Mechanics III.

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Lecturer:

Tutor:

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Department of Mechanics, Biomechanics and Mechatronics

Synopsis:

Mechanics III deals with the basic concepts of dynamics. Methods of solving the dynamics of mass particle and body motion and their systems are described. Methods for describing and solving vibrations of systems.

Requirements:

Syllabus of lectures:

Introduction – example of use in practice. Modeling. Dynamics of systems of particles.

Dynamics of systems of particles. Dynamics of body. Mass distribution in a body.

D'Alembert principle. Inertial effects of motion.

Balancing of rotating bodies. Free body diagram method. Newton-Euler equations.

Dynamics of multibody systems.

The principle of virtual work and power in dynamics. Lagrange equations of 2nd type. Reduction method.

Reduction method. Vibrations of systems with 1 DOF. Free vibrations. Forced vibrations excited by harmonic force.

Forced vibrations excited by rotating unbalanced mass. Kinematic excitation. Accelerometer, vibrometer.

Forced vibrations of systems with 1 DOF excited by general periodic force and by general force. Introduction to nonlinear vibration.

Vibration of systems with two DOFs, torsional vibration.

Bending vibration, determination of critical speed, dynamic absorber.

Stability of motion. Hertz theory of impact.

Approximate theory of flywheels.

Syllabus of tutorials:

1. Dynamics of particle. Experimental determination of moments of inertia.

2. Dynamics of systems of particles.

3. Mass distribution in a body. Dynamics of body. Balancing of rotating bodies.

4. Inertial effects of motion. D'Alembert equations.

5. Free body diagram method. Newton-Euler equations.

6. Dynamics of multibody systems.

7. The principle of virtual work and power in dynamics.

8. Lagrange equations of 2nd type. Reduction method.

9. Vibrations of systems with 1 DOF. Free vibrations. Forced vibrations excited by harmonic force.

10. Forced vibrations of systems with 1 DOF excited by general periodic force and by general force.

11. Torsional vibrations of systems with two DOFs. Free vibrations. Forced vibrations.

12. Bending vibration. Determination of critical speed.

13. Hertz theory of impact. Stability of motion. Approximate theory of flywheels.

Study Objective:

The aim of the course is to master the construction of a mechanical and mathematical model of the dynamics of a mechanical system in both planar and spatial variants and methods of analytical solution. Mastering the solution of vibrations of systems with 1 and 2 degrees of freedom.

Study materials:

Beer F.P., Johnson E.R.: Vector Mechanics for Engineers. Statics and Dynamics. McGraw-Hill, New York 1988.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: