cable are given as

    The tension and curvature expressions are respectively

    where

    Equation(11)shows that when the sag-to-span ratioD/H≤1/8,P0≥ρgL.By taking the Taylor expansion of Eq.(10),the following equation is obtained:

    The dimensionless curvature is k=KL=ρgL/P0,and can be regarded as a small perturbation parameter.By expanding Eq.(8)and omitting k2and higher-order terms,the dynamic equations of small sag are obtained as follows:

    To obtain the dimensionless governing equation of motion,the transformations of the variables and parameters are introduced as

    Substitution of these parameters into Eq.(13)yields the following equations:

    Because the vibration in the tangential direction of the suspension cable does not play a major role,the vibration in the L1direction is ignored,which yields

    therefore,

    where

    Substitution of Eq.(17)into Eq.(15)yields the following equations:

    The boundary conditions are given as

    The Galerkin method is used to separate the variables,and the partial differential equations are then transformed into ordinary differential equations:

    The in-plane vibration mode is as follows:

    with

    whereωis determined by the following characteristic equation:

    The out-of-plane vibration mode is as follows:

    The torsional mode is

    By applying the Galerkin procedure to the dimensionless governing differential equation of motion,i.e.,by substituting Eqs.(22)–(27)into Eq.(20),the three-degree-of-freedom ordinary differential equations of the cable motion are obtained as follows:

    Equation(28c)is a linear differential equation,and equations(28a)and(28b)are uncoupled.Therefore,the solution of Eq.(28c)can be substituted into the other two equations,thereby reducing the three-degree-of-freedom governing equation into a two-degree-of-freedom governing equation.According to the theory of forced vibration,the solution of Eq.(28c)yields

    where

    Substitution of Eqs.(29)and(30)into Eqs.(28a)and(28b)yields the following equations:

    By substituting the one-term expansion

    into Eq.(31)and equating the coefficient of the harmonics to zero,an algebraic equation relating the frequencyωwith the amplitudes A1and A2can be obtained.

    3.Analysis of amplitude–frequency property

    The introduction of a small perturbation parameterεinto Eq.(31)yields the following equations:

    By the method of multiple scales,the following equations are obtained:

    where T0=t and T1=εt.

    The differential operator is

    where Dk=?/?Tkand k=0,1,...

    Considering the case of principal parametric resonance,i.e.,1/2 subharmonic resonance and 2:1 internal resonance,the following expressions are obtained:

    whereσ1andσ2are two detuning parameters,andΩ1=2.0.

    By substituting Eqs.(33)–(35)into Eq.(32),the following equations are obtained:The polar form solution of Eq.(36)is

    Substitute Eq.(39)into Eq.(38)and let the secular term be zero,then the following equations will be yielded:

    The averaged equation in the polar form of the iced suspended cable is derived as

    Let A2and A3be denoted in the following forms:

    and substitute Eq.(42)into Eq.(41)and separate the real part and imaginary part,then the averaged equation in polar form will be obtained below.

    By equating the coefficients of sine and cosine in Eq.(43)to zero,the relationship between the amplitude–frequency characteristics is obtained as follows:

    To study the complex dynamics of the iced cable,the amplitude–frequency characteristics curves of system(31)are analyzed.However,the analytical solutions of system(31)are very difficult to obtain;therefore,the following two special cases are considered:

    (i)the two modes are weakly coupled;

    (ii)the two modes are strongly coupled.

    For case(i),assume a3=1 in Eq.(44a)and a2=1 in Eq.(44b),then the amplitude–frequency relationship of the weakly coupled system will be expressed as

    Figures 2 and 3 respectively present the amplitudes a2and a3versus detuning parameterσ1and B2under different values of damping coefficientμ1.The results demonstrate that the increase of the damping coefficientμ1will lead to the decrease in the amplitudes a2and a3.Moreover,figures 2 and 3 present the hardening properties of the stiffness and jump phenomenon of the amplitude based on the amplitude–frequency curve.

