Course objectives:
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To introduce students to the problems of the dynamics of the more complicated body motions such as rotational, spherical, screw and general spatial motions.
Bases of analytical mechanics and its practical application to the modelling of mechanical systems with finite number of degree of freedom and the ability to assemble corresponding equations of motion.
To obtain matrix calculus knowledge for modelling of the vibrating linear systems with finite number of degree of freedom.
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Requirements on student
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Credit requirements:
Elaboration and delivery of the credit problem.
Examination requirements:
Active knowledge of lecturing problems and the capability to apply the obtained experience to solve concrete problems.
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Content
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1. Lecture: Dynamics of rotating motion.
Practice: Reaction forces calculation and the balancing of rotating bodies.
2. Lecture: Dynamics of spherical motion.
Practice: Examples and exploitation of the stabilizing effect of spherical motion.
3. Lecture: Dynamics of screw and general spatial body motion.
Practice: Examples of screw and general spatial motion.
4. Lecture: Bases of analytical mechanics and virtual work principle in statics and dynamics.
Practice: Assemblage of the equations of motion, equilibrium problem solution using virtual work principle.
5. Lecture: Use of the Lagrange equations to the motion modelling of the mechanical systems.
Practice: Assemblage of the equations of motion of the systems having one or more degrees of freedom.
6. Lecture: Discrete models of the linear vibrating mechanical systems in matrix form.
Practice: Assemblage of the equations of motion of the linear vibrating systems in matrix form by means of dynamical equilibrium method, virtual work principle and Lagrange equations.
7. Lecture: Eigenfrequencies, mode shapes, spectral and modal matrices.
Practice: Orthogonality of the mode shapes. Free vibration of the conservative systems with finite number of degree of freedom.
8. Lecture: Modal method of the response investigation of the conservative and weakly non-conservative systems.
Practice: Examples of response calculation of the weakly non-conservative systems excited by impulse, step and general excitation.
9. Lecture: Steady state response to periodical and harmonic excitation
Practice: Response to harmonic or periodical excitation caused by unbalanced mass or by kinematic harmonic excitation.
10. Lecture: Vibration of the non-linear systems with one degree of freedom.
Practice: Free vibration of the non-linear systems with one degree of freedom. Steady state response to harmonic excitation.
11. Lecture: Finite element modelling of the vibrating continuum.
Practice: Longitudinal vibrating of bars. Submission of the credit problem
12. Lecture: Torsion vibration of shafts and shaft systems using finite element method.
Practice: Torsion vibration of the transfer systems.
13. Lecture: Bending vibration solution of the beam systems using finite element method.
Practice: Application of the finite element method to multibody-pipeline systems.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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65
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Graduate study programme term essay (40-50)
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70
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Total
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135
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
definovat základní pojmy z mechaniky tuhých těles |
klasifikovat jednotlivé druhy pohybů tělesa a soustavy těles v rovině |
vysvětlit základní pojmy z oblasti statiky a kinematiky |
vysvětlit pravidla použití metod lineární algebry a vektorové analýzy v kinematice rovinných soustav těles |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
navrhnout matematický model pro řešení dynamických problémů těles a soustav těles v rovině |
posoudit zda se jedná o úlohu kinetostatickou nebo o úlohu vlastní dynamiky |
řešit diferenciální rovnice 1. řádu metodou separace proměnných |
řešit pohybové rovnice hmotného bodu popř. soustav |
vypočítat základní typy integrálů |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
klasifikovat metody analytické mechaniky a definovat metodu pro sestavení pohybových rovnic |
popsat a klasifikovat mechanické systémy konající rotační, sférický nebo obecný prostorový pohyb tělesa |
definovat pojmy z teorie kmitání, jako vlastní frekvence, vlastní tvary kmitu, rezonance apod. |
popsat pravidla sestavení matematického modelu lineárních kmitavých systémů v maticovém tvaru |
Skills - skills resulting from the course: |
provést numerické řešení nelineárních matematických modelů popisujících chování systémů konajících sférický pohyb |
řešit chování lineárních kmitavých systémů buzených libovolným typem buzení |
řešit chování lineárních kmitavých systémů, které jsou uvedeny do pohybu jen vlivem nenulových počátečních podmínek |
určit analyticky a numericky vlastní frekvence a vlastní tvary kmitu lineárních systémů s více stupni volnosti |
určit setrvačné a vnější účinky působící na tělesa konající rotační, sférický nebo obecný prostorový pohyb |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Written exam |
Skills - skills achieved by taking this course are verified by the following means: |
Oral exam |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
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