Impact & Shock (impact)
Purpose
Estimate impulse, average impact force, and dynamic stress during short-duration velocity changes. Screens structural components against yield during drop, collision, or shock loading using simplified dynamic load factors.
Physics & theory
Impulse-momentum theorem: . For mass experiencing velocity change over impact duration , average force can exceed static load by dynamic amplification factor for elastic systems.
Dynamic stress compared to yield gives safety factor. Short impact durations (milliseconds) produce high forces; energy absorption through plastic deformation or damping reduces peak stress below rigid estimate.
Dynamic analysis requires careful identification of mass, stiffness, and damping distribution. Natural frequencies depend on boundary conditions — a cantilever beam has fundamentally different modes than a simply supported beam of the same dimensions.
Damping limits resonant amplification; lightly damped structures (( zeta < 0.05 )) can see transmissibility peaks exceeding 10 near resonance. Separation margin between operating excitation and natural frequency should typically exceed 15–20% for rotating machinery.
Governing equations
Numerical method
Closed-form impulse and average force (engine). Impact duration converted from milliseconds to seconds with minimum floor s. Dynamic stress from force over cross-section area; design status flagged at SF thresholds.
Inputs
| Parameter | Description |
|---|---|
mass | Moving mass |
velocityChange | Speed change magnitude |
impactDuration | Contact time (ms) |
crossSectionArea | Load-bearing area (mm²) |
yieldStrength | Material yield (MPa) |
Outputs
- Impulse, average force, dynamic stress, safety factor, design status (safe/warning/critical).
Design codes & checks
- Indicative: Dynamic load factor / yield safety factor
Assumptions & limitations
- Uniform average force over duration; no force-time waveform.
- Single DOF; no wave propagation or stress concentration.
- Impact duration must be estimated or measured — highly uncertain.
- Plastic energy absorption not subtracted from impulse.
Verification
- CI:
impact-indicative-01.json - Engineer sign-off: validation-master-checklist.md
References
- Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 4.
- Rao, S. S. Mechanical Vibrations, 6th ed., shock response.
- MIL-STD-810. Environmental Engineering Considerations and Laboratory Tests.
- Barrow, H. D. Applied Mechanics, impact problems.
- Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.