    Fig.2.Weak coupling amplitude–frequency(a)A1 and(b)A2 versusσ1 under different damping coefficients.

    Fig.3.Weak coupling amplitude–frequency(a)A1 and(b)A2 versus B2 under different damping coefficients.

    For case(ii),assume a3=2 in Eq.(44a)and a2=2 in Eq.(44b),then the strongly coupled system will be obtained as follows:

    Fig.4.Strong coupling amplitude-frequency(a)A1 and(b)A2 versusσ1 under different damping coefficients.

    Figures 4 and 5 respectively present the amplitudes a2and a3versus detuning parametersσ1and B2under different values of damping coefficientμ1.Like case(i),with the increase of the damping coefficientμ1,the amplitudes a2and a3decrease.In addition,with the constant change of parameters,the amplitude of the system will present a jump phenomenon.It can be seen that the amplitudes in case(ii)are larger than those in case(i),which is due to the differences between the two cases.

    Fig.5.Strong coupling amplitude–frequency(a)A1 and(b)A2 versus B2 under different damping coefficients.

    4.Numerical simulations of periodic and chaotic motions

    Numerical simulations are performed to determine the periodic motion and chaotic motion of the iced suspended cable.The numerical integration of Eq.(31)is performed by using the Runge–Kutta algorithm with variable precision∈[0.0001,0.01].[38]More specifically,the transient effects are avoided by dropping the first 60% of the simulating time:2000 s.The excitation V is a main controlling parameter in the research of the nonlinear dynamic behaviors of cables,and is selected as the controlling parameter to discover the complicated nonlinear dynamics.The parameters are set to be as follows:E=0.9×1011Pa,G=0.4×1011Pa,g=9.8 N/kg,L=400 m,ρ=0.92 kg/m,ρair=1.2 kg/m3,R=10×10?3m,and um=1 m.

    In this section,the emphasis is placed on the influence of external excitation on the motion of a three-degree-of-freedom iced suspended cable structure.The horizontal wind speed V is taken as the control parameter.The amplitude of the wind speed pulse is constant,and the amplitude umof the bearing motion is assumed to be a constant value.The dependence of the three-degree-of-freedom iced cable on the horizontal wind speed V is investigated.Considering the parametric and external excitation on the iced cable,there exist abundant dynamic behaviors.The dynamic motions of the iced cable under different wind speeds are calculated based on the torsional vibration of the three-degree-of-freedom system which occurs in a single cycle.Table 1 exhibits the typical examples of the motion forms of the iced cable under different wind speeds.The bifurcation diagrams of the two degrees of freedom v2and v3versus wind speed V are presented in Figs.6(a)and 6(b),respectively and figure 6(c)shows the largest Lyapunov exponent of v2.When V∈[0.78,0.88],V∈[1.36,1.75],and V>1.9,the system exhibits the typical characteristics of chaotic motion.

    Table 1.Typical examples of motion forms of iced cable under different wind speeds.

    Fig.6.Bifurcation diagram of v2 and v3 under different values of wind speed V1.

    Fig.7.Periodic motion of iced cable obtained when V=0.83 m/s.

    Fig.8.Multi-periodic motion of iced cable obtained when V=0.94 m/s.

    Fig.9.Chaotic motion of iced cable obtained when V=1.17 m/s.

    In each of Figs.7–9,panels(a)and(c)respectively show the phase portraits on the planes(v2,˙v2)and(v3,˙v3),panels(b)and(d)respectively represent the waveforms on the planes(t,v2)and(t,v3),and panels(e)and(f)respectively display the three-dimensional phase portrait in space(v2,˙v2,v3)and the frequency spectrum on plane(frequency,v2).It should be noted that the frequency spectrum can be used to distinguish between periodic motion and chaotic motion.The results reveal that there exist one-periodic motion(Fig.7),multiperiodic motion(Fig.8),and chaotic motion(Fig.9)when the system is under the action of different resonance mechanisms,including in-plane parametric resonance and out-of-plane superharmonic resonance.Moreover,the displacement of the vibration is found to be enhanced with the increase of the wind speed.

