Hi,
in the stuctural mechanic, the stiffness matrix is usually symetric, but if there is a guide on the structure, then it results to unsymmetric matrix. In the couple field analysis there are many cases, in which the matrix is unsymetric. To my know the matrix is also unsymmetic in the accoustic analysis. Normally you can only implemented the full (direct) solution methode in the case of  unsymeteric matrix, so the modal superposition is not valid. Any suggestion?

regards

Even the presence of a guide in strutural mechanics problems desnt affect the symmetry. The symmetry  is attribute to the bettis law or maxwell reciprocal theorem of the system. One has to see where at all this is violated. In formulation where in apart from the field variable as unknown if the derivatives are taken as unknowns in some cases ther is likely hood of higher derivaties not follwing reciprocal law
raj

You can use modal superposition if the system is unsymmetric..you just have to find the right and left eigenvectors of the generalized problem.

hi,
i think that the stiffness matrix of a structure per se (betti's law) is symmetric, but if guie is presence then there is a so called 'quasi stiffness matrix' due to the displacement dependenci of the load increment, i.e load correction matrix (non linear effect). This quasi stiffness matrix is in general unfortunately unsymmetric. But, there are some specials strategies/algorithmics to handle with such unsymmetric matrix (see : Argyris et al in : A General FE-Program system for nonlinear problems in structural mechanics.

regards

Hi all,
thanks FEA_BEM, you are right that the unsimmetry of matrix when guide is precense is due to the non linearity. or do you have another idea about this raj?
pja, i am interested in your way solving the unsymetric matrix with left and right eigenvectors, can you please hint me to some text books, or this is only your idea?
I have actually referred to ANSYS solution capabilities about this matter. I have thought that ANSYS is right, because modalsuperposition presumes that the generalized matrix is diagonal and hence symmetric.
Thanks for your hint.

regards

Look at papers by Dowell,Hall and Thomas on reduced order
models of for aerodynamic systems which are non self-adjoint
systems. The gist of it is as follows. Say you have
a nonlinear system
{dq/dt}=[Q]+{B(t)} (1)
 where the q's are the flow variables and Q is a nonlinear function of the q's and B is the "forcing" term. If you linearize the system about some static solution
[Q(qo1,qo2,...)]+{Bo}={0} (2)
 you get a linear system of equations
{dq_pert/dt}=[J]{q_pert}+{B_pert} (3)
where q_pert is the small perturbation solution about the static solution and J is the Jacobian matrix [\partial Q/ \partial q]..however this Jacobian matrix is not symmetric so if one wants to use an eigenvalue expansion to solve one has to solve for the right and left eigenvectors(after setting B_pert to zero in equation 3):

lambda{q_r}=[J]{q_r}    (4)
lambda{q_l}=transpose([J]){q_l} (5)

where the orthogonality is now

transpose({q_l})[J]{q_r}=0 (6)
transpose({q_l}){q_r}=0 (7)

where q_l and q_r are eigenvectors
for two different eigenvalues. So now if one wants to use an eigenvalue solution of equation 3 one expands q_pert as
{q_pert}=[Er]{a_pert} (8)
where Er is the matrix of right eigenvectors and a are the modal coordinates. Putting this into equation 3 and multiplying through by [El],the matrix of the left eigenvectors, and using the orthogonality conditions of equations 6 and 7(along with assuming that the eigenvectors are normalized s.t.
[El][Er]=) (9)
one gets
{da_pert/dt}=[LAMBDA]{a_pert}+[El]{B_pert} (10)
where [LAMBDA] is the diagonal matrix of eigenvalues.