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CH von Kerczek's blog

Torque of Prismatic Beams of Piecewise Rectangular Cross Section

I present in this note a finite difference method and Scilab computer programs to
numerically solve the Saint-Venant theory for torsion of prismatic beams (shafts, bars) of
piecewise rectangular cross section. The purpose of this note is mostly educational, for I
believe that it is quite instructive to not only solve these problems analytically whenever
possible but also explore solutions numerically of common configurations for which one
cannot readily obtain analytical solutions. The same kind of problems occur in heat transfer,

Free Vibrations of Nonuniform Timoshenko Beams II

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.

Forced Vibration of Prismatic Beams

Attached is a computer program, written in Scilab and easily convertible to Matlab, that computes and dsiplays vibrations of prismatic beams forced by a sinusoidal point force. One can impose a variety of boundary conditions, including ones with end masses, springs and dampers. I show several examples. This might be a useful pedagogical item to play around with.

I have similar programs and write-ups for free vibrations of Euler Bernoulli beams and Timshenko beams with variable properties. If any would be interested I would willing to post them too.

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