MATLAB scripts for "Harmonic Balance based Nonsmooth Modal Analysis of unilaterally constrained discrete systems"

This project is an implementation of FEM/HBM, a numerical method performing nonsmooth modal analysis for 1D systems with variable cross-section. Details of this numerical method can be found in paper "Harmonic Balance based Nonsmooth Modal Analysis of unilaterally constrained discrete systems" by Tianzheng Lu and Mathias Legrand. The method is implemented in MATLAB, by Tianzheng Lu.

To run the code, run "main.m". Users could adjust the following configurations:

change_rate: change rate of a bar with linear varying cross-section. For other geometry of bar user could define stiffness/mass matrix arbitrarily.
Ta: time array for continuation
m: number of harmonics
method: spatial discretization method
n: number of spatial discretization
oversampling: model reduction rate. 
cd: n_h in paper. Determine time step lenght in HBM integral, dt = T/m/cd
rho: Arbitary Constant in Signorini residual equation
g0: initial gap

If you have any questions or suggestions, please contact us by tianzheng.lu@mail.mcgill.ca