mass in the eigenvalue problem

[ali2012]

we know that in the eigenvalue problem, opensees needs mass matrix and stiffness matrix .

also we know that we can define masses in the opensees only in nodal masses

for a one beam with distributed mass, assuming nodal mass can cause large errors for determining natural frequencies.

now my question is that: can we determine the exact natural frequencies and mode shapes for a beam with two simple supported?
what is the solution?
i need this answer very much

thanks a lot

[vesna]

To get close to exact value of periods and mode shapes you need to define several masses along the element length. This means that you have to define several nodes and thus several elements along the element length.

[ali2012]

thanks a lot
why this strong software can not solve this problem exactly??

even i discretize this beam to very node, i can not assign these nodes rotational masses. in the real, rotational masses exist.
question: what about a shell or plate defined with block2d and elasticmembraneplatesection?
should we define very nodes for that too? when we define elasticmembraneplatesection, we enter the rho(mass density)
should for the exact solution for plate or shell define a very large number of nodes or opensees distribute mass over the entire shell or plate?
thanks a lot

[vesna]

because it is FE software. Once you brake a continuum into discrete elements you loose exactness.

if in 2D the third mass argument is for rotational mass.

mass density arguments when defining elements are used to calculate lumped masses.

[ali2012]

thanks vesna
i got it.

[alexntua]

Hello

[alexntua]

Hello i have i have a 2d beam with 10 nodes and 9 elements and i need a formula in order to calculate the rotational mass (the third mass argument).
Could you please help me ?
Thanking in advance
Alex