6. Equations of Motion of SDOF System for Mass as well as Base Excitation
The chapter emphasizes the analysis of dynamic responses in Single Degree of Freedom (SDOF) systems, which are essential for understanding structural behavior during seismic events. Key concepts include equations of motion for mass and base excitation, free and forced vibrations, and the impact of damping on seismic response. The chapter also covers practical considerations in earthquake engineering and highlights the significance of using SDOF models in designing resilient structures.
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What we have learnt
- An SDOF system can effectively represent the dynamic behavior of structures under seismic loads.
- Damping significantly influences the performance of a structure during an earthquake.
- Effective seismic design incorporates understanding of both mass and base excitation.
Key Concepts
- -- Single Degree of Freedom (SDOF) System
- A mechanical system characterized by a single coordinate to describe motion, involving mass, spring, and damper.
- -- Damping Ratio (ζ)
- A dimensionless measure that describes how oscillations in a system decay after a disturbance, affecting energy dissipation.
- -- Free Vibration
- The oscillation of a mechanical system without external forces, described by its natural frequency.
- -- Base Excitation
- A condition in which the ground motion affects a structure at its base, applying forces indirectly rather than directly on the mass.
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