Learning Forum

[Federico Bassi]

Hi,

I am having difficulties on correlating the axial stiffness of a simple cube between a modal and a static structural analysis.

I am analyzing the cube shown below, that has the following properties:

Cube Length L = 10 mm, Elastic Modulus E = 1050 MPa, Density rho = 7850 kg/m^3, Normal displacement fixed at one side.

According to theory, the stiffness is equivalent to K = E A / L = 1.05E4 N/mm, where A = L^2 = 100 mm^2. The axial natural frequency of the cube is then equal to: f = 1/(2*pi())*sqrt(K/M), where M is the mass of the cube (0.00785 kg). The axial natural frequency is then calculated as 5821 Hz. However, according to modal analysis results, the axial natural frequency is way higher, f = 8948 Hz.

For this reason, I have performed a static analysis to check the stiffness of the cube by applying a unit force at one face. The obtained displacement (u = 9.52E-5 mm), confirms an axial stiffness K = F/u = 1.05E4 N/mm. Please note that for static analysis convergence, I have fixed the displacement of one vertex on the fixed displacement side.

Could you please help me understand what I am doing wrong in such a simple simulation?

Thank you in advance.

[Erik Kostson]

 

 

 

 

 

 

 

Hi

The resonance for the first long. mode is not like ~K/M so not as a mass spring system.

It is more like this.In a rod or bar (fixed at one end) the freq. of the first long. mode is given by: freq. = c_speed_longwave/(4*L) – input the values (E=1050E6,rho=7850, and L=0.01 m) and one gets about 9000 Hz which is not far from the Ansys results.
c_speed_longwave ~ sqrt(E_modulus/rho_density)

For more info on elastic waves and structural vibrations see perhaps some text books (e.g.: Wave Motion in Elastic Solids)

Hope this helps.

Erik