    5.Conclusions

    In this paper,the theory of nonlinear dynamics is used to investigate the wind-excited vibration response of an iced suspended cable.The effects of the system under both external and parametric excitation are investigated.Using Hamilton’s principle,a dynamic model of a three-degree-of-freedom iced suspended cable is first established.Then,the approximate equation in the case of small sag is derived,as shown in the dimensionless equation.The amplitude–frequency characteristics are obtained using the harmonic balance method.The perturbation equation is analyzed using the method of multiple scales,and the averaged equation is derived and used to capture the behaviors of the system under the action of inplane parametric resonance and out-of-plane superharmonic resonance.Based on the numerical simulation,the nonlinear vibration responses of the iced cable under parametric excitation and external excitation caused by horizontal wind are determined.The numerical results reveal that the iced suspended cable presents a periodic motion,multi-periodic motion,and chaotic motion under in-plane parametric resonance and out-of-plane main resonance.It is found that with the increase of the wind speed,the behavior of the system changes from a one-periodic motion into a multi-periodic motion,and finally into a chaotic motion.Compared with the results of a two-degree-of-freedom iced suspended cable,the effect of torsional vibration on the system cannot be neglected.Furthermore,theoretical analysis reveals that the vibration of the iced cable can be effectively controlled,which could be a useful technique to ensure the safety of the cable structure.

