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Unit 5 Mechanical Vibrations A mechanical vibration is an oscillatory，periodically repeated motion of a particle or body about a position of equilibrium .An engineer is frequently confronted with the problem of machinery and structures.机械振动是质点或物体在其平衡位置附近所作的震荡的，周期性的往复运动。 工程师经常面临机械振动的问题，因为在某种程度上他们在几乎所有的机械和结构中遇到过这些问题Most vibrations are undesirable in machines and structures because they produce excessive stresses or repeated stresses; 大多数的震动在机械和结构中是不希望存在的，因为震动会产生附加应力或者交变应力。cause added wear;increase bearing loads; induce fatigue;create acute passenger discomfort in planes，ships，trains，buses，and automobiles;and absorb energy that could otherwise do useful work. 引起额外磨损，增大轴承载荷，导致疲劳破坏，使飞机、船、火车及汽车上的乘客产生严重的不舒服感，并且振动会吸收本可以做有用功的能量。The collapse of the Tacoma Narrows Bridge in 1940 is an example of structural failure due to excessive stresses produced by vibrations. The accuracy of precision instruments，tools，and machines may be impaired by excessive vibrations. 1940年（发生的）塔克马窄桥的垮塌事件就是一个因为震动产生的附加应力导致结构失效的例子。 精密仪器、工具和电脑的准确性可能被附加的震动所损坏 Rotating machine parts require careful balancing in order to prevent damage from vibrationoriginal text 旋转机械零件需要仔细的平衡,以防止振动的造成的伤害。 When part of the propeller of an airplane is shot off or breaks off in flight the propeller is no longer symmetrical，and the vibrations from the engine may tear the engine from the plane unless it can be stopped in time.original text 当飞机的螺旋桨的（某）部分在飞行中被打掉或断裂，（这时）螺旋桨不再是对称的，来自引擎的振动会把引擎从飞机上扯下来,除非它可以被及时的停止。 The vibrations produced in an automobile by the engine or by driving on rough roads set up repeated stresses in certain parts that can eventually lead to fatigue failure of the members.original text 由引擎产生的震动或由于在崎岖的道路上行驶产生的震动施加在某部分的交变应力最终会使其发生疲劳失效 When a particle or body that is supported by a system of springs，a shaf t，a beam，or any other elastic system is disturbed from its position of equilibrium by the application and sudden removal of an additional force the particle or body will vibrate. original text 当被弹簧，杆，线或者其他弹性系统支撑的质点或物体，在被干扰或者受到外力的作用使其偏离平衡位置，质点或物体就会发生震动。translated text23Unit 5 Mechanical Vibrations Some common example are the vertical vibratory motion of body A in Fig.1.19.(a) when it is displaced vertically from its equilibrium position on a helical spring and then released ; translated text25Unit 5 Mechanical Vibrations the vertical vibratory motion of body B of Fig.1.19.(b) when it is displaced from its equilibrium position on a flexibletranslated text27Unit 5 Mechanical Vibrations and the motion of the pendulum bob C in Fig.1.19.(c) as it swings in a vertical plane when supported by a cord of negligible massoriginal text28Unit 5 Mechanical Vibrationstranslated text29Unit 5 Mechanical Vibrations Fig .1 .20(a)shows a body W suspended from a support by a spring and hanging at its equilibrium position. If the body is pulled from its equilibrium position by a force F and released，it will，in the absence of any frictional forces，continue to oscillate about the equilibrium position indefinitely .original text 图1.20 a中所示的物体W，悬挂弹簧上，处于平衡位置。当它在力F的作用下拉离平衡位置时被释放，在没有摩擦阻力时，它将在平衡位置附近做连续性不断地摆动。translated text31Unit 5 Mechanical Vibrations Fig.1.20 (b)shows a graph of the displacement，y，of the body W from its equilibrium position as a function of time . One of the fundamental properties of mechanical vibrations is that the motion repeats itself at definite interval of time . The period ,T ,of the oscillation is the minimum amount of elapsed time before the motion starts to repeat itself . The motion completed in one period cycle . original text32Unit 5 Mechanical Vibrations 图1.20b 中所示为物体W偏离平衡位置的距离y对时间的图像。机械振动的基本内容之一就是在一段时间内的重复运动。震动的周期，T，是它开始重复运动之前，运动时间的最小值。运动在一个周期内完成。translated text33Unit 5 Mechanical Vibrations The frequency，f，of the oscillation is the number of cycles which occur in a given unit of time ;the customary unit is cycles per second，cps，or hertz，Hz，It should be noted that the frequency is the reciprocal of the period，or，in equation form，f=1/Toriginal text34Unit 5 Mechanical Vibrations 震动的频率，f，是单位时间内所做的循环的次数。常用的单位是周期/秒，cps，赫兹，hz。值得注意的是，频率和周期是互相联系的或者说，用一个方程式f=1/T。