Review of the dynamic behavior of single-degree-of-freedom (SDOF) systems with damping.
Free vibration, harmonic vibration – frequency response, transient response.
Equations of motion for deformable bodies and continuous structural media.
Spatial discretization of structural dynamics problems using the Finite Element Method (FEM).
Equations of motion. Approximate methods in structural dynamics: classical methods (Rayleigh, Rayleigh–Ritz, Galerkin, assumed modes).
Dynamic response of discrete physical systems with multiple degrees of freedom without damping.
Free vibrations. Eigenvalues – eigenmodes, physical interpretation, properties.
Methods for calculating eigenvalues and mode shapes.
Modal superposition analysis.
Reduction methods for multi–degree-of-freedom systems.
Forced vibration under harmonic excitation – frequency response.
Transient response under arbitrary dynamic excitation.
Time-domain transient response analysis using time integration.
Direct (explicit) and indirect (implicit) time-integration methods.
Nonlinear vibrations and stability of dynamical systems:
free vibration, self-excited oscillations, external, parametric, and internal resonance.
Applications: dynamic response of mechanical structures; determination of the dynamic behavior of complex mechanical structures and systems using finite element programming; dynamic responses.
- Teacher: Ιωάννης Αντωνιάδης
- Teacher: Χρήστος Γιακόπουλος
- Teacher: Αθανάσιος Χασαλεύρης
ECTS : 5
Language : el, en
Learning Outcomes : Upon successful completion of the course, the student will be able to:
(Knowledge)
- Explain the dynamic behavior of single-degree-of-freedom (SDOF) systems with or without damping.
- Describe free, harmonic and transient responses in linear dynamic systems.
- Recognize the equations of motion for deformable bodies and continuous structural systems.
- Understand classical approximate methods in structural dynamics (Rayleigh, Rayleigh–Ritz, Galerkin, assumed modes).
- Analyze eigenvalues, eigenmodes and their physical interpretation in multi-degree-of-freedom systems.
- Explain nonlinear vibration phenomena, stability and different resonance mechanisms (external, parametric, internal).
(Skills)
- Formulate equations of motion for linear and nonlinear mechanical systems.
- Apply spatial discretization using the Finite Element Method (FEM).
- Compute eigenvalues and mode shapes, and perform modal superposition analysis.
- Implement reduction methods (system condensation) for large vibration models.
- Analyze forced vibration under harmonic excitation and compute frequency response.
- Perform transient response analysis using time-integration techniques.
- Evaluate structural dynamic behavior using FEM-based computational tools.
(Competences - Autonomy & Responsibility)
- Develop numerical vibration models for real mechanical structures.
- Select appropriate analysis methods (modal analysis, time integration, FEM) depending on the problem.
- Interpret dynamic analysis results to assess vibratory behavior and potential resonance issues.
- Synthesize solutions for complex dynamic systems using finite-element simulation tools.
- Apply vibration theory to real engineering applications and complex mechanical structures.