    猜你喜歡
    張偉
    文化名家
    ——張偉
    昨天 今天
    金秋(2020年14期)2020-10-28 04:15:40
    Solvability for Fractional p-Laplacian Differential Equation with Integral Boundary Conditions at Resonance on Infinite Interval
    Relationship between characteristic lengths and effective Saffman length in colloidal monolayers near a water-oil interface?
    藝術(shù)百家:張偉 何是雯
    看得到的轉(zhuǎn)變
    中華家教(2018年9期)2018-10-19 09:30:00
    藝術(shù)廣角
    數(shù)學(xué)潛能知識月月賽
    Organotemplate-free Hydrothermal Synthesis of SUZ-4 Zeolite: Influence of Synthesis Conditions*
    真的記住了
    故事會(2014年10期)2014-05-14 15:24:18
    国产av国产精品国产| 啦啦啦视频在线资源免费观看| av又黄又爽大尺度在线免费看| 日本vs欧美在线观看视频| 最新的欧美精品一区二区| 国产精品av久久久久免费| 国产在线免费精品| 国产伦理片在线播放av一区| 日韩欧美一区视频在线观看| 999精品在线视频| 丝袜脚勾引网站| 热re99久久国产66热| 夫妻午夜视频| 亚洲内射少妇av| 欧美日韩视频精品一区| 叶爱在线成人免费视频播放| 午夜福利一区二区在线看| 午夜精品国产一区二区电影| 麻豆精品久久久久久蜜桃| 亚洲国产精品成人久久小说| 亚洲综合精品二区| 亚洲四区av| 久久精品国产综合久久久| 黑人欧美特级aaaaaa片| 一级片'在线观看视频| 亚洲av成人精品一二三区| 久久99精品国语久久久| 国产熟女欧美一区二区| 国产一区二区激情短视频 | 超碰成人久久| 啦啦啦视频在线资源免费观看| 制服人妻中文乱码| 亚洲精品国产一区二区精华液| 视频区图区小说| 大香蕉久久成人网| 最新的欧美精品一区二区| 母亲3免费完整高清在线观看 | 亚洲精品aⅴ在线观看| 深夜精品福利| 一本一本久久a久久精品综合妖精 国产伦在线观看视频一区 | 男人舔女人的私密视频| 一个人免费看片子| 18禁动态无遮挡网站| 丝袜喷水一区| av在线app专区| 另类精品久久| 午夜激情av网站| 99九九在线精品视频| 中文字幕最新亚洲高清| 亚洲色图综合在线观看| av国产精品久久久久影院| 午夜老司机福利剧场| 国产精品一区二区在线不卡| 亚洲欧美成人精品一区二区| www.自偷自拍.com| 丝袜脚勾引网站| 国产精品久久久久久av不卡| 亚洲欧洲精品一区二区精品久久久 | 伊人亚洲综合成人网| 不卡视频在线观看欧美| 日本91视频免费播放| 晚上一个人看的免费电影| 男人爽女人下面视频在线观看| 亚洲 欧美一区二区三区| √禁漫天堂资源中文www| 欧美bdsm另类| 亚洲精品视频女| 大陆偷拍与自拍| 伦精品一区二区三区| 女人久久www免费人成看片| 99精国产麻豆久久婷婷| 深夜精品福利| 欧美+日韩+精品| 久久av网站| 久久狼人影院| 少妇的逼水好多| 精品国产乱码久久久久久男人| 欧美激情极品国产一区二区三区| 天天操日日干夜夜撸| 高清黄色对白视频在线免费看| 满18在线观看网站| 日本-黄色视频高清免费观看| 免费观看av网站的网址| 99国产综合亚洲精品| 中文字幕另类日韩欧美亚洲嫩草| 