Course detail

# Dynamics II - Linear Vibration

The course is focused on teaching linear vibrations of systems with concentrated and distributed parameters (strings, beams, plates, membranes and shells). The course is aimed at comparing analytical and numerical solutions to problems that overlap with numerical solutions to general problems that do not have an analytical solution. Students will be practically acquainted with a number of numerical methods aimed at solving their own problems and solving the system response to various exciting effects. Students will have to program different numerical methods themselves to demonstrate their understanding.

Learning outcomes of the course unit

The students will have detailed knowledge of vibration of systems with single and several degrees of freedom. They will be able to calculate eigenfrequencies and responses of these systems with different types of excitation. They will be able to solve practical problems that can be modeled in this way. The student will have knowledge of the vibration of basic continuum bodies. They will be able to create models using finite element method and multi-body systems. The students will be able to apply the basic numerical methods for solving problems of linear vibrations.

Prerequisites

Linear algebra, differential equations, strength of materials, kinematics of particles and bodies, dynamics of particles and bodies, numerical methods of linear algebra and ODE solutions, MATLAB or Python programming.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

BREPTA, Rudolf, TUREK, František a PŮST, Ladislav. Mechanické kmitání. Vyd. 1. Praha: Sobotáles, 1994. 589 s. Technický průvodce; sv. 71. Česká matice technická; roč. 99 (1994), č. 438. ISBN 80-901684-8-5. (CS)
de Silva, C. (Ed.). (2005). Vibration and Shock Handbook. Boca Raton: CRC Press, https://doi.org/10.1201/9781420039894 (EN)
Inman, D. J. (1994). Engineering vibration. Englewood Cliffs, N.J: Prentice Hall. (EN)

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Seminars are focused on practical topics.

Assesment methods and criteria linked to learning outcomes

The course-unit credit is granted under the condition of active participation in seminars and gain at least 20 points of 40. The points can be obtained by elaboration of partial tasks and presentations. The gained points from the exercise is part of the final classification of the subject.
Final examination: The exam is divided into two parts. The evaluation of the exam is based on the classifications of each part. If one of the parts is graded F, the final grade of the exam is F. The content of the first part is a test, of which a maximum of 30 points can be obtained. The content of the second part is a solution of typical problems. It is possible to gain up to 30 points from this part. The form of the exam, types, number of examples or questions and details of the evaluation will be given by the lecturer during the semester.
The final evaluation is given by the sum of the points gained from the exercises and exam. To successfully complete the course, it is necessary to obtain at least 50 points, where the maximum of 100 ECTS points can be reached.

Language of instruction

Czech

Work placements

Not applicable.

Aims

The aim of the course is to build on and deepen the knowledge of linear vibrations acquired in the course Dynamics. Students get to knowing with linear vibrations of systems with one, two and N degrees of freedom for systems with concentrated parameters. From systems with distributed parameters the course will be focused on strings, beams, membranes, plates and shells. Both analytical solution and necessary numerical methods will be learning.

Specification of controlled education, way of implementation and compensation for absences

Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge. One absence can be compensated for by elaboration of substitute tasks.

Classification of course in study plans

• Programme N-IMB-P Master's

specialization BIO , 1. year of study, winter semester, 5 credits, compulsory
specialization IME , 1. year of study, winter semester, 5 credits, compulsory

• Programme N-MET-P Master's, 1. year of study, winter semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Introduction to dynamic vibration systems, systems modeling, damping.
2. Vibrations of systems with one degree of freedom
3. Vibrations of systems with one degree of freedom
4. Methods of vibration visualization, systems with one degree of freedom
5. Vibrations of systems with two degrees of freedom, dynamic dampers
6. Vibrations of systems with n degrees of freedom
7. Numerical methods for solving systems with n degrees of freedom
8. Numerical methods for solving systems with n degrees of freedom
9. Vibrations of strings and beams
10. Vibrations of membranes and plates
11. Vibrations of shells
12. Approximate methods of continuum vibration solution
13. Summary

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

1. Introduction to vibration of dynamic systems, building model, derivation of dynamic equations
2. Analytical and numerical solution of systems with one degree of freedom.
3. Analytical and numerical solution of systems with one degree of freedom.
4. Characteristics of vibration systems
5. Semestral project
6. Vibrations with n degrees of freedom, problem of eigenvalues
7. Vibrations with n degrees of freedom, system response to excitation
8. Numerical methods applicable to systems with n degrees of freedom
9. Vibrations of strings and beams
10. Vibrations of membranes and plates
11. Vibrations of shells
12. Semestral project
13. Semestral project

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