Academic project · Mechanical vibrations

Structural vibration and PTMD analysis.

Modal analysis of a three-degree-of-freedom structure and numerical evaluation of a passive tuned mass damper.

Damped structural response from the passive tuned mass damper analysis — Damped response with the selected PTMD parameters

Structure: 3 degrees of freedom
Method: Euler–Lagrange · eigenanalysis
Damper: Passive tuned mass damper
Tool: MATLAB

01 · Structural model

Natural frequencies and mode shapes.

I derived the equations of motion for the three-degree-of-freedom structure and used eigenanalysis to calculate its natural frequencies and mode shapes.

The undamped impulse response established the baseline used to evaluate the passive tuned mass damper.

Three-degree-of-freedom structural vibration model — Structural model.

Mode shapes of the structural model — Calculated mode shapes.

02 · PTMD study

Parameter sweep and response comparison.

MATLAB parameter sweeps were used to select passive tuned mass damper values and compare the damped and undamped responses.

Undamped structural response used as the PTMD baseline — Undamped baseline response.

Damped response after adding the PTMD — Response with the selected PTMD.

03 · Result and limits

Peak displacement below the implemented criterion.

The selected damper produced a 0.0673 m peak response, below the 0.0700 m criterion implemented in the analysis and about 6.4% below the undamped peak.

The assignment and report use slightly different wording for the acceptance criterion, and the result was not physically validated. The page therefore reports the implemented numerical comparison only.

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