岛国毛片在线播放| 久久久久国产网址| 欧美最新免费一区二区三区| 女人久久www免费人成看片| 国产成人精品久久二区二区91 | 国产精品久久久av美女十八| 日韩制服丝袜自拍偷拍| 亚洲国产欧美日韩在线播放| 老汉色∧v一级毛片| 国产精品蜜桃在线观看| 一级a爱视频在线免费观看| 久久精品夜色国产| 在线 av 中文字幕| 一二三四在线观看免费中文在| 在线 av 中文字幕| 亚洲精品成人av观看孕妇| 美国免费a级毛片| 日韩免费高清中文字幕av| 国产精品久久久久久精品电影小说| 国产在视频线精品| 我要看黄色一级片免费的| 国产片特级美女逼逼视频| 日本欧美国产在线视频| a级毛片黄视频| 亚洲欧美一区二区三区国产| 少妇 在线观看| 精品少妇一区二区三区视频日本电影 | 免费看不卡的av| 热99久久久久精品小说推荐| 欧美激情 高清一区二区三区| www.av在线官网国产| 亚洲精品美女久久久久99蜜臀 | 两个人看的免费小视频| 自拍欧美九色日韩亚洲蝌蚪91| 免费av中文字幕在线| 久久久久国产一级毛片高清牌| 欧美精品国产亚洲| 国产精品一区二区在线不卡| 成人漫画全彩无遮挡| 欧美中文综合在线视频| 黑人猛操日本美女一级片| 午夜免费鲁丝| 亚洲婷婷狠狠爱综合网| 水蜜桃什么品种好| 99久久人妻综合| 老女人水多毛片| 国产精品不卡视频一区二区| 欧美变态另类bdsm刘玥| 1024香蕉在线观看| 日韩精品免费视频一区二区三区| 日本欧美视频一区| 久久精品国产a三级三级三级| 妹子高潮喷水视频| 久久精品国产亚洲av天美| 中文字幕制服av| 亚洲精品成人av观看孕妇| 欧美日韩亚洲高清精品| 国产老妇伦熟女老妇高清| 国精品久久久久久国模美| 男女国产视频网站| 成年女人毛片免费观看观看9 | 深夜精品福利| 在线精品无人区一区二区三| 亚洲av日韩在线播放| 日本av免费视频播放| 精品久久蜜臀av无| 制服人妻中文乱码| 亚洲情色 制服丝袜| 中国国产av一级| 精品一区在线观看国产| 欧美中文综合在线视频| 午夜久久久在线观看| 夫妻午夜视频| 国产精品一区二区在线不卡| 久久99热这里只频精品6学生| 最近中文字幕高清免费大全6| 免费观看性生交大片5| 卡戴珊不雅视频在线播放| 高清不卡的av网站| 一区二区三区四区激情视频| 天堂8中文在线网| 国精品久久久久久国模美| 美女福利国产在线| 一级毛片我不卡| 国产老妇伦熟女老妇高清| 免费看av在线观看网站| 中文字幕制服av| 乱人伦中国视频| 97在线人人人人妻| 美女中出高潮动态图| 日韩,欧美,国产一区二区三区| 香蕉丝袜av| 国产黄色免费在线视频| 日韩不卡一区二区三区视频在线| 各种免费的搞黄视频| 色视频在线一区二区三区| 久久国内精品自在自线图片| 亚洲国产欧美日韩在线播放| 国产又爽黄色视频| 亚洲精华国产精华液的使用体验| 国产白丝娇喘喷水9色精品| 国产高清不卡午夜福利| 汤姆久久久久久久影院中文字幕| 99久久中文字幕三级久久日本| 欧美精品av麻豆av| 久久久久久久精品精品| 我要看黄色一级片免费的| 蜜桃国产av成人99| 男人舔女人的私密视频| 亚洲伊人色综图| 亚洲久久久国产精品| 波野结衣二区三区在线| 久久99精品国语久久久| 久久精品久久久久久噜噜老黄| 十分钟在线观看高清视频www| 青春草亚洲视频在线观看| 久久午夜综合久久蜜桃| 黄色毛片三级朝国网站| 免费日韩欧美在线观看| 日韩 亚洲 欧美在线| 99久国产av精品国产电影| 国产亚洲一区二区精品| av在线app专区| 国产不卡av网站在线观看| av.在线天堂| 中文欧美无线码| 最近最新中文字幕免费大全7| 青春草亚洲视频在线观看| 秋霞在线观看毛片| av在线app专区| 欧美老熟妇乱子伦牲交| 国产男女超爽视频在线观看| 熟女电影av网| 亚洲人成电影观看| 国产成人91sexporn| 熟女少妇亚洲综合色aaa.