Description of the tutorials

Module Tutorials

This pyHarm module consists of a series of Jupyter Notebooks that are built in the objective of understanding Harmonic Balance Method and its key characteristics. The tutorials are built in thematic blocks. The blocks are described in the sections below.

Block 01 : Introduction to Harmonic Balance Method

This block regroups three tutorials that introduce basic concepts for the HBM and treating them using pyHarm in an inductive way. A supplementary tutorial is given as well in order to challenge the learner. The Table below details the theme introduced by each tutorial.

Tuto	Name	Summary
001	Time Intergration	This tutorial introduces the HBM method and tries to weight the pros and cons of the method versus the classical time integration method in the linear case.
002	Alternating Frequency Time scheme	This tutorial introduces the AFT scheme used for computing non-linear functions that are explicit in the time domain. It uses the simple pendulum as an exemple that drives all the tutorial.
003	Predictor/Corrector	This tutorial introduces the prediction/correction scheme used in the FRF_NonLinear analysis of pyHarm. This shows the impact of using a continuation method for convergence. Some user-made predictors are coded and compared to more complex and efficient state of the art predictor methods.
004	SkyScrapper	This tutorial is a challenging tutorial to conclude the first block of tutorial. It consists of a whole study over a skyscrapper represented by a lumped model. In this tutorial, custom user forcing are coded in order to represent earthquake and wind loadings and damping systems are added to the building to damp the main resonances.

Block 02 : Introduction to friction phenomenon

This block regroups three tutorials that introduce the friction phenomenon in an HBM framework. It is advised to do this block after the previous one as many components are important. The Table below details the theme introduced by each tutorial.

Tuto	Name	Summary
005	Introduction to friction	This tutorial introduces the friction effects through the use of a \(`\tanh{}`\) function. This also introduces the coding of a non-linear element into pyHarm for the first time. The effect of friction over the damping is studied on a simple test case in order to see the sensitivity of the damping effect with the constitutive parameters of friction.
006	Bladed disk with ring damper	This tutorial treats a lumped mass model of a full bladed disk. A ring damper is added to the bladed disk in order to dampen resonances.
007	Super-element and 3D blade	This tutorial shows the Craig-Bampton methodology for reducing a dynamical model. The method is applied onto a simple beam test case and the performance of the reduced order model is compared with the full order model. A forced response analysis is then made on a provided super-element of a 3D academic blade

Block - non-regression test base

This block is constituted of a single Jupyter Notebook file and constains all the test cases that are present in the non-regression test base. It can be used to see the look of the Forced Response Curves of those test cases as well as seing examples of inputs for pyHarm.