Natural frequencies for a plate

[damped]

hi,

I am trying to find the natural frequency for a FFFF plate using classical frequency parameters :

n1=13.47; n2=19.6; n3=24.27; n4=63.16; n5=68.5;

in the equation

W*a^2*sqrt(D/rho)=n(i) where

D =(E*h^3)/(12*(1-nu^2)), flexural rigidity
a = 10 in, side of a square
h=0.0325 in, thickness of the plate
rho = 2.523e-4, density for the aluminum material
nu = 0.3 poissons ratio for the aluminum material
i = 1,2,3,4,5
W = circular frequency in rad/sec

when I am using the above said values and trying to find W and there by f, frequency in hertz for the plate the frequency values are very small and different from the results from ansys(I am using shell element for the plate as its thickness is very small compared to its side).

Am i doing anything wrong in the calculation or is there any mistake the formula.

Can anyone give me the equations to find natural frequencies for FFFF square plate both undamped and damped(single layered-Extensional or free-layer damping) and also the equationto find loss factor equation for a damped FFFF square plate (free layer damping).

(or) could you let me know the goo source to find all the above stuff.

thank you,
sri.

 

[Denial]

I cannot vouch for your n(i) values, but superficial examination suggests two immediate problems with your formula:
(a) As a general rule, frequency is proportional to the square root of stiffness/mass: your formula has this inverted.
(b) Dimensional consistency, as well as point (a), require that you multiply rho by h.

 

[damped]

hi Denial,

You are right its my mistake, I have printed the formula wrong, the formula should be(after taking terms on the right side),

W=(n(i)/a^2)*sqrt(D/rho*h)

actually I was finding the frequencies in matlab I didnt enclose the (rho*h) while dividing 'D' as above. So it initially was dividing the 'D' term with rho and multilying the result with 'h'. I should have had enclosed the denominator term in the brackets as shown below

W=(n(i)/a^2)*sqrt(D/(rho*h))

Any how your pointing out of my simple mistake helped me correct the frequency equation after going through it once again in the matlab.
I have got the answers right now.
Thanks for your help Denial.

thank you,
sri.