| 黄色毛片三级朝国网站| 少妇熟女欧美另类| av在线app专区| 欧美老熟妇乱子伦牲交| 国产精品av久久久久免费| 久久久久久久久久久久大奶| 99香蕉大伊视频| 亚洲精品国产一区二区精华液| 国产精品女同一区二区软件| 色播在线永久视频| 亚洲精品日本国产第一区| 人妻系列 视频| 日日啪夜夜爽| 欧美变态另类bdsm刘玥| 久久精品人人爽人人爽视色| 成人毛片60女人毛片免费| 黄片无遮挡物在线观看| 国产97色在线日韩免费| 国产日韩一区二区三区精品不卡| av女优亚洲男人天堂| 国产色婷婷99| 欧美人与善性xxx| 成年美女黄网站色视频大全免费| 久久精品亚洲av国产电影网| 99热网站在线观看| 一二三四中文在线观看免费高清| 亚洲精品国产av蜜桃| 国产一区二区激情短视频 | 捣出白浆h1v1| 成年动漫av网址| 日本黄色日本黄色录像| 男女免费视频国产| 国产黄频视频在线观看| av片东京热男人的天堂| 又粗又硬又长又爽又黄的视频| 色吧在线观看| 成人18禁高潮啪啪吃奶动态图| 午夜福利影视在线免费观看| 国产成人欧美| 日韩精品免费视频一区二区三区| 国产av精品麻豆| 超色免费av| 高清av免费在线| 亚洲成人手机| 欧美 日韩 精品 国产| 久久亚洲国产成人精品v| 国产成人精品久久久久久| 日本色播在线视频| 久久热在线av| 久久精品夜色国产| 国产一区有黄有色的免费视频| 美女脱内裤让男人舔精品视频| 最黄视频免费看| 久久99热这里只频精品6学生| 亚洲三区欧美一区| 久久久精品免费免费高清| 一级片免费观看大全| 69精品国产乱码久久久| 久久久久人妻精品一区果冻| 一边摸一边做爽爽视频免费| 80岁老熟妇乱子伦牲交| 国产成人精品无人区| 性少妇av在线| xxxhd国产人妻xxx| 国产精品久久久久久久久免| 涩涩av久久男人的天堂| 成年人免费黄色播放视频| 午夜日本视频在线| 午夜久久久在线观看| 免费在线观看视频国产中文字幕亚洲 | 国产亚洲午夜精品一区二区久久| 热re99久久国产66热| 妹子高潮喷水视频| 高清在线视频一区二区三区| 不卡视频在线观看欧美| 美女大奶头黄色视频| 亚洲av.av天堂| 亚洲四区av| 久久精品国产鲁丝片午夜精品| kizo精华| 满18在线观看网站| 亚洲一级一片aⅴ在线观看| 美女福利国产在线| 中文字幕制服av| 不卡视频在线观看欧美| 在线观看免费日韩欧美大片| 日韩制服骚丝袜av| 91在线精品国自产拍蜜月| 亚洲五月色婷婷综合| 人妻 亚洲 视频| 国产女主播在线喷水免费视频网站| 亚洲美女视频黄频| 国产成人av激情在线播放| 国产亚洲一区二区精品| 亚洲国产精品999| 午夜日本视频在线| 日韩av免费高清视频| 一区二区三区乱码不卡18| 久久久久久人人人人人| 一区福利在线观看| 90打野战视频偷拍视频| 最黄视频免费看| 黄色怎么调成土黄色| 亚洲精品中文字幕在线视频| 伦精品一区二区三区| 制服丝袜香蕉在线| 午夜激情久久久久久久| 老司机亚洲免费影院| 97在线人人人人妻| 久久久久久久久久久免费av| 男人操女人黄网站| 在线观看美女被高潮喷水网站| 伊人久久大香线蕉亚洲五| 亚洲av电影在线进入| 中国三级夫妇交换| 好男人视频免费观看在线| 新久久久久国产一级毛片| 夫妻性生交免费视频一级片| 国产欧美日韩综合在线一区二区| 两个人看的免费小视频| 国产成人欧美| 看十八女毛片水多多多| 国产精品秋霞免费鲁丝片| 免费在线观看视频国产中文字幕亚洲 | av天堂久久9| 99热全是精品| 精品少妇一区二区三区视频日本电影 | 纯流量卡能插随身wifi吗| 亚洲,欧美,日韩| 99香蕉大伊视频| 国产成人免费无遮挡视频| 精品99又大又爽又粗少妇毛片| 中文字幕人妻丝袜一区二区 | 熟女av电影| 91午夜精品亚洲一区二区三区| 男女高潮啪啪啪动态图| 日韩一区二区三区影片| 在线精品无人区一区二区三| 色婷婷av一区二区三区视频| 欧美国产精品va在线观看不卡| 国产日韩欧美亚洲二区| 国产熟女欧美一区二区| 一本色道久久久久久精品综合| 国产精品熟女久久久久浪| 日本wwww免费看| 亚洲国产最新在线播放| 国产又色又爽无遮挡免| 久久99精品国语久久久| 看免费av毛片| www.