Inside the Racket: Modelling Frame Vibration with MATLAB and ANSYS

💻 The first open parametric framework for tennis racket frame vibration analysis.

At a glance

Tools: MATLAB · ANSYS · Finite Element Analysis

Skills Demonstrated: Parametric Modelling, Quantitative Data Analysis, Validation & Testing, Python/MATLAB scripting, Structured Problem Solving, Technical Communication

Result: Validated to <0.5% against published experimental data across three independent benchmarks — deformation, frequency, and stress

The Result

Four findings with direct design implications emerged from the 13-configuration study. Each one maps a specific geometric parameter to a measurable structural outcome.

📐 383.6 Hz simulated. 382 Hz experimental. Error: <0.5%.

Validated against Russell (2014), Banwell (2014), and Kotze (2000) — three independent published benchmarks, three aligned results.

The Problem

Most published FEA studies of tennis rackets use a single fixed geometry — one specific racket, modelled by hand. That answers "how does this racket vibrate?" but not the more useful question: how does racket shape drive vibrational behaviour?

You can't compare what you can't vary. You can't optimise what you can't compare.

When I searched the literature, no open parametric geometry framework existed. That gap defined the project.

Why This Matters for Racket Pulse

Racket Pulse's premise — that a sensor can read racket speed, spin, and impact point from frame vibration — only holds if vibration signatures are measurable, repeatable, and distinguishable across different impact conditions.

This dissertation provided that proof.

The validation against Russell, Banwell, and Kotze quantified what Racket Pulse needed to assume: the physics is real, the signatures are reproducible, and a sensor at the throat would see a clean, structured signal.

→ Read the Racket Pulse case study

The Parametric Framework

Six input parameters. One complete racket geometry, ready for FEA.

Three approaches were considered: manual CAD in SpaceClaim, importing manufacturer drawings, or parametric MATLAB scripting. Manual CAD was rejected because it locks the study to a single geometry. Manufacturer drawings were unavailable. Parametric scripting won: without it, only one racket could have been studied.

The script went through three iterations. The first produced symmetrical elliptical curves with no control over throat shape. After reviewing Grant et al. (2022, 2024), independent variables were exposed for head width, aspect ratio, beam dimensions and shaft length, at which point the geometries began matching real racket proportions.

A Quick Look — Interactive Geometry Explorer

Input

Adjust any of the six parameters and the frame outline updates in real time using the same parametric equations behind the MATLAB script. The baseline configuration matches the racket used to seed the FEA study.

Output

The Pipeline

1. Generate geometry in MATLAB from six input parameters → export as DXF
2. Import into ANSYS SpaceClaim → convert 2D outline to 3D surface body using beam height and wall thickness
3. Apply orthotropic graphite/epoxy material properties (Taraborrelli et al., 2019)
4. Apply clamped-handle boundary condition simulating a player's grip
5. Run mesh convergence study — early runs showed >5% frequency variation between mesh refinements; converged element size adopted and held constant across the full study
6. Solve modal analysis → extract first six natural frequencies and mode shapes
7. Extract regional stress data at throat, hoop, shaft, and handle

⚠️ The mesh convergence step was unplanned. Early results varied by more than 5% between mesh refinements. Recognising that and responding rather than accepting the default output was one of the more important engineering calls in the project.

Key Findings

Validation

Three independent validation points all aligned:

Throat Stress is Localised and Asymmetric

The fundamental bending mode loaded one side of the throat substantially more than the other two struts. This asymmetry does not appear in any of the literature reviewed at project start. It emerged from the simulation and prompted a new discussion section on throat geometry as a critical design variable — one not in the original scope.

Parameter Sensitivities (13-configuration OFAT study)

What I'd Do Next

• String-bed modelling: using LINK180 line elements to capture string-frame coupling, currently abstracted out
• Dynamic transient FEA: to capture inertial effects during the 4–6 ms ball-impact window
• Experimental validation: via Digital Image Correlation (DIC) and accelerometry on physical rackets
• Optimisation coupling: wrap the framework in a loop to minimise throat stress for a target frame mass, turning the analysis tool into a design tool

Four Things I Learned

1. Parametric thinking opens the door to comparative analysis. Without the flexible geometry model, only one racket could have been studied and the conclusions would have been correspondingly narrower.
2. Trust validation, not assumption. The unplanned mesh convergence study was the difference between a credible result and a flawed one.
3. The most interesting results are the ones you didn't predict. The asymmetric throat stress wasn't in any source literature. Looking carefully at unexpected outputs rather than treating them as noise is a discipline I'll carry into every analytical role.
4. A small original contribution is worth more than a polished replication. Reproducing a single known result would have been easier. Building the parametric framework produced something nobody else had.

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