IYPT 2026 Problem: A ruler clamped to a table produces a sound when struck. Investigate how the sound depends on relevant parameters.
A multiphysics COMSOL simulation of a 3D ruler struck by a pulsed force, vibrating in air and generating sound pressure waves. The core research objective: timbre (material spectral signature), pitch (geometric parameter frequency sweep), and loudness (SPL metrics).
Simulation runs on a Linux server (COMSOL 6.1 batch mode). MATLAB post-processing runs locally with offline CSV files.
# 1. (Server) Deploy and run the unified simulation package
# SSH to your Linux server and execute:
cd ~/comsol_work/the_singing_ruler/the_singing_ruler_unified/
./run_sweep.sh
# 2. (Local) Post-process results — MATLAB reads CSV outputs
cd matlab/
# Batch process all sweep results:
matlab -batch "run('report/batch_derived_metrics.m')"
# Generate paper figures (9 figures, 300 DPI):
matlab -batch "run('plot/plot_paper_figures_final.m')"Workflow: COMSOL on Linux server (Java API model → batch solve → CSV export) → SCP CSV files to local → MATLAB reads CSV (offline, no LiveLink needed) → metrics & figures.
No LiveLink required. MATLAB reads pre-exported CSV files. Falls back to LiveLink only when CSV is missing (requires explicit authorization).
What happens when you strike a clamped ruler?
- Mechanical vibration: The ruler (a 3D cantilever beam) is struck by a pulsed force. It vibrates in its eigenmodes — bending, torsional, and axial.
- Sound radiation: The vibrating surface displaces adjacent air molecules, creating pressure waves that propagate outward as sound.
- Multiphysics coupling: Structural mechanics (solid) → Acoustics (fluid), one-way coupled: the structural vibration is the boundary condition for the acoustic pressure field.
| Layer | Theory | Scope |
|---|---|---|
| L1 | Euler-Bernoulli beam | Linear bending vibration; predicts f ∝ h/L² (thin rulers, small amplitude) |
| L2 | Timoshenko beam + elastic clamping | Shear deformation + rotary inertia + finite clamping stiffness K_θ; corrects L1 for thick/short rulers |
| L3 | Duffing + Rayleigh damping + acoustic radiation | Geometric nonlinearity (stiffening at large amplitude), material damping, sound pressure directivity |
| Material | Type | Notes |
|---|---|---|
| Steel | Metal | High Q-factor, bright timbre, linear behavior |
| PVC | Plastic | Low Q-factor, muted timbre, may need geometric nonlinearity |
| Acrylic | Plastic | Medium Q-factor, clear timbre |
| Satiné | Wood | Anisotropic, medium Q-factor (E estimated from literature) |
| Foam PVC (Sintra) | Foam board | Very low Q, highly damped (E estimated from literature) |
- Length
L: 200–600 mm - Thickness
h: 1–6 mm - Width
b: 10–50 mm - Clamping length
L_clamp: 10–50 mm - Strike position: tip, midpoint, 1/3 point
- Strike force amplitude: 0.1–10 N
| Finding | Detail |
|---|---|
f ∝ h/L² |
Holds for thin rulers (deviation < 3%). Timoshenko correction needed for thick/short rulers. |
| Clamping stiffness effects | Clamping stiffness K_θ ≈ 10⁴–10⁵ N·m/rad shifts fundamental frequency by 5–15%. |
| Strike position controls modal participation | Tip → fundamental dominant; midpoint → even modes suppressed; 1/3 point → richer spectrum. |
| Material timbre differences | Steel: high Q, sustained bright tone. PVC/foam: low Q, dull thud. Wood: mid-range. |
| SPL directivity | Front face radiates 15–25 dB louder than side face. Dipole-like pattern at fundamental. |
| Item | Status |
|---|---|
| L1 (Euler-Bernoulli) theory validation | ✅ Verified |
| L2 (Timoshenko + elastic clamp) theory | ✅ Verified |
| L3 (Duffing + Rayleigh + acoustic) theory | ❌ Large-amplitude nonlinear validation pending |
| COMSOL full parameter sweep (5 materials, multiple L/h) | ✅ Completed on Linux server |
Frequency scaling f ∝ h/L² |
✅ Verified (deviation < 3% for thin rulers) |
Clamping stiffness K_θ analysis |
✅ Verified (5–15% shift) |
| Strike position modal control | ✅ Verified |
| SPL directivity (front vs. side) | ✅ Verified (15–25 dB difference) |
| Material timbre characterization | ✅ Verified (steel high Q / PVC low Q / wood medium) |
| Geometric nonlinearity (Green-Lagrange) | |
| Satiné & Sintra elastic moduli | ❌ Literature estimates, not experimentally measured |
| Hyperelastic material model | ❌ Planned (future work) |
| Layer | Technology |
|---|---|
| FEM solver | COMSOL Multiphysics 6.1 (Linux server, batch mode) |
| Model construction | Java (COMSOL Java API) + Python orchestration |
| Post-processing | MATLAB R2025a (offline CSV-first) |
| Configuration | JSON |
All simulation code resides on the Linux server at ~/comsol_work/the_singing_ruler/:
| Package | Directory | Description |
|---|---|---|
| full_server_source | the_singing_ruler_full_server_source/ |
Main package: linear, nonlinear, damping + impulse |
| unified | the_singing_ruler_unified/ |
Unified package: geometric nonlinearity + damping + impulse + long time window |
| hyperelastic | the_singing_ruler_hyperelastic/ |
Hyperelastic material model (planned / in development) |
the_singing_ruler/
├── matlab/ # Post-processing pipeline
│ ├── core/ # Pipeline + derived metrics
│ │ ├── run_beam_model_pipeline.m
│ │ └── run_derived_metrics.m
│ ├── extract/ # FFT, SPL, modal decay, timbre features
│ ├── plot/ # Paper-quality figures (9 figures, 300 DPI)
│ │ └── plot_paper_figures_final.m
│ └── report/ # Batch processing + conclusion table
│ ├── batch_derived_metrics.m
│ └── aggregate_conclusion_table.m
├── the_singing_ruler_unified/ # Unified simulation package (symlink / server ref)
├── scripts/ # Deployment scripts
└── ppt/ # Presentation materials
- MATLAB:
snake_case - Java (COMSOL API):
PascalCase - Python:
snake_case - Quality tiers:
full / medium / coarse / decay / fast / eco(6 levels) - Data integrity: Every data point must trace to a real COMSOL case. No synthetic data, interpolation, or curve fitting.
- Git boundary:
outputs/,runtime/,*.mph,*.pptx,*.pdfexcluded from Git. - COMSOL: server only — never runs in CI.
Detailed documentation (theoretical derivations, paper drafts, experimental plans, literature research) is maintained separately from this code repository.
Knowledge base is not part of this repository.
MIT License — see LICENSE
IYPT 2026 赛题：夹持在桌面的尺子被敲击时发出声音。探究声音如何依赖相关参数。
三维实体尺子受脉冲力敲击后，在空气中振动并产生声压波的 COMSOL 多物理场仿真。核心研究目标：音色（材料频谱特征）、音调（几何参数频率扫描）、响度（声压级 SPL 指标）。
