fbafec96-0132-47db-a67a-f07bcb583d03 18 4 5 false false 0 10 decimal

&[DATE] &[TIME] - &[FILENAME]

x φ A a x * cos * B a x * sin * + C a x * cosh * + D a x * sinh * + :

syst

x φ 0 ≡

x φ x 1 diff (0 ≡

E I.1 * x φ x 2 diff * (0 ≡

E I.I * x φ x 3 diff * (0 ≡

Use parenthesis to avoid SMath equal syntax.

BC are

0 φ 0 ≡ 0 φ' 0 ≡ 21 sys

L φ'' 0 ≡ L φ''' 0 ≡ 21 sys

from equation 1

C syst 1 el x 0 ≡ at C solve maple : A -

from quation 2

D syst 2 el x 0 ≡ at D solve maple : B -

from quation 3

B syst 3 el x L ≡ at B solve maple : a L * cos a L * cosh + (A * a L * sin a L * sinh + / -

We have non-trivial solutions only if (1 + cos * cosh ) is zero:

can't make this to remember symbolic evaluation

zz syst 4 el x L ≡ at symbolic simplify maple : 2 E * I.I * a 3^* 1 a L * cos a L * cosh * + (* A * a L * sin a L * sinh + / 0 =

Using dummy values:

A 1 - :

L 1 :

E 1 :

I.I 1 :

sl syst 4 el x L ≡ at a 010 solve : 1.8751 4.6941 7.8548 31 mat

k Plot x φ a sl k el ≡ at x 0 L lele cases :

1 Plot 2 Plot 3 Plot 3 1 sys 1 1 line