自偷自拍.com| 熟女电影av网| av又黄又爽大尺度在线免费看| 免费日韩欧美在线观看| 久久精品熟女亚洲av麻豆精品| 欧美精品一区二区大全| 久久久精品94久久精品| 韩国av在线不卡| 欧美老熟妇乱子伦牲交| 街头女战士在线观看网站| 在线观看美女被高潮喷水网站| 亚洲精品中文字幕在线视频| 亚洲精品美女久久久久99蜜臀 | 2021少妇久久久久久久久久久| 在线观看一区二区三区激情| 亚洲国产精品一区二区三区在线| 大片电影免费在线观看免费| 人妻少妇偷人精品九色| 捣出白浆h1v1| 最近最新中文字幕免费大全7| 2021少妇久久久久久久久久久| 国产成人午夜福利电影在线观看| 午夜日本视频在线| 日本av手机在线免费观看| 欧美成人午夜免费资源| 叶爱在线成人免费视频播放| 一本—道久久a久久精品蜜桃钙片| 亚洲婷婷狠狠爱综合网| 丝瓜视频免费看黄片| 黑丝袜美女国产一区| 精品久久蜜臀av无| 下体分泌物呈黄色| 亚洲在久久综合| 99热国产这里只有精品6| 国产成人免费无遮挡视频| tube8黄色片| 精品人妻偷拍中文字幕| 成人漫画全彩无遮挡| 亚洲精品在线美女| 女性生殖器流出的白浆| 色吧在线观看| 午夜日韩欧美国产| 青春草视频在线免费观看| 在线观看免费日韩欧美大片| 热re99久久国产66热| 中文字幕制服av| 大话2 男鬼变身卡| av一本久久久久| 美女视频免费永久观看网站| 老汉色av国产亚洲站长工具| 成人黄色视频免费在线看| 王馨瑶露胸无遮挡在线观看| 亚洲精品一二三| 免费播放大片免费观看视频在线观看| 欧美 亚洲 国产 日韩一| 亚洲,欧美,日韩| av片东京热男人的天堂| 久久人人爽人人片av| 伦理电影大哥的女人| 有码 亚洲区| 国产深夜福利视频在线观看| 国产精品偷伦视频观看了| 国语对白做爰xxxⅹ性视频网站| 亚洲三级黄色毛片| 看非洲黑人一级黄片| 亚洲av免费高清在线观看| 熟女av电影| 精品一区二区三区四区五区乱码 | 国产精品久久久久久精品古装| 免费高清在线观看日韩| 熟女少妇亚洲综合色aaa.| 成人二区视频| 成人亚洲欧美一区二区av| 亚洲欧洲日产国产| 女人被躁到高潮嗷嗷叫费观| 你懂的网址亚洲精品在线观看| 欧美少妇被猛烈插入视频| 中文字幕亚洲精品专区| 国产成人精品久久久久久| 精品第一国产精品| 日日啪夜夜爽| 视频在线观看一区二区三区| 91精品国产国语对白视频| 高清黄色对白视频在线免费看| 熟女电影av网| 天堂8中文在线网| 新久久久久国产一级毛片| 久久久久精品久久久久真实原创| 成人亚洲精品一区在线观看| 一本—道久久a久久精品蜜桃钙片| 国产精品99久久99久久久不卡 | 成人二区视频| 精品国产乱码久久久久久男人| 久久影院123| 欧美成人精品欧美一级黄| 国产免费福利视频在线观看| 亚洲国产欧美网| 亚洲久久久国产精品| 精品久久蜜臀av无| 国产精品蜜桃在线观看| 日韩一本色道免费dvd| 一二三四中文在线观看免费高清| 久久这里有精品视频免费| 久久久久久伊人网av| 国产精品久久久久久精品古装| 亚洲激情五月婷婷啪啪| 一级毛片我不卡| 中文字幕人妻丝袜一区二区 | 中文精品一卡2卡3卡4更新| 精品亚洲乱码少妇综合久久| 欧美精品一区二区免费开放| 国产精品久久久久久精品电影小说| 成人免费观看视频高清| 一级毛片电影观看| 久久久a久久爽久久v久久| 