Structural Dynamics, Vibrations, and Aeroelasticity
Dynamic Response of Structures
Single- and Multi-Degree Systems
The canonical oscillator is Its undamped natural frequency is and damping ratio is In multi-degree systems, modal analysis decouples the equations approximately into independent generalized coordinates.
For the system , the undamped natural frequency is
The natural frequency of the undamped system depends on stiffness and mass.
Correct answer: B:
What phenomenon occurs when forcing frequency approaches a natural frequency?
Response amplitude can increase dramatically near resonance, especially for low damping.
Correct answer: Resonance
Modal Analysis and Aeroelasticity
Modes and Coupling
Mode shapes represent independent vibration patterns of a structure. In coupled systems, fluid forces can introduce destabilizing feedback, leading to flutter, vortex-induced vibration, or galloping. Aeroelastic analysis combines structural stiffness, mass distribution, and aerodynamic loading to identify stable operating limits.
Vibration Concepts
| Concept | Meaning | Design implication |
|---|---|---|
| Natural frequency | Preferred oscillation rate | Avoid excitation near it |
| Damping | Energy dissipation | Reduces peak response |
| Mode shape | Spatial deformation pattern | Guides sensor and actuator placement |
| Flutter | Self-excited instability | Requires stability margin |
Why is damping important in vibration design?
Damping dissipates mechanical energy and helps suppress large oscillations.
Correct answer: B: It dissipates energy and reduces response amplitude
What is a mode shape?
Mode shapes describe how different parts of the structure move relative to one another.
Correct answer: A characteristic deformation pattern associated with a natural frequency
Engineering Judgment
A structure can be statically safe but dynamically unsafe; dynamic loads, fatigue, and instability must be assessed separately.