Hi,
I have a question about how to write down the following problem in a thesis.
I have a standing sinusodial wave with amplitude:
|\hat{q}_n|
which I want to express as superposition of two traveling waves. Would you suggest do write the sum in the last line like I did, or has somebody a...
Actually the real part of N looks good (plotting it in Matlab). However, I'm not sure about my imaginary part. It's more like a trial and error approach...
To the background: I want to compute the the aerodynamic work on a traveling wave. I have a complex pressure p and surface displacement z...
Hi,
I'm not sure about the the normal vector N on a complex function
z(x,t) = A e^{i(\omega t + \alpha x)}
My approach is that (\overline{z} beeing the conjugate of z):
\Re{(\mathbf{N})} = \frac{1}{\sqrt{\frac{1}{4}(\partial x + \overline{\partial x} )^2 + \frac{1}{4}(\partial z +...
Thanks for your post. I start with dx. I can write
e^{2i(\omega t + \alpha x)} = \cos{(2\omega t + 2\alpha x)} + i \sin{(2\omega t + 2\alpha x)}
and then for the first term
\cos{(2\omega t + 2\alpha x)} = \cos{(2\omega t)}\cos{(2\alpha x)} - \sin{(2\omega t)}\sin{(2\alpha x)}
Thus, the first...
Hi,
I try to solve this integral, but I failed... I have tried Euler's formula but it only got more and more complex. Can anyone help me?
\int_{0}^{T}\int_{0}^{L}\frac{e^{2i(\omega t+\alpha x)}}{\sqrt{1-a e^{2i(\omega t+\alpha x)}}}dx dt
Hi,
following the attached paper I try to find the general solution of the following wave equation:
\frac{1}{a^2} \frac{\partial^2 \phi}{\partial t^2} + \frac{2M}{a}\frac{\partial^2 \phi}{\partial x \partial t} + \overline{\beta}^2 \frac{\partial^2 \phi}{\partial x^2} =...
I made some progress to get equation (14) and (15). Not sure if I can already corellate the fourer constant alpha with the wave number.
The equation of motion:
\begin{equation}
\frac{1}{a^2}\frac{\partial^2\phi}{\partial t^2} + \frac{2M}{a} \frac{\partial^2 \phi}{\partial x \partial t} +...
I don't know. This doesn't help. What could he have done? I've heard that Duhamel's principle could be an approach of solving non-homogenious PDEs like the wave equation. Could the solution have something to do with this approach?
Substituting (13) in (2) gives:
\begin{equation}...
Hi,
I have a problem following the solution of a linearized potential flow equation in a publication by Fung.
The problem describes potential flow over an oscillating plate. A boundary layer is approximated by defining a subsonic layer over the panel and supersonic flow above the subsonic...