translated text35Unit 5 Mechanical Vibrations The amplitude，A，of the oscillation is the maximum displacement，either linear or angular，of the body from its equilibrium position.original text36Unit 5 Mechanical Vibrations 震动的振幅，A，是距其平衡位置（震动的）最大位移，不管是直线运动还是摆动。translated text37Unit 5 Mechanical VibrationsMechanical vibrations which are maintained by elastic，and sometimes gravity，forces are called free vibrations. Once started，a free vibration，frequently called a natural vibration，continues to oscillate at its natural frequency. original text38Unit 5 Mechanical Vibrations 被松紧带保持的机械振动，有时同时在重力，及其他力的作用下被称作自由振动。一旦开始，自由振动经常被称作固有振动，连续的以它的固有频率摆动。translated text39Unit 5 Mechanical Vibrations A forced vibration is produced and maintained by a periodic exciting force external to the system，and it takes place at the frequency of the exciting force.If the system is nearly frictionless and contains no dissipative elements，the amplitude of the forced oscillation will become very large when the frequency of the exciting force is close to the natural frequency of the system.original text40Unit 5 Mechanical Vibrations 受迫振动是振动系统在周期性的外力作用下产生并保持的，并以外力的频率运动。如果系统是无摩擦的而且不包含任何能量损失，在驱动力的频率接近固有频率的时候是，受迫振动的振幅会变得越来越大。translated text41Unit 5 Mechanical Vibrations Thus, although the frequency of a forced vibration is independent of the natural frequency of the elastic system，the resulting amplitude is affected by both frequencies. Vibrations are also classified as damped or undamped . When friction，air resistance，viscous damping，and all other resisting forces are negligible the vibration is undamped. original text42Unit 5 Mechanical Vibrations 因此，尽管受迫振动的频率和弹性系统的固有频率无关，但是产生的振幅却受这两个频率的影响。振动也可以分类为阻尼振荡和无阻尼振荡。当摩擦力，空气阻力，粘滞阻力，及其他阻力可忽略时，这时的振动式无阻尼振动。translated text43Unit 5 Mechanical Vibrations When any of these effects is appreciable the body has damped vibrations. In practice there is always a frictional damping force which will eventually stop a free vibration，even though it may be neglected for many purposes.original text44Unit 5 Mechanical Vibrations当这些阻力中的任何一个不可忽略时，物体做阻尼振动。实际上，总有由摩擦力产生的阻尼力最终使自由振动停止，即使这个力可以因某种目的被忽略。translated text45Unit 5 Mechanical Vibrations If the motion of a particle or body is constrained so that its position can be completely specified by one coordinate,it is said to have a single degree of freedom. original text46Unit 5 Mechanical Vibrations 如果质点或物体的运动是被约束的，以至于它的位置完全可以用一个坐标表示，被称为具有单一的自由度。translated text47Unit 5 Mechanical Vibrations If the system can vibrate in two direction or is composed of two articles that can each vibrate independently in one direction, it is said to have two degrees of freedom because two coordinates are required to specify the position of the system at any instant. original text48Unit 5 Mechanical Vibrations 如果系统可以在两个方向振动，或者由可分别在一个方向上单独振动的两个运动组成的，则被成为有两个自由度，因为任意时刻的系统位置需要两个坐标指定。translated text49Unit 5 Mechanical Vibrations For example, a system composed by a spring as indicated in Fig.1.21(a), which vibrated in a vertical direction only, has one degree of freedom. original text50Unit 5 Mechanical Vibrations 例如，如图1.21(a)中，由一个弹簧组成的只在垂直方向上震动的系统，有一个自由度。translated text51Unit 5 Mechanical Vibrations A system composed of two particles which move vertically and are supported as indicated in Fig.1.21(b) has two degrees of freedom because two coordinates are required to locate the particles at any instant. original text52Unit 5 Mechanical Vibrations 如图1.21(b)中，由两个质点组成的沿垂直方向运动的系统有两个自由度，因为其需要两个坐标指定任意时刻质点的位置。translated text53Unit 5 Mechanical Vibrations A system composed of one particle supported by four springs and constrained to move in a vertical plane as indicated in Fig.1.21(C) has two degrees of freedom because two coordinates are required to locate the particle in the vertical plane at any instant. original text54Unit 5 Mechanical Vibrations 如图1.21(c),由四根弹簧固定的质点组成的系统，在垂直面内运动，有两个自由度，因为其需要两个坐标指定任意时刻质点的位置。translated text55Unit 5 Mechanical Vibrations A single rigid body has，in general，six degrees of freedom，since it may have translation in three coordinate directions and it may also rotate about three coordinate axes. original text56Unit 5 Mechanical Vibrations 一个单一的刚体有六个自由度，因为它可以沿三个坐标轴平移，还可以绕三个坐标轴旋转。translated text57Unit 5 Mechanical Vibrations58
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