A nonlinear water accumulation analysis in Python

August 23, 2017

Frames One of my first packages in Python is a program for analysing 2D Frames called anaStruct. I wrote this in the summer of 2016 and learned a lot by doing so. When it was ‘finished’ I was really enthusiastic and eager to give it some purpose in the ‘real’ engineering world. My enthusiasm wasn’t for long though. I wrote a fem package that can compute linear force lines. The real world however isn’t so linear. ... Read more

What should be explained in the Dutch SBR-B Guideline!

May 7, 2017

The Dutch SBR guideline is intended to help you process vibration data and help you determine when a vibration signal can cause discomfort to persons. It seems to me however, that the SBR-B guideline does not have the intention to be understood. They seem to help you by making a super abstract of scientific papers and by giving you a few keywords so you can Google it yourself. This post will elaborate on two formula’s given in the guideline. ... Read more

Writing a fourth order Runga Kutta solver for a vibrations problem in Python (Part 1)

April 13, 2017

Problem If you want to solve a vibrations problem with a force acting on the system you often need to find the solution in nummerical algorithms. Say you have got a single degree of freedom mass spring system as shown in the figure below. SDOF damped mass spring system The differential equation of this system is: \[ mu'' + cu' + ku = F\] When the force that acts on the system is a function, this problem can be solved with symbolical maths by solving the differential equation. ... Read more

Writing a fourth order Runga Kutta solver for a vibrations problem in Python (Part 2)

April 13, 2017

This post continues where part 1 ended. In order to increase the accuracy of our function solver we are going to use a 4th order Runga Kutta algorithm. The basics are the same as with the Euler method. However the dy part of the 4th order method is more accurately computed. Definition The incremental values of this method are defined as: \[ y_{n+1} = y_{n} + \frac{h}{6}(k_{1} + 2k_{2} +2k_{3} + k_{4})\] \[ t_{n+1} = t_{n} + h \] With the factors k1 - k4 being: ... Read more

Writing a fourth order Runga Kutta solver for a vibrations problem in Python (Part 3)

April 13, 2017

This post continues where part 2 ended. The Runga Kutta algorithm described in last post is only able to solve first order differential equations. The differential equation (de) for a single mass spring vibrations problem is a second order de. \[ mu'' + cu' + ku = F\] Note that in this equation: u” = acceleration a u’ = velocity v u = displacement Before we can solve it with a Runga Kutta algorithm we must rewrite the base equation to a system of two first order ode’s. ... Read more

(c) 2017 Ritchie Vink.