| Subject name (in Hungarian, in English) | Nonlinear vibrations | |||
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Nonlinear Vibrations
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| Neptun code | BMEGEMMNWVI | |||
| Type | study unit with contact hours | |||
| Course types and number of hours (weekly / semester) | course type: | lecture (theory) | exercise | laboratory excercise |
| number of hours (weekly): | 1 | 1 | 0 | |
| nature (connected / stand-alone): | - | individual | - | |
| Type of assessments (quality evaluation) | exam | |||
| ECTS | 3 | |||
| Subject coordinator | name: | Dr. Szabó Zsolt | ||
| post: | associate professor | |||
| contact: | szazs@mm.bme.hu | |||
| Host organization | Department of Applied Mechanics | |||
| http://www.mm.bme.hu/ | ||||
| Course homepage | http://www.mm.bme.hu/targyak/?BMEGEMMNWVI | |||
| Course language | english | |||
| Primary curriculum type | mandatory | |||
| Direct prerequisites | Strong prerequisite | none | ||
| Weak prerequisite | ||||
| Parallel prerequisite | ||||
| Milestone prerequisite | at least obtained 0 ECTS | |||
| Excluding condition | BMEGEMMMW06 | |||
Aim
The aim of the course is to acquaint students with the basic concepts of the dynamic study of the basic equations of nonlinear mechanical systems, the traditional and modern methods of solving equations of motion; draws attention to the vibrational phenomena occurring in engineering practice which cannot be explained by the theory of linear vibrations in the knowledge base of basic education. In addition to the most common computer methods in engineering practice, the application of numerical simulation, the presentation of approximate analytical methods that develop the approach and are important in the parameter-dependent presentation of results is also emphasized.
Learning outcomes
Competences that can be acquired by completing the course
Knowledge
He was informed about the main types of nonlinearities occurring in mechanical models and their significance. He possesses basic analytical and numerical methods of examining equations of motion. It distinguishes between autonomous and non-autonomous dynamic systems. He is aware of the different basic types of elementary bifurcations. He knows the phase plane method, the concept of the Poincaré index, the relationship between the number of equilibrium situations and indices. Understands estimation methods for the period of vibrations occurring in conservative nonlinear systems. Knows the effect of progressive and degressive stiffness on the resonance curve of an excited system. He knows the analytical methods of stable and unstable vibrations and boundary cycles related to the dynamic loss of stability. He is aware of the concept of center multitude, an approximate analytical definition. He is aware of the importance of nonlinear damping forces in the formation of boundary cycles.
Ability
Identifies nonlinear effects in mechanical models. Apply analytical and numerical methods to the study of nonlinear equations of motion. Identifies elementary bifurcations that occur in one-dimensional dynamical systems. Use the plane topological relationships of the phase to determine equilibrium situations. Calculates an approximate estimate of the period of vibrations of conservative systems. Defines a parameter-dependent bifurcation diagram of equilibrium situations. Interpret each branch of the resonance curve of a nonlinear excited system. It distinguishes between the types of boundary cycles that appear in the case of sub- and supercritical Hopf bifurcation. Calculates the approximate amplitude of a limit cycle close to the critical bifurcation parameter value. Improves your knowledge of analytical and numerical methods.
Attitude
He constantly monitors his work, results and conclusions. Expands your knowledge of studying nonlinear vibrations. Open to the use of information technology tools. It seeks to learn and apply novel mathematical and numerical methods. It develops your ability to provide accurate and error-free problem solving, engineering precision and accuracy.
Independence and responsibility
Collaborates with the instructor and fellow students to expand knowledge. Accepts well-founded professional and other critical remarks. In some situations, as part of a team, you work with your fellow students to solve tasks. With his knowledge, he makes a responsible, well-founded decision based on his analyzes. Checks the robustness of equipment operating near the stability limit to interference.
Teaching methodology
The course consists of one hour of theoretical and one hour of practical course per week. The understanding of the theoretical materials presented in the lecture is aided by the examples presented in the exercises. During the lecture, the most important parts of the material are conducted on a board in order for the joint work to help the students understand the curriculum. The animations and examples projected on the theoretical courses further help to master the curriculum. The materials used in the lectures and exercises can be downloaded by the students. During the semester, students can check the acquisition of knowledge through the solution of two compulsory homework tasks, for which we provide regular consultations.
Support materials
Textbook
Dr. Ludvig Győző: Dynamics of Machines. Technical Technical Publishing House, 1993, Budapest. ISBN: 963-10-4802-0.
Jordan, DW, Smith, P .: Nonlinear Ordinary Differential Equations. Oxford University Press, 2007. ISBN: 019-92-0825-5.
Rand, R .: Topics in Nonlinear Dynamics with Computer Algebra. Gordon and Breach, 1994. ISBN: 019-92-0825-5.
Lecture notes
There is no note available for the subject when filling in the form, its earliest publication date is 2020.
Online material
http://www.mm.bme.hu/targyak/?BMEGEMMNWVI
Validity of the course description
| Start of validity: | 2019. September 1. |
| End of validity: | 2025. July 15. |
General rules
Learning outcomes are assessed on the basis of two mid-year written performance measurements (partial performance assessment) and an oral exam. Partial performance assessment (homework): a complex way of evaluating the knowledge, ability, attitude, as well as independence and responsibility type competence elements of the subject, the form of which is the individual homework. The exam is a way of evaluating the knowledge and ability-type competence elements of the subject in the form of an oral answer, which, in addition to taking the necessary lexical knowledge into account, also assesses their knowledge of their practical role and significance.
