How do I install the Modal Analysis skill?

Run npx skillmds@latest add ashfordeou/modal-analysis in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

Is Modal Analysis safe to use?

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Which AI agents work with Modal Analysis?

This skill is tagged as working with Claude Code, Claude.ai, OpenAI Codex. SKILL.md is an open format, so most agents that read a skills directory can load it too.

Is Modal Analysis free to use?

Yes. Installing skills from SkillMD is free. This skill is licensed under Apache-2.

Who published Modal Analysis?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Modal Analysis by ashfordeou — Agent Skill

Name: Modal Analysis
Author: ashfordeOU

Modal Analysis

Use when you must run a modal analysis of a two degree of freedom mass-spring structural model: compute the natural frequencies in rad/s and Hz, derive the mode shape ratios, and check an excitation frequency against the natural frequencies for resonance risk. Units are SI: masses in kg, stiffnesses in N/m, frequencies in rad/s and Hz. Trigger: modal analysis, natural frequency, mode shape, resonance, eigenvalue, vibration, two degree of freedom.

ashfordeOU 8320104 3 files · 15.3 KB Updated Sep 17, 2026

File contents

Modal Analysis (structures/fem/modal-analysis)

Use when the task is modal analysis of a two degree of freedom (2-DOF) mass-spring structural model: computing natural frequencies in rad/s and Hz, deriving mode shape ratios, and checking resonance risk against an excitation frequency. Units are SI: masses in kg, stiffnesses in N/m, frequencies in rad/s and Hz.

Domain quick reference

Modal analysis solves the generalized eigenvalue problem (K - w^2 M) phi = 0 for the natural frequencies w and the mode shape vectors phi of an undamped system.
A 2-DOF model grounded at both ends has stiffness matrix K = [[k1+k2, -k2], [-k2, k2]] and mass matrix M = diag(m1, m2); the two natural frequencies are the roots of det(K - w^2 M) = 0.
Each natural frequency has an associated mode shape: the relative motion of the two masses, expressed here as the ratio phi2/phi1.
Forcing near a natural frequency drives large response amplitudes; a resonance check flags excitation frequencies inside a tolerance band around any natural frequency.
FAR-25 (25.301-25.307) sets the certification context for structure loads and proof; this skill computes the modal quantities that feed vibration-sensitive assessments, not the loads themselves.

Workflow

Gather the two masses (kg) and the two spring rates (N/m) of the grounded 2-DOF model.
Compute the natural frequencies in rad/s with natural_frequencies and in Hz with frequencies_hz.
Derive the mode shape ratio for each mode with mode_shapes (normalized to a first component of 1.0).
Check the excitation frequency with resonance_check (default tolerance band 10% of each natural frequency).
Interpret the verdict: resonance True means the excitation sits inside the band of a natural frequency; detune stiffness or mass to move the natural frequencies away.

Pitfalls

Mixing units: the module is all-SI (kg, N/m, rad/s, Hz); convert inputs before calling the functions.
Forgetting that the coupling spring k2 appears in both diagonal entries of K (as k1+k2 and as k2).
Reading mode shape ratios as absolute displacements; they describe relative motion only.
Using an overly wide resonance tolerance band; 10% of the natural frequency is the default.
Applying a 2-DOF result to a structure that needs more degrees of freedom to represent its modes.

Behavior contract (gate 3)

The modal logic is exercised by the gate 3 contract test: scripts/test_modal_analysis_logic.py against scripts/modal_analysis_logic.py (stdlib unittest, offline). Run: python3 scripts/test_modal_analysis_logic.py

Compliance

FAR-25 is referenced, not reproduced: standards-map.yaml marks it gated: false and reference-only: true; only the summary paraphrase above is used, never standard text.
compliance: STANDARDS-REF, gated: false.

---name: modal-analysisdescription: Use when you must run a modal analysis of a two degree of freedom mass-spring structural model: compute the natural frequencies in rad/s and Hz, derive the mode shape ratios, and check an excitation frequency against the natural frequencies for resonance risk. Units are SI: masses in kg, stiffnesses in N/m, frequencies in rad/s and Hz. Trigger: modal analysis, natural frequency, mode shape, resonance, eigenvalue, vibration, two degree of freedom.license: Apache-2.0---# Modal Analysis (structures/fem/modal-analysis)Use when the task is modal analysis of a two degree of freedom (2-DOF)mass-spring structural model: computing natural frequencies in rad/sand Hz, deriving mode shape ratios, and checking resonance riskagainst an excitation frequency. Units are SI: masses in kg,stiffnesses in N/m, frequencies in rad/s and Hz.## Domain quick reference- Modal analysis solves the generalized eigenvalue problem (K - w^2 M) phi = 0 for the natural frequencies w and the mode shape vectors phi of an undamped system.- A 2-DOF model grounded at both ends has stiffness matrix K = [[k1+k2, -k2], [-k2, k2]] and mass matrix M = diag(m1, m2); the two natural frequencies are the roots of det(K - w^2 M) = 0.- Each natural frequency has an associated mode shape: the relative motion of the two masses, expressed here as the ratio phi2/phi1.- Forcing near a natural frequency drives large response amplitudes; a resonance check flags excitation frequencies inside a tolerance band around any natural frequency.- FAR-25 (25.301-25.307) sets the certification context for structure loads and proof; this skill computes the modal quantities that feed vibration-sensitive assessments, not the loads themselves.## Workflow1. Gather the two masses (kg) and the two spring rates (N/m) of the grounded 2-DOF model.2. Compute the natural frequencies in rad/s with natural_frequencies and in Hz with frequencies_hz.3. Derive the mode shape ratio for each mode with mode_shapes (normalized to a first component of 1.0).4. Check the excitation frequency with resonance_check (default tolerance band 10% of each natural frequency).5. Interpret the verdict: resonance True means the excitation sits inside the band of a natural frequency; detune stiffness or mass to move the natural frequencies away.## Pitfalls- Mixing units: the module is all-SI (kg, N/m, rad/s, Hz); convert inputs before calling the functions.- Forgetting that the coupling spring k2 appears in both diagonal entries of K (as k1+k2 and as k2).- Reading mode shape ratios as absolute displacements; they describe relative motion only.- Using an overly wide resonance tolerance band; 10% of the natural frequency is the default.- Applying a 2-DOF result to a structure that needs more degrees of freedom to represent its modes.## Behavior contract (gate 3)The modal logic is exercised by the gate 3 contract test:scripts/test_modal_analysis_logic.py againstscripts/modal_analysis_logic.py (stdlib unittest, offline). Run:python3 scripts/test_modal_analysis_logic.py## Compliance- FAR-25 is referenced, not reproduced: standards-map.yaml marks it gated: false and reference-only: true; only the summary paraphrase above is used, never standard text.- compliance: STANDARDS-REF, gated: false.

Frequently asked questions