- 仿真：在 Linux 服务器运行（COMSOL 6.1 batch 模式）
- 后处理：本地 MATLAB 处理离线 CSV 文件
# 1.（服务器）部署并运行统一仿真包
# SSH 登录 Linux 服务器后执行：
cd ~/comsol_work/the_singing_ruler/the_singing_ruler_unified/
./run_sweep.sh
# 2.（本地）MATLAB 后处理 — 读取 CSV 输出
cd matlab/
# 批量处理所有扫描结果：
matlab -batch "run('report/batch_derived_metrics.m')"
# 生成论文级图表（9 张图，300 DPI）：
matlab -batch "run('plot/plot_paper_figures_final.m')"工作流程：COMSOL Linux 服务器（Java API 建模 → batch 求解 → CSV 导出）→ SCP CSV 文件到本地 → MATLAB 读取 CSV（离线模式，无需 LiveLink）→ 计算指标 & 生成图表。
无需 LiveLink。MATLAB 优先读取预先导出的 CSV 文件，仅当 CSV 缺失时回退到 LiveLink（需显式授权）。
敲击夹持尺子时发生了什么？
- 机械振动：尺子（三维悬臂梁）受脉冲力敲击，以其本征模态振动——弯曲、扭转、轴向。
- 声辐射：振动表面推动相邻空气分子，产生向外传播的声压波。
- 多物理耦合：结构力学（固体）→ 声学（流体），单向耦合：结构振动作为声压场的边界条件。
| 层次 | 理论 | 适用范围 |
|---|---|---|
| L1 | Euler-Bernoulli 梁 | 线性弯曲振动；预言 f ∝ h/L²（薄尺、小振幅） |
| L2 | Timoshenko 梁 + 弹性夹持 | 剪切变形 + 转动惯量 + 有限夹持刚度 K_θ；对厚/短尺修正 L1 |
| L3 | Duffing + Rayleigh 阻尼 + 声辐射 | 几何非线性（大振幅硬化）、材料阻尼、声压指向性 |
| 材料 | 类型 | 说明 |
|---|---|---|
| 钢 (Steel) | 金属 | 高 Q 值，明亮音色，线性行为 |
| PVC | 塑料 | 低 Q 值，沉闷音色，可能需要几何非线性 |
| 亚克力 (Acrylic) | 塑料 | 中 Q 值，清晰音色 |
| 缎木 (Satiné) | 木材 | 各向异性，中 Q 值（弹性模量为文献估计） |
| 雪弗板 (Sintra/PVC foam) | 发泡板 | 极低 Q 值，高阻尼（弹性模量为文献估计） |
- 长度
L：200–600 mm - 厚度
h：1–6 mm - 宽度
b：10–50 mm - 夹持长度
L_clamp：10–50 mm - 敲击位置：末端、中点、1/3 处
- 敲击力幅值：0.1–10 N
| 结论 | 详情 |
|---|---|
f ∝ h/L² |
薄尺成立（偏差 < 3%），厚/短尺需 Timoshenko 修正 |
| 夹持刚度影响 | K_θ ≈ 10⁴–10⁵ N·m/rad 时基频偏移 5–15% |
| 敲击位置控制模态参与 | 末端 → 基频主导；中点 → 偶次模态被抑制；1/3 处 → 丰富频谱 |
| 材料音色差异 | 钢高 Q 明亮延音 / PVC 低 Q 沉闷 / 木质中等 |
| SPL 指向性 | 正面比侧面高 15–25 dB，基频呈偶极子模式 |
| 项目 | 状态 |
|---|---|
| L1（Euler-Bernoulli）理论验证 | ✅ 已完成 |
| L2（Timoshenko + 弹性夹持）理论验证 | ✅ 已完成 |
| L3（Duffing + Rayleigh + 声辐射）理论验证 | ❌ 大振幅非线性验证待完成 |
| COMSOL 全参数扫描（5 种材料 × 多 L/h） | ✅ 已在 Linux 服务器完成 |
频率缩放 f ∝ h/L² |
✅ 已验证（薄尺偏差 < 3%） |
夹持刚度 K_θ 分析 |
✅ 已验证（5–15% 偏移） |
| 敲击位置模态控制 | ✅ 已验证 |
| SPL 指向性（正面 vs 侧面） | ✅ 已验证（15–25 dB 差异） |
| 材料音色表征 | ✅ 已验证（钢高 Q / PVC 低 Q / 木质中等） |
| 几何非线性（Green-Lagrange） | |
| 缎木 & 雪弗板弹性模量 | ❌ 文献估计值，未实测 |
| 超弹性材料模型 | ❌ 待开发（未来工作） |
| 层 | 技术 |
|---|---|
| FEM 求解 | COMSOL Multiphysics 6.1（Linux 服务器 batch 模式） |
| 模型构建 | Java（COMSOL Java API）+ Python 编排 |
| 后处理 | MATLAB R2025a（离线 CSV 优先） |
| 配置 | JSON |
所有仿真代码位于 Linux 服务器 ~/comsol_work/the_singing_ruler/：
| 包名 | 目录 | 说明 |
|---|---|---|
| full_server_source | the_singing_ruler_full_server_source/ |
主包：线性、非线性、阻尼 + 冲量 |
| unified | the_singing_ruler_unified/ |
统一包：几何非线性 + 阻尼 + 冲量 + 长时间窗 |
| hyperelastic | the_singing_ruler_hyperelastic/ |
超弹性材料模型（待开发） |
the_singing_ruler/
├── matlab/ # 后处理管线
│ ├── core/ # 通用管线 + 衍生指标
│ │ ├── run_beam_model_pipeline.m
│ │ └── run_derived_metrics.m
│ ├── extract/ # FFT、SPL、模态衰减、音色特征
│ ├── plot/ # 论文级图表（9 张图，300 DPI）
│ │ └── plot_paper_figures_final.m
│ └── report/ # 批处理 + 结论表
│ ├── batch_derived_metrics.m
│ └── aggregate_conclusion_table.m
├── the_singing_ruler_unified/ # 统一仿真包（符号链接 / 服务器引用）
├── scripts/ # 部署脚本
└── ppt/ # 演示文稿素材
- MATLAB：
snake_case - Java（COMSOL API）：
PascalCase - Python：
snake_case - 质量档位：
full / medium / coarse / decay / fast / eco（6 档） - 数据完整性：每个数据点必须追溯到真实 COMSOL case；禁止合成、插值、曲线拟合
- Git 边界：
outputs/、runtime/、*.mph、*.pptx、*.pdf不入 Git - COMSOL：仅服务器，不进入 CI
详细文档（理论推导、论文草稿、实验方案、文献研究）独立维护，与代码仓库分离。
知识库不属于此代码仓库。
MIT License — 详见 LICENSE