理论力学教学课件PPT静力学基础.ppt

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1、多媒体双语授课系统,一、理论力学的研究对象,理论力学是研究：物体机械运动一般规律的科学。所谓机械运动是指：物体在空间的位置随时间而发生变化的 一种运动形式。例如：地球的运转，车辆的行使，机器的运转等。物体的静止是机械运动的特殊形式。,二、理论力学的性质和任务,在工科院校它是一门理论性较强的技术基础课。理论力学既不是一门专业课，也不是一门单纯的基础课，在工科院校它是一门理论性较强的技术基础课，也就是说，它的理论在工程技术中有广泛的应用，凡搞工程技术的人一般都要学习这门课程。,性质:,主页,任务：（即：作用）（1）是学习后续课程（如材料力学、机械原理、机械设计等）的基础；（2）应用理论力学基本理论

2、，结合专业知识解决工程实际问题。,三、理论力学的内容 具体分为三部分：静力学、运动学、动力学 静力学：研究力系的简化合成与平衡条件；运动学：用几何的观点研究点和刚体的运动规律；动力学：研究力的作用和机械运动变化 之间的关系。,主页,Statics,Kinematics,Dynamics,Fundamentals of analytical mechanics,Fundamental knowledge of vibration,Examples,主页,basis of statics,Statics,导言,第一篇：静力学,basic force systems,general coplanar

3、 force systems,force systems in space and the center of gravity,equilibrium problems with friction,Statics,1.静力学基础,2.基本力系,3.平面力系,4.空间力系与 重心,5.摩擦平衡问 题,introduction,静力学,主页,本章学习指导,basis of statics,静力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,met

4、hods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,本章学习指导,basis of statics,静力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,在静力学中，可以把物体处于“平衡”理解为物体相对于地面保持静止或相作匀直线运动。例如：图1-1 静止的建筑物 图1-2

5、匀速行使的汽车 这些都是平衡的例子，平衡是机械运动的特殊情况。,图1-1,图1-2,Equilibrium,Rigid bodydoes not deform under load,Definition of a force,Effect of a force,Representation of a force,力的表示法,力的效应,力的定义,刚体,平衡,basis of statics,静力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,m

6、ethods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,但我们知道：任何物体受力都会发生变形。例如：车床主轴在切削过程中发生弯曲变形；车辆驶过一座桥时，桥梁发生弯曲变形，桥墩发生压缩变形；因此，“刚体”实际上是不存在的，它是一种抽象化的力学模型，至于在一个问题中能否将物体视为刚体，不仅取决于变形的大小，还取决于问题的要求。,Equilibrium,Rigid body,Definition of a force,Effect of a force,Representation of a force,力的表示法,力的效应,力的定义,刚体,

7、平衡,basis of statics,静力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,图1-3,力是物体间的相互机械作用，这种作用使物体的形态或者运动状态发生变化。,外效应：力使物体运动状态发生改变的效应-理论力学课程中研。内效应：力使物体形状发生改变的效应-材料力学等课程中研究。,Equilibrium,Rigid bo

8、dydoes not deform under load,Definition of a force,Effect of a force,Representation of a force,力的表示法,力的效应,力的定义,刚体,平衡,basis of statics,静力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,Defin

9、ition of a force,Effect of a force,Equilibrium,Rigid bodydoes not deform under load,Definition of a force,Effect of a force,Representation of a force,力的表示法,力的效应,力的定义,刚体,平衡,basis of statics,静力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods

10、of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,力是物体间的相互机械作用，这种作用使物体的形态或者运动状态发生变化。,外效应：力使物体运动状态发生改变的效应-理论力学课程中研。内效应：力使物体形状发生改变的效应-材料力学等课程中研究。,Definition of a force,Effect of a force,Equilibrium,Rigid bodydoes not deform under load,Definition of a force,Effect of a force,Representation of a force,力

11、的表示法,力的效应,力的定义,刚体,平衡,basis of statics,静力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,力是物体间的相互机械作用，这种作用使物体的形态或者运动状态发生变化。,外效应：力使物体运动状态发生改变的效应-理论力学课程中研。内效应：力使物体形状发生改变的效应-材料力学等课程中研究。,Definition

12、 of a force,Effect of a force,主页,力的三要素：大小、方向、作用点（或作用）。我们可以用如图所示的 矢量 F 表示力。或者用数学分析式表示力:其中：F1,F2,F3表示力沿直角坐标轴上的分力，它们是矢量。X、Y、Z 表示力在直角坐标轴上的投影，它们是代数量。,Equilibrium,Rigid bodydoes not deform under load,Definition of a force,Effect of a force,Representation of a force,力的表示法,力的效应,力的定义,刚体,平衡,basis of statics,静

13、力学基础,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,Representation of a force,思考：分力大小=投影？,axiom of addition and subtraction equilibrium force systems,axiom of action and reaction,axiom of equi

14、librium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,axiom of two forces equilibrium,

15、静力学基础,刚化公理,axiom of rigidization,axiom of rigidization,力的平行四边形公理,Parallelogram axiom/law,transmissibility of force,axiom of addition and subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibriu

