TransWikia.com

Manual vs Fusion360 calculation of natural frequency of beam

Engineering Asked on July 26, 2021

I’m trying to uncover the natural frequency of a mass-less beam with 2 masses attached but getting different answers from Fusion360 vs a hand calculation.

Beam and lengths displayed in a drawing

L1=1m, L2=2m, m1=10kg, m2=20kg, Young’s=21010^9Pa, H=0,04m, B=0,02m I=H^3B

My current way of calculating the natural frequencies via matlab is:

alpha11 = 2*L1^3 / (6*E*I);
alpha12 = L1^2*(3*L2-L1) / (6*E*I);
alpha21 = alpha12;
alpha22 = 2*L2^3 / (6*E*I);

A = [alpha11 alpha12
     alpha21 alpha22];

K = inv(A);

M = [m1 0
     0 m2];

omega_n = sqrt( eig(inv(M)*K) );
omega_1 = min(omega_n);
omega_2 = max(omega_n);

f1 = omega_1 / (2*pi);
f2 = omega_2 / (2*pi);

This results in f1 = 3,18 Hz & f2 = 28,57 Hz

When running the same beam in fusion the downwards natural frequencies are f1 = 29,4 Hz & f2 = 10279 Hz.

enter image description here

In fusion the beam had to be given a minimum density of 0,001 g/cm³.

What could be the cause for the natural frequencies differing this much? What am I doing wrong? Any help is deeply appreciated!

EDIT

To clarify the fusion setup. The beam is constrained against xyz-movement in the end. The masses are added as point-masses in the middle of the beam (only acting on a small area)

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP