Dynamics and Vibration Analysis Skill Skill

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

Analysis Setup
- Define mass distribution accurately
- Include structural stiffness
- Apply appropriate boundary conditions
- Request sufficient modes

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 |

Modal Participation Factors

Effective Mass

Meff = (phi^T * M * r)^2 / (phi^T * M * phi)

Where:
phi = mode shape
M = mass matrix
r = direction vector

Mode Selection
- Include modes with significant effective mass
- Typically capture 90%+ of total mass
- Consider all excitation directions

Harmonic Response Analysis

Frequency Range
- Start below first mode
- Include all modes of interest
- Extend beyond highest excitation frequency
Damping Specification | Damping Type | Typical Values | |--------------|----------------| | Structural steel | 1-3% critical | | Aluminum | 0.5-2% | | Bolted joints | 2-5% | | Elastomers | 5-20% |
Response Quantities
- Displacement amplitude and phase
- Acceleration at critical points
- Dynamic stress at notches
- Reaction forces

Random Vibration Analysis

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
- Calculate stress PSD
- Determine zero-crossing frequency
- Apply Steinberg or Dirlik methods

Shock Response Spectrum (SRS)

SRS Generation
- Time history to SRS conversion
- Q factor specification
- Frequency resolution
Design Verification
- Compare component modes to SRS
- Calculate maximum response
- Apply dynamic amplification

Transient Dynamic Analysis

Time Step Selection

dt <= T_min / 20

Where:
T_min = period of highest frequency of interest

Integration Methods
- Implicit (Newmark): Large time steps, unconditionally stable
- Explicit: Small time steps, high-frequency accuracy
- Modal superposition: Efficient for linear systems

Process Integration

ME-009: Dynamics and Vibration Analysis

Input Schema

{
  "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"]
}

Output Schema

{
  "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"
  }
}

Best Practices

Verify mass and stiffness before modal analysis
Include sufficient modes to capture total effective mass
Use measured damping values when available
Validate models with experimental modal analysis
Consider nonlinear effects for large amplitudes
Document all damping assumptions

Integration Points

Connects with FEA Structural for model input
Feeds into Test Correlation for validation
Supports Fatigue Analysis for vibration-induced fatigue
Integrates with Mechanism Design for rotating machinery

Agent Skills: Dynamics and Vibration Analysis Skill

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