Assessment methods
Detailed description of mid-term assessments
| Mid-term assessment No. 1 | ||
| Type: | formative assessment, simple | |
| Number: | 2 | |
| Purpose, description: | The basic aim of the partial performance assessment is to examine the existence of attitudes and learning outcomes belonging to the autonomy and responsibility competence group. The way to do this is to create two individual homework documents. The topic of the tasks is based on the parts of the material told before the publication. The content and form requirements and evaluation principles of the completed homework are clearly included in the assignment and the website of the subject. You can get up to 10 points with one task. | |
Detailed description of assessments performed during the examination period
Elements of the exam:
| Written partial exam | ||
| Obligation: | does not apply | |
| Description: | ||
| Oral partial exam | ||
| Obligation: | mandatory (partial) exam unit, failing the unit results in fail (1) exam result | |
| Description: | The oral exam is a way of assessing the knowledge and ability-type competence elements of the subject in the form of an oral answer on the drawn topic. The exam focuses primarily on the qualitative contexts and technical application of the acquired knowledge, for the systematization of which 15-20 minutes of preparation time is provided. The oral exam is a way of assessing the knowledge and ability-type competence elements of the subject in the form of an oral answer on the drawn topic. The exam focuses primarily on the qualitative contexts and technical application of the acquired knowledge, for the systematization of which 15-20 minutes of preparation time is provided. | |
| Practical partial exam | ||
| Obligation: | does not apply | |
| Description: | ||
The weight of mid-term assessments in signing or in final grading
| ID | Proportion |
|---|---|
| Mid-term assessment No. 1 | 100 % |
The condition for signing is that the score obtained in the mid-year assessments is at least 40%.
The weight of partial exams in grade
| Type: | Proportion |
|---|---|
| Oral partial exam | 100 % |
Determination of the grade
| Grade | ECTS | The grade expressed in percents |
|---|---|---|
| very good (5) | Excellent [A] | above 90 % |
| very good (5) | Very Good [B] | 85 % - 90 % |
| good (4) | Good [C] | 70 % - 85 % |
| satisfactory (3) | Satisfactory [D] | 56 % - 70 % |
| sufficient (2) | Pass [E] | 40 % - 56 % |
| insufficient (1) | Fail [F] | below 40 % |
The lower limit specified for each grade already belongs to that grade.
Attendance and participation requirements
Must be present at at least 70% (rounded down) of lectures.
At least 70% the exercises (rounded down) must be actively attended.
Special rules for improving, retaken and replacement
The special rules for improving, retaken and replacement shall be interpreted and applied in conjunction with the general rules of the CoS (TVSZ).
| Can the submitted and accepted partial performance assessments be resubmitted until the end of the replacement period in order to achieve better results? | ||
| NO | ||
| Taking into account the previous result in case of improvement, retaken-improvement: | ||
| new result overrides previous result | ||
| The way of retaking or improving a partial assessment for the first time: | ||
| partial assesment(s) in this group can be improved or repeated once up to the end of the repeat period | ||
Study work required to complete the course
| Activity | hours / semester |
|---|---|
| participation in contact classes | 28 |
| mid-term preparation for practices | 7 |
| elaboration of a partial assessment task | 8 |
| exam preparation | 21 |
| additional time required to complete the subject | 26 |
| altogether | 90 |
Validity of subject requirements
| Start of validity: | 2019. September 1. |
| End of validity: | 2025. July 15. |
Primary course
The primary (main) course of the subject in which it is advertised and to which the competencies are related:
Common on all MSc programmes
Link to the purpose and (special) compensations of the Regulation KKK
This course aims to improve the following competencies defined in the Regulation KKK:
Knowledge
- Student has the knowledge of the general and specific characteristics, boundaries and main developments of the field, its links with related disciplines.
- Student has the detailed knowledge of the context, theories and terminology of the field.
- Student has a detailed knowledge of legal regulations and ethical standards relevant to the field of specialisation.
Ability
- Student carries out a detailed analysis of the various concepts that make up the knowledge base of the field, synthesising and synthesising the broad and specific contexts and making an appropriate assessment of them.
- Student identifies specific professional problems using a multifaceted, interdisciplinary approach, and explores and formulates the detailed theoretical and practical background needed to solve them.
- Student has a high level of knowledge transfer skills in the field, and is able to use and process publication sources in Hungarian and foreign languages, and has effective information research and processing skills in the field.
Attitude
- Student takes decisions in new, complex and strategic decision-making situations and in unexpected situations, taking full account of legal and ethical standards.
- Student strives to put the latest developments in student's field at the service of student's own development.
- Student understands and represents the active citizenship and literacy elements that define the key issues in their field.
Independence and responsibility
- Student demonstrates a high degree of autonomy in thinking through and developing broad and specific professional issues on the basis of given resources.
- Student is involved in research and development projects, mobilises student's theoretical and practical knowledge and skills in a project team in an autonomous way, in cooperation with the other members of the team, in order to achieve the objective.
- Student independently applies a wide range of methods and techniques in practice in contexts of varying complexity and predictability.
Prerequisites for completing the course
|
Knowledge type competencies
(a set of prior knowledge, the existence of which is not obligatory, but greatly facilitates the successful completion of the subject) |
none |
|
Ability type competencies
(a set of prior abilities and skills, the existence of which is not obligatory, but greatly contributes to the successful completion of the subject) |
none |