16、m of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,1.4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,axiom of addition and subtrac

17、tion equilibrium force systems,主页,静力学基础,axiom of addition and subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibrium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom o

18、f two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,注:此公理是研究力系合成和力的分解的基础。,Parallelogram axiom/law,主页,静力学基础,答1：合力不一定大于分力。,2.力的分力与力的投影是否相等？,1.合力是否一定大于分力？,思考,axi

19、om of addition and subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibrium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,答2：在直角坐标系下分力与投影大小

20、相等，非直角坐标系下二者不相等。,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,静力学基础,思考,axiom of addition and subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibilit

21、y of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibrium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,met

22、hods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,axiom of action and reaction,主页,静力学基础,axiom of addition and subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibrium of three forces,作用力与反作用

23、力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,axiom of rigidization,静力学基础,思考,axiom of addition and

24、subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibrium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts

25、 of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,静力学基础,axiom of addition and subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and re

26、action,axiom of equilibrium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,trans

27、missibility of force,主页,静力学基础,axiom of equilibrium of three forces,axiom of addition and subtraction equilibrium force systems,axiom of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibrium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边

28、形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,静力学基础,思考：,axiom of addition and subtraction equilibrium force systems,axiom

29、of rigidization,刚化公理,transmissibility of force,Parallelogram axiom/law,axiom of action and reaction,axiom of equilibrium of three forces,作用力与反作用力公理,三力平衡定理,力的可传性,力的平行四边形公理,加减平衡力系公理,两力平衡公理,axiom of two forces equilibrium,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,commo

30、n Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,主页,静力学基础,自由体：在空间可作任意位移的物体称为自由体。非自由体：在空间位移受到限制的物体称为非自由体。,约束：限制非自由体位移的物体称为该非自由体的约束。约束反力：约束作用于非自由体(被约束体)的力，称为约束反力。,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engin

31、eering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ball-and-socket joint with frictionless,flexible Cablecord of negligible weight,constraints/supports and constraint force,free body and non-free body,自由体与非自由体,约束与约束反力,柔索,光滑接触面,光滑圆柱铰链,二力杆,光滑球铰链,滚动支座,固定铰链支座

32、,颈轴承与推轴承,链杆约束,固定端约束,cylindrical hinge with frictionless,a two-force body,sliderradial bearing or hinge and thrust bearing or hinge,hinge staff-a two-force body,Built-in(cantilever)support,主页,free body and non-free body,constraints/supports and constraint force,contact on frictionless surface,静力学基础,例

33、如：火车运行时受轨道的约束，轨道对火车车轮施加约束反力；物品 放在行李架上不会掉下来，受支架的约束，支架对物品施加约束 反力；车床主轴转动时受轴承的约束，那么轴承对轴施加约束反 力。静力学中的主要问题之一，就是要确定约束反力的大小和方 向，下面介绍几种工程中常见的几类约束，重点说明如何确定约 束反力的方向(约束力的大小由后面平衡方程求解)。,约束特性：只能承受拉力，能阻碍物体沿绳索伸长方向的位移。约束反力：方位沿绳索本身，指向背离物体，使物体受拉。例如：电棒用链条悬挂，受力如图所示：起吊机用钢丝绳起吊重物，受力如图所示。皮带轮受皮带拉力，受力如图所示,basis of statics,fund

34、amental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ball-and-socket joint with frictionless,flexible Cablecord of negligible weight,constraints/supports and constraint force,fre

35、e body and non-free body,自由体与非自由体,约束与约束反力,柔索,光滑接触面,光滑圆柱铰链,二力杆,光滑球铰链,滚动支座,固定铰链支座,颈轴承与推轴承,链杆约束,固定端约束,cylindrical hinge with frictionless,a two-force body,sliderradial bearing or hinge and thrust bearing or hinge,hinge staff-a two-force body,Built-in(cantilever)support,主页,flexible Cablecord of negligib

36、le weight,contact on frictionless surface,静力学基础,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ball-and-socket joint with frictionless,flexible Cableco

37、rd of negligible weight,constraints/supports and constraint force,free body and non-free body,自由体与非自由体,约束与约束反力,柔索,光滑接触面,光滑圆柱铰链,二力杆,光滑球铰链,滚动支座,固定铰链支座,颈轴承与推轴承,链杆约束,固定端约束,cylindrical hinge with frictionless,a two-force body,sliderradial bearing or hinge and thrust bearing or hinge,hinge staff-a two-for

38、ce body,Built-in(cantilever)support,约束特性：只能承受拉力，能阻碍物体沿绳索伸长方向的位移。约束反力：方位沿绳索本身，指向背离物体，使物体受拉。例如：电棒用链条悬挂，受力如图所示：起吊机用钢丝绳起吊重物，受力如图所示。皮带轮受皮带拉力，受力如图所示,flexible Cablecord of negligible weight,主页,contact on frictionless surface,静力学基础,约束特性：只能阻碍物体沿着接触点公法线朝向约束的位移,而不 能阻碍物体沿接触点切线方向的位移。约束反力:方向沿接触点的公法线而指向被约束物体。,basi

