Thanks again for the reply. It's not that simple unfortunately, due to the axial load term. There is still only one natural frequency as ##s_{1}## and ##s_{2}## are functions of ##\omega^{2}##: $$s_{1}=\sqrt{\gamma-\sqrt{\left[\gamma^{2}+\xi\omega^{2}\right]}}$$ and...
I'm solving for the vibrations of an Euler-Bernoulli beam subject to a tensile axial load ##P.## The governing equation that I've solved is $$\rho A\frac{\partial^{2}w(x,t)}{\partial t^{2}}=-EI\frac{\partial^{4}w(x,t)}{\partial x^{4}}+P\frac{\partial^{2}w(x,t)}{\partial x^{2}}-\rho Ag\text{, }$$...
Thanks very much for the replies. What you both say makes a lot of sense, and is definitely the case with a simple solution such as ##
w(x,t)=\sum_{n=1}^{\infty}q_{n}(t)C_{n}sin(s_{2}x)\text{.}## Here, as you say, any even derivative will be a multiple of the original function.
In the function...
We know that modes of vibration of an Euler-Bernoulli beam are given by eigenfunctions, with the natural frequency of each mode being given by its eigenvalue. Thus these modes are all mutually orthogonal.Can anything be said of the derivatives of these eigenfunctions? For example, I have the...
Hi there,
I'm solving the equation for the transverse vibrations of a Euler-Bernoulli beam fixed at both ends and subject to axial loading. It's a similar problem to that described by Rao on page 355 of his book "Vibration of Continuous Systems" (Google books link), except the example he uses...
Aaah, I'm with you now, that all makes much more sense. This link helped me too: http://en.wikipedia.org/wiki/Complex_number#Absolute_value_and_argument
Thanks very much once more, I really appreciate the help.
I'm trying to sketch the nyquist plot of
$$\frac{j\omega-1}{j\omega+1}$$
but can't seem to calculate the argument correctly. I think it should be $$\arctan(-\omega) - \arctan(\omega) = -2\arctan(\omega)$$ but this doesn't give the correct nyquist plot behaviour for $\omega \to 0$ and...