Code: mk3mrezg04xx17-en
ECTS Credit Points: 4
Evaluation: exam
Year, Semester: 1st year, 2nd semester
Its prerequisite(s): Engineering Physics, Mathematics I
Further courses are built on it: Yes/No
Number of teaching hours/week (lecture + practice): 2+2
Topics:
Motion of a particle:
position, velocity and acceleration and the mathematical relations between them, description of the motion of the particle in Cartesian coordinate system and Frenet-frame, Newton’s laws and differential equation of the motion of the particle, theorems of kinetics, force fields, kinetic, potential and mechanical energy, constrained motion along a two or three dimensional curve
Motion of a rigid body:
description of the translational, rotational and general plane motion of a rigid body, concept and determination of the instantaneous centre of zero velocity and acceleration, rolling motion without slipping, description of the plane motion of a rigid body in a time interval, centre of mass, momentum and angular momentum, moment of inertia and its calculation, mechanical work, Newton’s laws and theorem of kinetics for rigid bodies, rotating and swinging of the body about an axis, rolling without slipping
Vibrations:
Description and classification of vibratory motions and vibrating systems. Basic definitions and properties of vibratory motion. Investigation of the elements of vibrating systems: masses and inertial elements, flexible and damping elements. Investigation of the dynamic models. Two ways for the generation of motion equations: the D’Alembert’s principle and the Lagrange equations of motion. Investigation and properties of the free vibrations of single DOF undamped and damped systems. Solution of the homogenous motion equation. Investigation and properties of the forced vibrations of single DOF undamped and damped systems. Basic types of forced vibrating systems. Multiple DOF systems: introduction, basic properties, natural frequencies and modes, modal transform and decoupling.
Literature:
Compulsory:
- Russel C. Hibbeler: Engineering Mechanics – Statics and Dynamics, Prentice Hall, 2006. Isbn-13 9780132215091
- Lakshmana C. Rao, J. Lakshminarasimhan, Raju Sethuraman, Srinivasan M. Sivakumar: Engineering Mechanics: Statics and Dynamics, PHI Learning Pvt. Ltd., 2004. Isbn 8120321898, 9788120321892
- Jerry Ginsberg: Engineering Dynamics, 3rd edition, Cambridge University Press, 2007. Isbn-13: 978-0521883030
- Meirovitch, Leonard: Fundamentals of Vibration, McGraw-Hill Publishing Company, 2000. Isbn 0071181741
Recommended:
- Ferdinand P. Beer, E. Russell Johnston, Jr.: University of Connecticut, Mechanics for Engineers: Statics and Dynamics (Package), 4th Edition, ©1987, Isbn-13 9780070045842
- Joseph F. Shelley: 700 solved problems in vector mechanics for engineers, Volume II: Dynamics. (SCHAUM’S SOLVED PROBLEM SERIES), McGraw-Hill, 1990. Isbn 0-07-056687-9
| 1st week | 8th week |
|---|---|
| Registration week | 1st drawing week |
| 2nd week | 9th week |
| Lecture: Kinematics of a particle Scalar and vector position, velocity and acceleration and the mathematical relations between them. Description of the motion in Cartesian coordinate system and Frenet-frame. Special motion types: Motion with constant acceleration, circular motion. Practice: Particle kinematics problems | Lecture: Kinetics of a rigid body II Newton’s laws and theorem of kinetics for rigid bodies (impulse-momentum, angular impulse-angular momentum and work-energy theorems). Special motion types: Rotating and swinging about an axis, rolling without slipping. Practice: Rigid body kinetics problems |
| 3rd week | 10th week |
| Lecture: Kinetics of a particle I Newton’s laws and differential equation of the motion of the particle. Theorems of kinetics (impulse-momentum, work-energy and angular impulse-angular momentum theorems). Mechanical Power. Force fields (homogeneous, central and conservative). Kinetic, potential and mechanical energy. Practice: Particle kinetics problems | Lecture:Description and classification of vibratory motions and vibrating systems. Basic definitions and properties of vibratory motion. Investigation of the elements of vibrating systems: masses and inertial elements, flexible and damping elements. Practice: Reduction of masses. Replacement of rigid bodies by lumped masses. Reduction of springs and damping elements. |
| 4th week | 11th week |
| Lecture: Kinetics of a particle II Formulas for work and potential energy in homogeneous and central force fields. Motion of the particle in gravitational and elastic spring force fields. Constrained motion along a two or three dimensional curve. Practice: Particle kinetics problems II | Lecture: Investigation of the dynamic models. Two ways for the generation of motion equations: the D’Alembert’s principle and the Lagrange equations of motion. Practice: Generating the equations of motion for single- and multiple degrees of freedom (DOF) systems. |
| 5th week | 12th week |
| Lecture: Kinematics of a rigid body I Basic concepts (rigid body and disc, planar, translational, rotational and general plane motion). Connections between the velocity and acceleration of the different points of a rigid body undergoing translational, rotational and general plane motion. Instantaneous centre of zero velocity and acceleration and procedure for the determination of them with calculation and construction. Practice: Rigid body kinematics problems | Lecture: Investigation and properties of the free vibrations of single DOF undamped and damped systems. Solution of the homogenous motion equation. Practice: Calculation problems related to the free vibrations of single DOF undamped and damped systems. |
| 6th week | 13th week |
| Lecture: Kinematics of a rigid body II Rolling motion without slipping. Description of the plane motion of a rigid body in a time interval. Pole curves. Practice: Rigid body kinematics problems | Lecture: Investigation and properties of the forced vibrations of single DOF undamped and damped systems. Basic types of forced vibrating systems. Practice: Calculation examples of several kinds of forced vibrations in case of single DOF undamped and damped systems. |
| 7th week | 14th week |
| Lecture: Kinetics of a rigid body I Basic concepts: centre of mass, momentum and angular momentum, moment of inertia and its calculation, parallel axis theorem, mechanical work. Practice: Rigid body kinetics problems | Lecture: Multiple DOF systems: introduction, basic properties, natural frequencies and modes, modal transform and decoupling. Practice: Calculation problems related to the free and forced vibrations of multiple DOF undamped and damped systems. |
| 15th week | |
| 2nd drawing week |
Requirements
A, for a signature:
Participation at lectures and seminars is compulsory. Students must attend lectures and seminars and may not miss more than three of them during the semester. In case a student does so, the subject will not be signed and the student must repeat the course. Attendance at lectures and seminars will be recorded by the lecturer. Being late is equivalent with an absence. In case of further absences, a medical certification needs to be presented. Missed lectures must be made up for at a later date, being discussed with the tutor.
Students have to write two midterm tests during the semester. The first (40 points max) in the 8th, the second (40 points max) in the 14th week. At the end of the semester everybody will get a seminar grade on the basis of the table below:0-39 = Fail (1); 40-50 = Close fail (2); 51-60 = Improvement needed (3); 61-70 = Very good (4); 71-80 = Excellent (5)
If somebody fails then he has to write both tests in the 1st week of the exam period again. If the result is 40 points (50%) or better, then he can take an exam. If somebody has to repeat his midterm tests then his seminar grade can’t be better than (2).
There will be homework from week to week. Only students who have handed in all their homework at the time of the midterm test will be allowed to write it. The problems in the midterm tests will be selected from the homework assignments.
B, for a grade:
Everybody will get an exam grade for their exam. The final grade will be the average of the seminar and exam grade. If it is for example (3.5) then the lecturer decides if it is (3) or (4).