pycba.modal

PyCBA - free-vibration (modal) analysis.

Assembles a consistent mass matrix alongside the (Euler-Bernoulli) stiffness matrix and solves the generalized eigenproblem

\[\mathbf{K}\,\boldsymbol{\phi} = \omega^2\,\mathbf{M}\,\boldsymbol{\phi}\]

for the natural circular frequencies \(\omega\) and mode shapes \(\boldsymbol{\phi}\). Each span is internally refined into nseg Euler-Bernoulli sub-elements so the frequencies and mode shapes are accurate (a single element per span is far too coarse). Supports (including elastic springs) are applied at the original span nodes.

This first version covers prismatic, fixed-fixed spans (no moment releases, GAv or non-prismatic EI); the mass is given per span as a mass per unit length.

Functions

solve_modal

Free-vibration analysis of a pycba.beam.Beam.

Classes

ModalResults

Natural frequencies and mode shapes from a free-vibration analysis.