39、s of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ball-and-socket joint with frictionless,flexible Cablecord of negligible weight,constraints/supports and con

40、straint force,free body and non-free body,自由体与非自由体,约束与约束反力,柔索,光滑接触面,光滑圆柱铰链,二力杆,光滑球铰链,滚动支座,固定铰链支座,颈轴承与推轴承,链杆约束,固定端约束,cylindrical hinge with frictionless,a two-force body,sliderradial bearing or hinge and thrust bearing or hinge,hinge staff-a two-force body,Built-in(cantilever)support,contact on frict

41、ionless surface,contact on frictionless surface,主页,静力学基础,约束结构：两个物体A、B上钻同样大小的圆孔，并用圆柱销钉C 穿入圆 孔,将两个物体连接起来.约束特性：不能阻碍绕销钉轴线相对转动，可以阻碍沿半径方向（垂直 于轴线的任何方向）的任何位移。约束反力：在垂直于销钉轴线的平面内 并通过圆心，但方位和指向 不能确定。一般画受力图时 用F，表示，或者用两个正 交分力Fx,Fy表示，如图1-17 所示。,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of sta

42、tics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ball-and-socket joint with frictionless,flexible Cablecord of negligible weight,constraints/supports and constraint force,free body and non-free body,自由体与非自由体,约束与约束反力,柔索,光滑接触面

43、,光滑圆柱铰链,二力杆,光滑球铰链,滚动支座,固定铰链支座,颈轴承与推轴承,链杆约束,固定端约束,cylindrical hinge with frictionless,a two-force body,sliderradial bearing or hinge and thrust bearing or hinge,hinge staff-a two-force body,Built-in(cantilever)support,contact on frictionless surface,主页,cylindrical hinge with frictionless,静力学基础,注意：在画受

44、力图时，一般将A、B 两物体分开并将销钉 C 与其中 的一个物体相连。,约束结构：两个物体A、B上钻同样大小的圆孔，并用圆柱销钉C 穿入圆 孔,将两个物体连接起来.约束特性：不能阻碍绕销钉轴线相对转动，可以阻碍沿半径方向（垂直 于轴线的任何方向）的任何位移。约束反力：在垂直于销钉轴线的平面内 并通过圆心，但方位和指向 不能确定。一般画受力图时 用F，表示，或者用两个正 交分力Fx,Fy表示，如图所示。,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in en

45、gineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ball-and-socket joint with frictionless,flexible Cablecord of negligible weight,constraints/supports and constraint force,free body and non-free body,自由体与非自由体,约束与约束反力,柔索,光滑接触面,光滑圆柱铰链,二力杆,光滑球铰链,滚动支座,固定铰

46、链支座,颈轴承与推轴承,链杆约束,固定端约束,cylindrical hinge with frictionless,a two-force body,sliderradial bearing or hinge and thrust bearing or hinge,hinge staff-a two-force body,Built-in(cantilever)support,contact on frictionless surface,主页,cylindrical hinge with frictionless,静力学基础,注意：在画受力图时，一般将A、B 两物体分开并将销钉 C 与其中

47、 的一个物体相连。,约束结构：两个物体A、B上钻同样大小的圆孔，并用圆柱销钉C 穿入圆 孔,将两个物体连接起来.约束特性：不能阻碍绕销钉轴线相对转动，可以阻碍沿半径方向（垂直 于轴线的任何方向）的任何位移。约束反力：在垂直于销钉轴线的平面内 并通过圆心，但方位和指向 不能确定。一般画受力图时 用F，表示，或者用两个正 交分力Fx,Fy表示，如图1-17 所示。注意：在画受力图时，一般将A、B 两物 体分开并将销钉 C 与其中的一个 物体相连。,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,

48、common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ball-and-socket joint with frictionless,flexible Cablecord of negligible weight,constraints/supports and constraint force,free body and non-free body,自由体与非自由体,约束与约束反力,柔索,光滑接触面,光滑圆柱

49、铰链,二力杆,光滑球铰链,滚动支座,固定铰链支座,颈轴承与推轴承,链杆约束,固定端约束,cylindrical hinge with frictionless,a two-force body,sliderradial bearing or hinge and thrust bearing or hinge,hinge staff-a two-force body,Built-in(cantilever)support,contact on frictionless surface,主页,cylindrical hinge with frictionless,静力学基础,约束结构:两端用光滑铰

50、链与其他物体相连的杆件(直的或弯的),并且假设其自重不计。约束性质：可承受拉力或压力.因此链杆属于二力构件(在两力作用下 处于平衡的构件）。约束反力:沿着两端铰链中心的连线,等值、方向、共线。如图所示：,basis of statics,fundamental concepts of statics,1静力学基 本概念,axiom of statics,common Supports in engineering,4受力图画法,methods of drawing free-body diagrams,3工程中常见 约束,2静力学公理,Pin support,Roller support,ba