A computational laboratory framework for teaching modal parameter identification via frequency response function (FRF): A case study with noise sensitivity analysis on a three-dimensional frame

Teaching Frequency Response Function (FRF)-based modal identification is a well-known challenge in structural dynamics courses: the topic is mathematically demanding, and its practical subtleties — such as signal noise effects, estimator selection, and stability diagram interpretation — are difficult to convey through lectures alone. This paper proposes a reproducible computational laboratory framework to support undergraduate and graduate courses in structural dynamics and vibrations. The framework uses SAP2000™ for finite element modeling of a four-story, three-dimensional portal frame, and MATLAB™ native functions (modalfrf, modalsd, modalfit) for FRF computation and modal parameter identification via the Least Squares Complex Exponential (LSCE) method. Broadband white-noise excitation was applied computationally, and additive Gaussian noise was introduced into the simulated response signals to reproduce a controlled measurement-noise scenario. A structured noise-sensitivity study, conducted at levels of 5% to 30% of the maximum response amplitude, allowed students to observe how signal contamination differentially affects natural frequency and damping estimation across vibration modes. Results show that natural frequencies exhibit low sensitivity to noise, whereas damping ratios are significantly more vulnerable, particularly in higher modes. A pilot implementation with seven graduate students showed high technical performance (mean score of 96.4%) and positive perceptions of the methodology (overall mean of 4.67/5). By treating noise as a pedagogical variable, the framework transforms an often black-box signal-processing procedure into an explicit learning experience. The complete computational code is available on GitHub, allowing students and instructors to reproduce the analyses and adapt the routines for educational or research purposes.