CEE225 - Structural Dynamics

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Featured Homework (PDF)

Complete homework solution demonstrating MDOF building analysis, mode shape extraction, damping analysis, modal response, and response spectrum analysis.

Homework #11 – Summary

Comprehensive MDOF building analysis demonstrating:

Mode Shape Extraction
Statistical analysis of acceleration data to extract mode shapes using RMS ratios and correlation analysis
Damping Analysis
Logarithmic decrement method for computing damping ratios from free vibration decay
Modal Response Analysis
Time-history analysis using Newmark's method and modal superposition for 100% Loma Prieta ground motion
Response Spectrum Analysis
Spectral analysis with SRSS modal combination for peak response estimation

References: Chopra (2014); DeJong et al. (2025).

Additional Homework Example (PDF)

Complete homework solution demonstrating response spectrum analysis, modal analysis, and numerical methods in structural dynamics.

Homework #5 – Summary

Advanced topics in structural dynamics demonstrating:

Response Spectrum Analysis
Application of elastic design spectra for seismic analysis of SDOF systems
MDOF Systems
Modal analysis and response calculation for complex structural systems
Numerical Methods
Implementation and comparison of time-stepping algorithms for dynamic response
Earthquake Engineering
Ground motion analysis and structural response characterization

References: Chopra (2014); DeJong et al. (2025).

Additional Homework Example (PDF)

Foundational homework solution demonstrating free vibration analysis, impact dynamics, and experimental damping identification.

Homework #2 – Summary

Foundational concepts in structural dynamics demonstrating:

Problem 1
Mass suddenly released from stops; free vibration about static equilibrium. Solution: $u(t) = -\frac{3mg}{4k} \cos\left(\sqrt{\frac{k}{m}} \, t\right)$
Problem 2
Inelastic impact (bullet in block) followed by SDOF free vibration. Result: $u(t) = 0.247\,\sin(47.67 \, t)$ [in]
Problem 3
Vehicle suspension analysis with stiffness from static deflection. Result: $k = 1666.7$ lb/in, $\omega_n \approx 12.52$ rad/s, $\zeta \approx 0.647$
Problem 4
Bridge experiment (Davis–Cory walkway) with logarithmic decrement damping analysis. Result: $\zeta \approx 1.8\%$

References: Chopra (2014); DeJong et al. (2025); Staacks et al. (2018); Castellanos‑Toro et al. (2018).