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Harmonic Response of a Clamped-Clamped Beam – Matlab Analysis

This project focuses on the harmonic response analysis of a clamped-clamped beam under external excitation, using a basic finite element model and numerical processing with Matlab.

Model Overview

The beam is modeled using 4 finite elements. The stiffness and mass matrices are derived analytically and assembled to obtain the global system matrices.

Modal Analysis

Modal analysis is performed using Matlab's eig function, which provides:

  • Eigenvalues (from the diagonal of matrix D)
  • Eigenvectors (matrix Φ), representing the mode shapes

Mode shapes are plotted to visualize the vibrational behavior of the beam.

Frequency Response

The harmonic response is computed in two conditions:

  • Conservative system (no damping)
  • Dissipative system (with damping)

The results at node 2 (displacement, velocity, acceleration) show minimal difference between the numerical methods used, but clear contrast between the two dynamic regimes.

The frequency step is refined around the natural frequencies.