On Wed, May 28, 2008 at 9:24 PM, ahmet alper parker <aaparker at gmail.com>
wrote:
> I am trying to do a modal analysis with K the stiffness matrix and M the
> mass matrix and trying to find K*lamda=w^2*M*lamda. Looking at the matlabs
> help files, I discovered that I can use (M^-1.K) to calculate the
> eigenvalues and eigenvectors with the standard functions. But when I tried
> to find (according to my knowledge) the eigenvectors, The only method I know
> did not worked for the eigenvectors.
> For example
> writing w^2 in the equation and solving for lamda, the lamda is a vector
> and as far as I know I have to enter 1 to at least one of them, since they
> are not independent. Then I solve the others from the matrix equation.
>
>
> K:matrix([(12*E*I)/L^3,0,0],[0,(3.555555555555555*E*I)/L^3,-(3.555555555555555*E*I)/L^3],[0,-(3.555555555555555*E*I)/L^3,(7.111111111111111*E*I)/L^3]);
> M:matrix([(m*L)/2,0,0],[0,(5*m*L)/4,0],[0,0,(3*m*L)/2]);
> J:K-w^2*M;
> solve([determinant(J)=0;], [w]);
>
> I got eigenvalues correctly.
> subst((8*sqrt(sqrt(34)+8)*sqrt((E*I)/m))/(3*sqrt(15)*L^2), w, J);
> t:%;
> [lamda1=0,lamda2=(48*%r1^2-2046*%r1)/(325*%r1+410),lamda3=%r1];
>
> I get:
> [lamda1=0,lamda2=(48*%r1^2-2046*%r1)/(325*%r1+410),lamda3=%r1];
>
> when I try lamda1=0 and
> algsys([t[2,2]*lamda2+t[2,3]*lamda3=0, t[3,2]*lamda2+t[3,3]*lamda3=0],
> [lamda2,lamda3]);
>
> I get:
>
> [[lamda2=%r2,lamda3=-((sqrt(34)+2)*%r2)/6]];
>
> I get different lamdas...
> As you can see, the first set of lamdas are not %r1 proportional so when I
> give %r1 different values, I will get non proportional results...
> In the second, however, they are proportional to %r2,
>
> Which one is correct? (Or both wrong?)
>
> Regards
> A.A.Parker
>
>
>
>
>
>
>
> On Wed, May 28, 2008 at 8:39 PM, Raymond Toy (RT/EUS) <
> raymond.toy at ericsson.com> wrote:
>
>> ahmet alper parker wrote:
>>
>>> Dear all,
>>> I have a K matrix as
>>>
>>> K:matrix([(12*E*I)/L^3,0,0],[0,(3.555555555555555*E*I)/L^3,-(3.555555555555555*E*I)/L^3],[0,-(3.555555555555555*E*I)/L^3,(7.111111111111111*E*I)/L^3]);
>>> and an M matrix as
>>> M:matrix([(m*L)/2,0,0],[0,(5*m*L)/4,0],[0,0,(3*m*L)/2]);
>>> and I am trying to solve
>>> (K-w^2*M)*f=0 eigenvalue problem. (Solving for w eigenvalue and f
>>> eigenvector)
>>> When making manually by equating the determinant to zero and solving for
>>> w, I get the w correct. But when I tried to solve for f, I got different
>>> answers depending on the method I choose,
>>> First solving as a linear equation with 3 equations I get one set of
>>> eigenvectors,
>>> Second, first eigenvector's first term is zero. I get the first equation
>>> out of the system and solved for the rest two equations, I get different
>>> eigenvectors,
>>> Also, they are not proportional, I mean taking one of the eigenvector
>>> values as unity makes the other some value, however taking the other as unit
>>> makes the other another different value, in which I cannot properly unitize
>>> them. I mean, if I take the second value of the eigenvector 1 , the other
>>> (third) is say 0.5 however, if I take the third as 1 it does not make the
>>> second 2.
>>>
>>
>> I'm thoroughly confused by what you're saying here. Can you show what
>> you're actually doing?
>>
>> Ray
>>
>
>