I'm trying to grab the idea of the solution sequence of general dynamic anlaysis (modal anlysis) of structures where the general equation of structure stability is
m*x(t)'' + c*x(t)' + k*x(t) = F(t)
"m" is :mass matrix
"c" is :damping coefficent matrix
"k" is :spring coefficent matrix
x(t) is: displacement in sepcified direction
For the modal analys external force ( F(t)=0 ) is equal to 0 to get free-vibaration modes of structure, and if assume that there is no damping case, the equation takes the simple form of
m*x(t)'' + k*x(t)=0;
We have to write this equation for each floor, and later on we assembly the equations where they form the matrixes (mass, damp, etc..).
To solve the problem mathematicians introduce the
w :eigenvalue ; fi : eigenvector;
But nowhere I have seen that [m*x(t)'' + k*x(t)=0;] can be written as
Any help is appreciated!