- #1
sir_manning
- 66
- 0
Hi everyone
I'm modeling the dynamics of a cantilever that has a non-constant linear density profile, i.e.
[tex]\rho(x)=\rho_{1} \0 \leq x \leq x_{0} [/tex]
[tex]\rho(x)=\rho_{2} \0 x_{0} \leq x \leq l [/tex]
[tex]\rho(x)=0 \0 [/tex] otherwise
My differential equation is:
[tex] \frac{ d^4 \phi(x) } {d x^4} = \phi(x) \rho(x) [/tex]
I'm wondering what tools I should through at this thing. I was thinking Fourier transforms, so I re-wrote [tex] \rho(x) [/tex] as the difference between two box functions. However, when I take the transform I have the convolution of [tex] \Phi(x) [/tex], which is unknown, with some [tex] sinc [/tex] functions.
Could someone point me in the right direction for how to tackle an equation like this?
I'm modeling the dynamics of a cantilever that has a non-constant linear density profile, i.e.
[tex]\rho(x)=\rho_{1} \0 \leq x \leq x_{0} [/tex]
[tex]\rho(x)=\rho_{2} \0 x_{0} \leq x \leq l [/tex]
[tex]\rho(x)=0 \0 [/tex] otherwise
My differential equation is:
[tex] \frac{ d^4 \phi(x) } {d x^4} = \phi(x) \rho(x) [/tex]
I'm wondering what tools I should through at this thing. I was thinking Fourier transforms, so I re-wrote [tex] \rho(x) [/tex] as the difference between two box functions. However, when I take the transform I have the convolution of [tex] \Phi(x) [/tex], which is unknown, with some [tex] sinc [/tex] functions.
Could someone point me in the right direction for how to tackle an equation like this?