Course Details

Dynamics

Academic Year 2025/26

NDB018 course is part of 1 study plan

​ NPC-SIS Summer Semester 1st year

Course Guarantor

doc. Ing. Vlastislav Salajka, CSc.

Institute

Institute of Structural Mechanics

Language of instruction

Czech

Credits

4 credits

Semester

summer

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/295784

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  • 1. Assessment of civil engineering structures subjected by dynamic loads.
  • 2. Foundations the theory vibration of civil engineering structures. Models with single degree of freedom system (SDOF).
  • 3. Free Vibration. Response SDOF systems to specials form of excitation. Damping models.
  • 4. Measurement of frequencies and damping. Response of SDOF to general type of action.
  • 5. Numerical analysis of SDOF response. Frequency analysis. FFT.
  • 6. Continuous computational models – tension and bending of beam. Modal analysis. Vibration of plates.
  • 7. Newton law application. Hamilton principle.
  • 8. Multi degree of freedom models. Lagrange equations.
  • 9. Discrete and continuous models. Modal analysis of two degree of freedom models.
  • 10. Response solution using mode superposition method. Rayleigh method.
  • 11. Natural frequency and eigenvalue vectors characteristics. Rayleigh-Ritz method. General eigenvalues problem.
  • 12. Dynamic analysis by finite element method (FEM). Element matrices. The global system of equations Systems matrices. Modal analysis. Direct integration equations of motion.
  • 13. Response solution structures on seismic loads.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Calculation of equivalent stiffness and mass of models with single degree of freedom system (SDOF).
  • 2. Derivation of equation of motion of SDOF systems.
  • 3. Free vibration of undamped SDOF system – calculation of natural frequencies.
  • 4. Free vibration of undamped SDOF system – calculation of damping parameters.
  • 5. Response of SDOF system to harmonic excitation.
  • 6. Response of SDOF system to various type excitations (impulse, constant force etc.).
  • 7. Calculation of frequencies and modes of vibrations of continuous systems – rods and plates.
  • 8. Derivation of equation of motion system with 2DOF (translational and rotational motion).
  • 9. Assembly equation of 2DOF systems to calculate the frequencies and modes of vibrations and their solution.
  • 10. Assembly modal matrices. Using procedures for normalizing mode of vibration and plotting modes.
  • 11. Solution by mode-superposition method of the 2DOF system to harmonic excitation.
  • 12. Tuning dampers for vibration reduction simple systems.
  • 13. Derive elastic response spectra for solutions to seismic excitation.