Mechanical vibrations
Undergraduate · Engineering
Syllabus focus
Standard syllabus · STEM / applied
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Topics typically covered
Standard syllabus
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
STEM / applied
Applications and control of vibration
- Balancing of rotating machinery
- Vibration absorbers and tuned mass dampers
- Isolation mounts for sensitive equipment
- Signal processing: FFT for experimental modal analysis
- Rotordynamics and critical speeds (intro)
- Vehicle ride comfort and suspension tuning
- Structural health monitoring with vibration
- Human vibration exposure standards
- Lab: accelerometers, signal conditioners, and DAQ
- Design project: mitigate resonance in a structure
Nonlinear and advanced survey
- Nonlinear stiffness effects and jump phenomenon
- Self-excited vibrations: flutter and chatter intro
- Random vibration and PSD input (overview)
- Passive versus active vibration control
- Piezoelectric shunt damping
- MEMS resonators and micro-scale vibration
- Earthquake structural response link to dynamics
- Computational modal analysis validation
- FE vibrations topic alignment
- Industry case studies: turbine blade failures
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.