vibration-analysis

# Dynamics and Vibration Analysis Skill ## Purpose The Dynamics and Vibration Analysis skill provides expert capabilities for modal analysis, frequency response, and vibration characterization of mechanical systems, enabling systematic evaluation of dynamic behavior and resonance avoidance. ## Capabilities - Natural frequency and mode shape extraction - Modal participation factor analysis - Harmonic response analysis configuration - Random vibration (PSD) analysis - Transient dynamic response simulation - Shock response spectrum (SRS) analysis - Damping estimation and modeling - Vibration test correlation and model updating ## Usage Guidelines ### Modal Analysis #### Natural Frequency Extraction 1. **Analysis Setup** - Define mass distribution accurately - Include structural stiffness - Apply appropriate boundary conditions - Request sufficient modes 2. **Mode Shape Interpretation** ``` Mode 1-6: Rigid body modes (if unconstrained) Mode 7+: Flexible modes Modal Effective Mass > 5%: Significant participation ``` 3. **Frequency Targets** | Application | Typical First Mode Target | |-------------|--------------------------| | Machine mount | > 2x operating speed | | Building floor | > 8 Hz (human comfort) | | Aerospace | Per environment specification | | Automotive | Avoid engine orders | #### Modal Participation Factors 1. **Effective Mass** ``` Meff = (phi^T * M * r)^2 / (phi^T * M * phi) Where: phi = mode ...