Expert skill for modal analysis, frequency response, and vibration characterization of mechanical systems
Analyzes mechanical systems for modal frequencies, harmonic response, and vibration characteristics to evaluate dynamic behavior.
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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.
Analysis Setup
Mode Shape Interpretation
Mode 1-6: Rigid body modes (if unconstrained)
Mode 7+: Flexible modes
Modal Effective Mass > 5%: Significant participation
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 |
Effective Mass
Meff = (phi^T * M * r)^2 / (phi^T * M * phi)
Where:
phi = mode shape
M = mass matrix
r = direction vector
Mode Selection
Frequency Range
Damping Specification
| Damping Type | Typical Values |
|---|---|
| Structural steel | 1-3% critical |
| Aluminum | 0.5-2% |
| Bolted joints | 2-5% |
| Elastomers | 5-20% |
Response Quantities
PSD Input Definition
Acceleration PSD: g^2/Hz
Force PSD: N^2/Hz
Common profiles:
- MIL-STD-810
- NAVMAT P-9492
- Customer specification
Response Statistics
1-sigma response: RMS value
3-sigma response: RMS * 3 (99.7% probability)
Fatigue from Random Vibration
SRS Generation
Design Verification
Time Step Selection
dt <= T_min / 20
Where:
T_min = period of highest frequency of interest
Integration Methods
{
"structure": "FEA model reference",
"analysis_type": "modal|harmonic|random|transient|srs",
"boundary_conditions": {
"type": "fixed|free|constrained",
"locations": "array"
},
"excitation": {
"type": "base|force|pressure",
"frequency_range": [0, 2000],
"psd_profile": "array (if random)",
"time_history": "array (if transient)"
},
"damping": {
"type": "modal|Rayleigh|structural",
"value": "number or array"
},
"output_locations": ["node IDs or named selections"]
}
{
"modal_results": {
"frequencies": "array (Hz)",
"mode_shapes": "reference to shapes",
"effective_mass": {
"X": "array",
"Y": "array",
"Z": "array"
},
"cumulative_mass": "object"
},
"response_results": {
"max_displacement": "number (m)",
"max_acceleration": "number (g)",
"max_stress": "number (Pa)",
"location": "string"
},
"frequency_response": {
"frequencies": "array",
"amplitude": "array",
"phase": "array"
},
"random_statistics": {
"rms_values": "object",
"three_sigma_values": "object"
}
}
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