6.1 Natural Frequency and Mode Shape-Based Methods

Natural frequency and mode shape-based methods are key tools in structural health monitoring. They detect damage by identifying changes in a structure's dynamic properties, like natural frequencies and mode shapes, which are altered when damage occurs.

These methods use modal analysis to measure vibration responses and extract modal parameters. While they're effective for global damage detection, they can struggle with local damage. Advantages include non-destructive application, but limitations include sensitivity to environmental factors.

Fundamental Principles and Applications of Natural Frequency and Mode Shape-Based Methods

Principles of frequency-based damage detection

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• Natural frequency and mode shape-based methods detect damage by identifying changes in the dynamic properties of structures
• Natural frequencies represent the frequencies at which a structure naturally vibrates when subjected to dynamic loads (wind, earthquakes)
• Mode shapes characterize the deformed shape of a structure at each natural frequency (bending, torsion)
• Damage in a structure alters its stiffness and mass distribution leading to changes in natural frequencies and mode shapes
• Comparing the natural frequencies and mode shapes of a damaged structure to a healthy baseline enables damage detection and localization

Modal analysis for structural changes

• Experimental modal analysis measures the vibration response of a structure to extract modal parameters
  1. Accelerometers or laser vibrometers measure vibration response at various locations on the structure
  2. Modal parameter estimation techniques (Frequency Domain Decomposition, Eigensystem Realization Algorithm) extract natural frequencies and mode shapes from measured data
• Finite element model updating identifies changes in modal parameters due to damage
  1. Create a finite element model of the structure based on geometry, material properties, and boundary conditions
  2. Update the model by adjusting parameters to minimize differences between measured and predicted modal parameters
  3. Changes in updated model parameters indicate the presence and location of damage

Evaluation and Limitations of Natural Frequency and Mode Shape-Based Methods

Sensitivity of frequency-based methods

• Sensitivity of natural frequency and mode shape-based methods depends on:
  • Type and severity of damage (corrosion, fatigue cracks)
  • Location of damage relative to mode shapes
  • Number and distribution of sensors
  • Presence of environmental and operational variability (temperature, loading)
• More sensitive to global damage affecting overall structural stiffness
• Local damage (small cracks, impact damage) may not significantly affect global modal parameters and can be challenging to detect
• Improve effectiveness by:
  • Using a dense sensor network to capture local changes in mode shapes
  • Combining multiple modes to increase sensitivity to different damage types
  • Employing statistical pattern recognition to differentiate between damage-induced changes and environmental/operational variability

Advantages vs limitations in monitoring

• Advantages:
  • Non-destructive and applicable to various structures
  • Provide global information about structural health
  • Implementable with a small number of sensors
  • Modal parameters less sensitive to noise compared to other vibration-based features
• Limitations:
  • Limited sensitivity to local damage not significantly affecting global modal parameters
  • Require a baseline model of the healthy structure for comparison
  • Sensitive to environmental and operational variability (temperature, loading)
  • May require structural excitation to obtain measurable vibration responses
  • Extracting accurate modal parameters can be challenging in complex structures (closely spaced modes, high damping)