欧美日韩一级在线毛片| 免费看av在线观看网站| 国产精品偷伦视频观看了| 亚洲欧美一区二区三区久久| 国产不卡av网站在线观看| 18禁裸乳无遮挡动漫免费视频| 婷婷成人精品国产| 天天操日日干夜夜撸| 最近中文字幕高清免费大全6| 精品国产一区二区三区四区第35| 69精品国产乱码久久久| 国产老妇伦熟女老妇高清| 岛国毛片在线播放| 丰满乱子伦码专区| 97在线人人人人妻| 成人手机av| 女性被躁到高潮视频| 岛国毛片在线播放| 黑人猛操日本美女一级片| av在线app专区| 国产一区二区三区av在线| 我要看黄色一级片免费的| 精品人妻熟女毛片av久久网站| 日韩中文字幕视频在线看片| 欧美成人精品欧美一级黄| 超色免费av| 少妇 在线观看| 男的添女的下面高潮视频| 超碰成人久久| 夫妻性生交免费视频一级片| 色哟哟·www| 日本91视频免费播放| av免费观看日本| 亚洲欧美一区二区三区国产| 久久久久久久久久人人人人人人| 亚洲国产精品一区三区| 日韩视频在线欧美| 美女主播在线视频| 欧美成人午夜精品| 午夜福利在线免费观看网站| 我的亚洲天堂| av视频免费观看在线观看| 少妇人妻久久综合中文| 一级a爱视频在线免费观看| 日韩,欧美,国产一区二区三区| 男女边吃奶边做爰视频| 亚洲精品一区蜜桃| 欧美精品一区二区免费开放| 亚洲精品成人av观看孕妇| 亚洲欧美一区二区三区黑人 | 男女无遮挡免费网站观看| 中国三级夫妇交换| 极品少妇高潮喷水抽搐| 桃花免费在线播放| 久久久久久久大尺度免费视频| 成人毛片60女人毛片免费| 久久国产亚洲av麻豆专区| 欧美变态另类bdsm刘玥| 爱豆传媒免费全集在线观看| 黑人巨大精品欧美一区二区蜜桃| 欧美日韩精品成人综合77777| 国产精品99久久99久久久不卡 | 精品一品国产午夜福利视频| 国产欧美日韩综合在线一区二区| 热re99久久精品国产66热6| 五月伊人婷婷丁香| 中文字幕亚洲精品专区| 精品人妻偷拍中文字幕| 久久国内精品自在自线图片| 欧美日本中文国产一区发布| 午夜久久久在线观看| 精品99又大又爽又粗少妇毛片| 午夜日本视频在线| 亚洲av免费高清在线观看| 欧美人与善性xxx| 亚洲精品国产色婷婷电影| 美女午夜性视频免费| 在线观看三级黄色| 亚洲三区欧美一区| 中文天堂在线官网| 国产精品久久久久久精品电影小说| 看免费成人av毛片| 我的亚洲天堂| 成人亚洲精品一区在线观看| 人成视频在线观看免费观看| 日本爱情动作片www.在线观看| 久久久久国产网址| 在线观看美女被高潮喷水网站| 日本黄色日本黄色录像| 少妇猛男粗大的猛烈进出视频| 叶爱在线成人免费视频播放| 亚洲欧美一区二区三区久久| 成年美女黄网站色视频大全免费| a 毛片基地| 亚洲一码二码三码区别大吗| 人妻少妇偷人精品九色| 亚洲精品日韩在线中文字幕| 热re99久久精品国产66热6| 久久精品久久久久久噜噜老黄| 18禁观看日本| 久久这里只有精品19| 国产一区有黄有色的免费视频| 国产成人精品婷婷| 日韩欧美一区视频在线观看| 国产高清国产精品国产三级| 国产一区二区三区综合在线观看| 午夜免费鲁丝| 国产精品二区激情视频| av一本久久久久| 午夜福利一区二区在线看| 可以免费在线观看a视频的电影网站 | 久久国产精品大桥未久av| 一级毛片我不卡| 免费观看av网站的网址| 色播在线永久视频| 亚洲经典国产精华液单| 久久午夜福利片| 亚洲欧美精品自产自拍| 在线 av 中文字幕| 男女下面插进去视频免费观看| 国产黄色视频一区二区在线观看| 日韩一本色道免费dvd| 国产精品国产三级国产专区5o| 国产黄频视频在线观看| 亚洲国产成人一精品久久久| 亚洲国产av影院在线观看| 天天躁狠狠躁夜夜躁狠狠躁| 日韩中文字幕视频在线看片| 成年动漫av网址| 制服人妻中文乱码|