Problem with constrained modal calculation

Dan Bostwick
Dan Bostwick New Altair Community Member
edited October 2020 in Community Q&A

There seems to be an issue with constrained modal.

Model a simple cantilever beam, 100 x 200 x 1000mm and assign 304 stainless steel as the material.

  • The first two free modes calculate to 490.4Hz 2 node, short-way and 899.4Hz, 2 node tall way.  Accurate.  Excellent.  Note: 20mm global mesh.
  • Restrain one small surface and the modes are 79.78Hz short-way oscillation and 155.6Hz tall-way oscillation with 20mm global mesh.
    • Refining the mesh to 5mm at the restrained end, the modes are 79.75Hz and 155.5Hz.

Classical calculation of the first mode of a rectangular section cantilever beam is

  • Mode1=1.875^2*(E*I/(Rho*A*L^4)^0.5
  • I = b*d^3/12
    • Short-way:  I = 0.2m*0.1m^3/12 = 0.00001667m^4
    • Tall-way:  I = 0.1m*0.2m^3/12 = 0.00006667m^4
  • Mode 1, Short-way = 501.1Hz
  • Mode 1, Tall-way  = 1002Hz

Compare the free mode 'Inspire' results 490.4Hz and 899.4Hz to the restrained hand calculation 501.1Hz and 1002Hz and it is believable.

Why do the resonant frequencies drop so severely for the restrained cantilever beam model?  79.75 and 155.5Hz for the first two modes is not right.

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Answers

  • Dan Bostwick
    Dan Bostwick New Altair Community Member
    edited February 2020

    A physical test was run to confirm the constrained modal accuracy.  A steel ruler was clamped to our shaker table forming 10' and 11' long cantilever beams.  The primary resonant frequency of both beams was observed and recorded.  The first resonance of the 10' long cantilever was near 26.9 Hz.  The 'Inspire' calculated resonance for this same length was 27.78 Hz.  This confirms the accuracy of the constrained modal analysis in 'Inspire'.

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