Standard syllabus
Mechanical vibrations · Undergraduate · Engineering
Topics
Single-degree-of-freedom systems
- Equation of motion: m ẍ + c ẋ + k x = f
- Free vibration: natural frequency and damping ratio
- Underdamped, critically damped, and overdamped response
- Logarithmic decrement for damping estimation
- Harmonic forcing and steady-state amplitude
- Frequency response function magnitude and phase
- Resonance and dynamic amplification factor
- Base excitation and vibration isolation
- Rotating unbalance as harmonic excitation
- Energy methods for SDOF systems
Multi-degree-of-freedom systems
- Two-DOF systems: natural modes and frequencies
- Orthogonality of mode shapes for proportional damping
- Modal analysis and modal superposition
- Continuous systems: vibrating strings and beams
- Boundary conditions and characteristic equations
- Rayleigh's quotient for approximate frequencies
- Finite element modal analysis workflow
- Damping models: viscous, structural (intro)
- Beat phenomenon in closely spaced modes
- Measurement of FRFs with impact hammer testing
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