Theory

• State Space Model of Structural Dynamics
  • Partitioned Equation of Dynamic Equilibrium
  • Equation of Motion
  • Continuous LTI State-Space Representation
  • Discrete LTI State-Space Representation
• Modal Properties from State Space Realization
  • Eigendecompositions of \(\mathbf{A}_{c}\) and \(\mathbf{A}\)
  • Natural Frequencies and Modal Damping Ratios
  • Mode Shapes
• Eigensystem Realization Algorithm (ERA)
• Observer Kalman Filter Identification (OKID)
• System Realization by Information Matrix (SRIM)
  • Discrete-Time System Matrix Equation
  • Observability Matrix from Information Matrix
  • State Equation Matrices from Observability Matrix
  • Appendix: Manipulation of discrete-time system matrix equation into correlation matrix relationships