This post contains the equations of nonuniform Timoshenko beam theory, a seconf order finite difference method for the solution of the free vibrations thereof and a Scilab computer program implementation. The implementation also allows for the calculation of static deflection for a user specified load distribution that can also contain point loads. A number of static and free vibration examples are given.

I hope this can be useful to students and others.

An interesting application of non linear dynamics, including happiness with a simple 1D damped oscillator!

“Project of automatic balancing system for rigid
rotors”

ABSTRACT

Project description: The goal of vibration based structural health monitoring (SHM) is to replace costly inspection campaigns by real-time instrumentation and automated data processing in order to estimate the current state of health and the remaining lifetime of structures. For damage detection, automated data-based methods using adequate statistical techniques have been developed recently. This project deals with the next level of SHM which is damage localization and focuses on the problem of cracking in prestressed concrete. The challenge is to design a data-based damage localization system based on output-only ambient vibrations. The main ingredients of the proposed method are: (i) the use of very large strain sensor networks, (ii) the development of automated and efficient data processing methods based on local spatial filters or several layers of spatio-temporal filters, and (iii) alarm triggering techniques based on unsupervised learning methods. The major innovation in this project is the use of advanced computational techniques for the creation of a large data set of virtual campaigns which are used for the design and optimization of the SHM system. In addition to these virtual campaigns, experimental developments are also foreseen, with a specific emphasis on the evaluation of different techniques for dynamic strain measurements.

Hello!

The model I'm working on in LS-DYNA is a simple pyramid-shaped shell constrained along the bottom edges with all DOF taken. The material used is MAT_PIECEWISE_LINEAR_PLASTICITY. Above the model there's a LOAD_BLAST (Air burst) placed, which deforms the model after the explosion.
The issue is that the model seems to vibrate ininitely after the explosion, what can be seen on the attached images (first one shows the graph of "Rigid Body Displacement", second one shows close-up of the line within the yellow rectangle).

Please find attached the position description