AU kursuskatalog arkiv

Numerisk dynamik MESTCD1U01 (Q4) ( forår 2011 - 5 ECTS )

Rammer for udbud

• Uddannelsessprog: engelsk
• Niveau: Civil mekanik
• Semester/kvarter: 2/4
• Timer per uge: 10
• Deltagerbegrænsning:
• Undervisningssted: Århus
• Hovedområde: Ingeniørhøjskolen
• Udbud ID: 30111

Formål

The course objective is systematic modelling of kinematics and dynamics of machines represented as multibody systems. Based on matrix algebra, vector calculus and partial and time derivatives, machine components and their variation with time are represented in a mathematical format. The students will be able to derive complex joints such as bearings, couplers, cams and gears by use of fundamental geometric conditions such as cross and dot products. Force elements are derived for linear as well as rotational actuators, springs and bushings. The principle of virtual work is introduced in deriving the equations of motion for planar systems. Methods for numerical solution of position, velocity and acceleration of kinematic determined systems are introduced. The combined differential and algebraic equations describing the equations of motion and constraint equations are solved using numerical integrations techniques

Indhold

Introduction to multibody systems for describing machine performance

Introduction of geometric and algebraic vectors, reference frames

Matrix and vector operations, transformation of coordinates

Vector and Matrix differentiation, velocity and acceleration equations of a point in a fixed or moving reference frame

Matrix notation, partial derivatives, chain rule of differentiation

Generalized versus cartesian coordinates, Degrees of Freedom

Kinematic constraints, global or relative constraints between bodies or relative to ground

Absolute or relative driving constraints

Kinemtaic analysis, Newton Raphson, Gaussian Elimination applied to solving the kinematic problem, Redundant constraints, bifurcation and mechanism lock-up

Variational approach for deriving equations of motion

Virtual work, generalized forces, translational and rotational force elements

Introduction to Numerical integration, fixed versus variable step size integrators

Theory of modal reduction as applied to flexible bodies in multibody systems

Equations of motion of combined rigid and flexible body systems

Faglige forudsætninger

Basic dynamics, ordinary differiential equations, matrix algebra

Underviser

Ole Balling

Undervisnings- og arbejdsform

20 days of combined lectures (appr. 50%) and exercises (appr. 50%)

English

Litteratur

Edward J. Haug: Computer-Aided Kinematics and Dynamics of Mechanical Systems, Volume I: Basic Methods, Allym and Bacon, 1989

Own notes and examples

Læringsmål

• Explain the topology of machine systems
• Apply vector algebra to mathematically describe machine components
• Derive composite joints using basic geometric constraints
• Solve position, velocity and acceleration equations for kinematic determined systems
• Apply methods of virtual work to derive eoquations of motion
• Setup combined differential algebraic equations for constrained dynamic systems
• Explain modal reduction of flexible components for use ion multibody simulation
• Implement flexible bodies in multibody systems by use modal reduction in commercial grade software

Bedømmelse

Oral examination evaluated using the 7-step scale, internal marking