Rigid body
Transkript
Rigid body
What is Engineering Mechanics ? Study of the relations between the forces that act on bodies or fluids and the resultant motion that those bodies or fluids experience. Engineering Mechanics Mechanics of rigid bodies Statics Mechanics of fluids Dynamics Kinetics K.İder Mechanics of deformable bodies Kinematics ME 206 Dynamics 1 Rigid Body Mechanics Statics Equilibrium of rigid bodies, – at rest, or – move with constant velocity Relationship between internal and external forces Engineering Mechanics Mechanics of rigid bodies Statics Mechanics of fluids Dynamics Kinetics K.İder Mechanics of deformable bodies ME 206 Dynamics Kinematics 2 Rigid Body Mechanics Dynamics Analysis of rigid bodies in motion Engineering Mechanics Mechanics of rigid bodies Statics Mechanics of fluids Dynamics Kinetics K.İder Mechanics of deformable bodies ME 206 Dynamics Kinematics 3 Rigid Body Mechanics Kinematics Engineering Mechanics Study of the motion without reference to the forces that cause the motion. Motion: - Displacement - Velocity - Acceleration Mechanics of rigid bodies Statics Mechanics of fluids Dynamics Kinetics K.İder Mechanics of deformable bodies ME 206 Dynamics Kinematics 4 Rigid Body Mechanics Kinetics Engineering Mechanics Relates the forces acting on the body to its motion. Used – – K.İder Mechanics of rigid bodies Statics To find the motion caused by the applied forces. To determine the forces which are required to produce a desired motion. Mechanics of deformable bodies Mechanics of fluids Dynamics Kinetics ME 206 Dynamics Kinematics 5 Mechanics of deformable bodies Known as – Mechanics of materials – Strength of materials Advanced studies – Theory of elasticity – Theory of plasticity – Flexible multibody dynamics K.İder ME 206 Dynamics 6 Fluid mechanics Compressible – Ideal fluid – Viscous fluid Incompressible – Hydraulics K.İder ME 206 Dynamics 7 Historical Development Galileo(1564-1642) Newton(1642-1727) Euler, D’Alembert, Lagrange, Laplace, Coriolis, … Einstein(1879-1955) K.İder ME 206 Dynamics 8 Basic Quantities of Mechanics Space: The geometric region where an event occurs. Time : The interval between successive events. Mass : A quantitative measure of inertia. Inertia is the resistance of a body to a change in velocity. K.İder ME 206 Dynamics 9 Idealizations of Mechanics Particle: a body that – has mass – but negligible dimensions. Also, when the dimensions are irrelevant to its motion it can be treated as a particle, e.g. aeroplane, planet Rigid body: body whose change in shape is negligible compared to overall dimensons. (So particles remain at fixed distance from each other before & after applying a load.) Force: Action of one body on another. Vector quantity (magnitude and direction) - Direct contact - Remote action (gravitation, magnetic force) K.İder ME 206 Dynamics 10 Newton’s Three Laws of Motion Newton’s First Law A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this state if the resultant force acting on the particle is zero. K.İder ME 206 Dynamics 𝐹=0 11 Newton’s Three Laws of Motion Newton’s Second Law If the resultant force acting on a particle is not zero, then the particle experiences an acceleration 𝑎 that has the same direction as the force and a magnitude that is directly proportional to the force. K.İder ME 206 Dynamics 𝐹 = 𝑚𝑎 12 Newton’s Three Laws of Motion Newton’s Third Law For every action there is an equal and opposite reaction. The force of action and reaction between bodies are equal in magnitude, opposite in direction, and collinear. K.İder ME 206 Dynamics 13 Newton’s Laws of Motion 1st law } } Statics 3rd law 2nd law K.İder Dynamics ME 206 Dynamics 14 Newton’s Law of Gravitational Attraction G=66.73x10-12 m3/(kg.s2) K.İder ME 206 Dynamics 15 Newton’s Law of Gravitational Attraction K.İder ME 206 Dynamics 16 Acceleration of Gravity K.İder ME 206 Dynamics 17 Units K.İder ME 206 Dynamics 18 Calculations Prefixes Dimensional Homogenity 𝑠 = 𝑣𝑡 − 𝑚 K.İder 𝑚 𝑠 𝑠 1 𝑎𝑡 2 2 𝑚 2 𝑠 2 𝑠 ME 206 Dynamics 19 English – Turkish Dictionary Statics Statik deformable Şekil değiştirebilen fluid akışkan equilibrium denge internal iç external dış rigid Şekil değiştirmeyen, katı displacement Yer değiştirme velocity hız acceleration ivme strength mukavemet compressible sıkıştırılabilir viscous İç sürtünmeli hydraulics Sıvı bilimi elasticity Elastik şekil değişimi inertia eylemsizlik particle parçacık rest hareketsiz thrust itki projection izdüşüm cannon top orbit yörünge gravitation yerçekimi attraction çekme constant sabit Rounding off yuvarlama Dimensional homogenity Boyutsal uyumluluk magnitude büyüklük Distributed load Yayılı yük resultant bileşke component bileşen parallelogram paralelkenar resolution ayırma horizontal yatay vertical düşey coplanar Eşdüzlemsel Dynamics dinamik position konum intersecting kesişen T.Akyürek ME 204 Engineering Mechanics: Dynamics – Introduction to Dynamics 20