Mechanics II – Applied Dynamics

About this course

This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work. Students will also become familiar with the following topics: Lagrange’s equations for systems of particles and rigid bodies in planar motion, and linearization of equations of motion. The objective of the course is to provide basic knowledge of engineering dynamics to the students such that they can understand the basics of kinematics and kinetics for both particles and rigid bodies and their motion.

Expected learning outcomes

The aim of the course is to introduce the student to the basic principles of the dynamics of material point systems and rigid bodies.
Upon successful completion of the course the student will be able to: – recognizes the basic of kinematic and dynamic concepts in engineering problems – Evaluates the effect of forces on the motion of bodies in relation to the center of gravity and the moment of inertia. – Calculates the rotational and translational motion of a body under the influence of forces. – Develop equations of motion – Application of vector engineering theorems for solving complex motion problem Evaluation of the change of the kinetic state through the principles of work-energy and Impulse-Momentum

Indicative Syllabus

Introduction Kinematics of Particles – Velocity and acceleration – Linear and Curvilinear motion – Coordinate Systems (Cartesian, Polar, Tangential-normal, spherical) Dynamics of Particles – Newton second law – Linear and angular momentum – Conservative systems – The principle of momentum conservation – Impulse, impulsive motion, and impact – Motion of center of gravity – Orbital mechanics Kinematics of Rigid Bodies – Planar motion of rigid bodies – General 3d motion – Mechanisms – Rotating Frames of Reference – Coriolis – Instantaneous centers Dynamics of Rigid Bodies – Equations of motion – Linear and Angular Momentum conservation
– Work-Energy principle – Convervation of energy principle – Impulse momentum conservation Mechanical Vibrations – Equation of motion for the simple harmonic oscillator – Free vibrations, eigenfrequency – Damped free vibration, damping ratio – Forced Vibrations

Teaching / Learning Methodology

Lecture: the fundamentals of applied dynamics will be described using ppt presentations, demonstrating videos, Internet. The students are free to request help. The students are encouraged to solve problems and to use their own knowledge to verify their solutions before seeking assistance. Tutorial: a set of problems and group discussion topics will be arranged in the tutorial classes. Students are encouraged to solve problems before having solutions.

Recommended Reading

• Ferdinard P.Beer and E.Russell Johnston,Jr., Vector Mechanics for Engineers: Statistics and Dynamics, Fifth Edition, McGraw-Hill, 1988.
• R.C. Hibbeler, Engineering Mechanics: Statistics and Dynamics, Sixth Edition, MacMillan Publishing Company, USA 1992