Step 1: Mode Shape Extraction
Extract and normalize mode shapes from acceleration data using RMS ratios and correlation analysis. Analyze all three modes with statistical confidence metrics.
3-Story MDOF Building Vibration Analysis
Final Project - CEE225 Structural Dynamics
Complete analysis pipeline: Mode shapes, damping, modal response, and response spectrum analysis
Analysis Pipeline
Step 2: Damping Analysis
Compute damping ratios using logarithmic decrement method. Analyze free vibration decay for all three modes.
Step 3: Modal Response Analysis
Time-history analysis of building response to 100% Loma Prieta ground motion. Includes modal displacements, floor responses, base shear, and overturning moment with measured data comparison.
Step 4: Response Spectrum Analysis
Spectral analysis using design response spectrum with SRSS modal combination. Computes peak floor displacements and base shear from spectral ordinates.
Project Overview
This project implements a complete structural dynamics analysis workflow for a 3-story MDOF building structure. The analysis pipeline includes:
Mode Shape Extraction
Extraction of mass-normalized mode shapes from experimental acceleration data using RMS ratios and correlation analysis
Extraction of mass-normalized mode shapes from experimental acceleration data using RMS ratios and correlation analysis
Damping Analysis
Computation of damping ratios using logarithmic decrement method from free vibration decay
Computation of damping ratios using logarithmic decrement method from free vibration decay
Modal Response Analysis
Time-history analysis using modal superposition and Newmark's method for ground motion response
Time-history analysis using modal superposition and Newmark's method for ground motion response
Response Spectrum Analysis
Spectral analysis using design spectrum with SRSS modal combination for peak response estimation
Spectral analysis using design spectrum with SRSS modal combination for peak response estimation
Statistical Validation
Uncertainty quantification with coefficient of variation and 95% confidence intervals
Uncertainty quantification with coefficient of variation and 95% confidence intervals
Measured Data Comparison
Validation of computed responses against experimental floor accelerations and displacements
Validation of computed responses against experimental floor accelerations and displacements
Data Sources: Experimental acceleration measurements (L1AccX, L2AccX, L3AccX) from mode-specific excitations; 100% Loma Prieta at Palo Alto ground motion; Design response spectrum with multiple damping ratios