理论力学教案1

Engineering Mechanics (工程力学)

1.Introduction (绪论)

Objective (教学目标)：

1. Definition (理论力学的定义)

2. Study objects (研究对象)

3. Study contents (研究内容)

4. Study methods (研究方法)

5. Study aims (研究目的)

1. Definition (定义)理论力学(Theoretical Mechanics): 研究物体机械运动一般规律的科学。

2.Study objects (研究对象)：理论力学所研究的机械运动是速度远小于光速的宏观物体的机械运动；以牛顿总结的基本定律为基础，属于古典力学。

这种机械运动在日常生活和实际过程中经常遇到。

研究塔吊不致倾倒，确定所需配重

汽车通过轮胎作用在桥面上的力

桥面板作用在钢梁的力

齿轮啮合力

理论力学研究这种运动的最一般、最普遍的规律，是各门力学分支的基础。

3.Study contents (研究内容)：

Statics (静力学)：研究物体受力后平衡时的平衡条件，建立平衡方程。包括物体的受力分析和力系的简化等；

Kinematics (运动学)：从几何的角度研究物体的运动（轨迹、速度、加速度）不考虑引起运动的物理原因(只看现象，不管本质。)

Dynamics (动力学)：研究物体运动和作用力之间关系。

4. Study methods (学习方法)

Engineering approach:

a. Given: Carefully read the problem statement and list all the data provided. If a figure is required, sketch it neatly.

b. Find: State precisely the information that is to be determined.

c. Solution: Solve the problem, showing all the steps that you used in the analysis. Work neatly.

d. Validate: Many times, an invalid solution can be uncovered by simply asking yourself, “Does the answer make sense”.

5. Study aims (研究目的)

学习理论力学是解决工程问题的基础；理论力学是后续课的基础(材料力学、机械原理、机械零件、其它力学课程)。

·Statics and dynamics form the foundation of many engineering disciplines and are, therefore, essential to the training of an engineer.

Chapter 2. Basic Operations with Force Systems

(力系的基本运算)

Main contents：(主要内容)

Study how to use vector algebra to reduce a system of forces to a simpler, equivalent system.

· Concurrent force system; Nonconcurrent force system.

Objective：(教学目标)

1. Know the concept of force

2. Master concurrent force

3. Master moment of a force about a point

4. Master moment of a force about an axis

5. Master couples

6. Master changing the line of action of a force

2.2 Equivalence of vectors(矢量的等效)

Vector: a quantity that has magnitude and direction.矢量：具有大小和方向的量。Combination: applying parallelogram law for addition.

Equality: vectors have the same magnitude and direction.

Equivalence: If two vectors are interchanged without changing the outcome of the problem, they are called to be equivalent.

Note: Equality ≠ Equivalence (相等≠等效)

The types of vectors:

·Fixed vectors: Equivalent vectors have the same magnitude, direction and point of application.

· Sliding vectors: Equivalent vectors have the same magnitude, direction and line of action. · Free vectors: Equivalent vectors have the same magnitude and direction.

2.3 Force

Concept: the mechanical interaction between bodies. 力的定义：力定义为物体之间的相互机械作用。

Arising: direct contact between bodies; gravitational attraction. 力的产生：力产生于物体之间的直接接触；或万有引力。

Point of application of force: 力的作用点。

(Concentrated force)—集中力；(Distributed force)—分布力。

Line of action of a concentrated force: 集中力的作用线。

1. If the body is deformable, force is a fixed vector. In this case, one of its characteristics is its poit of application.

2. If the body is undeformable, force is a sliding vector.

Rigid body(刚体):在力的作用下物体内部任意两点之间的距离不变。(理想化模型) Characters: 性质The principle of transmissibility: 力的可传性原理

A force may be moved anywhere along its line of action without changing its external effects on a rigid body.