Transient Dynamic Response of a Clamp Beam with Different Inertia

This test lets you check analysis results for a beam with different inertia, in the context of a transient dynamic response case. You will use a 1D mesh.
This test proposed by AFNOR is used to validate the transient dynamic response solve algorithms.

Reference:

Guide de validation des prologiciels de calcul de structures, AFNOR Technique, SFM pp188-189.

 

Specifications

Geometry Specifications

Beams AC and DB:

  • l = AC = DB = 1.25 m

  • area = 2.872e-3 m2

  • Iy = 1.943e-5 m4

Beams CD:

  • L = CD = 2.5 m

  • area = 5.356e-3 m2

  • Iy = 8.356e-5 m4

The structure and the load being symmetrical, only one half of the beam is modeled.


Analysis Specifications

Young Modulus (material):
E = 200 GPa

Masses for Frequency Case:

  • Edge AC: Line mass density = 22.402 kg/m

  • Edge OC: Line mass density = 42.398 kg/m

Mesh Specifications:
Beam mesh with a mesh size equal to 62.5 mm

Restraints:

  • Clamp on A

  • Edges AC and CO: Rx = 0

  • Point O: Tx = Ty = Rx = Ry = Rz = 0

Loads:

  • q1 = 10000 N_m
    all beam long

  • t1 = 2.38e-2 s

  • t2 = 5.95e-2 s

  • Global damping = 0 %

 

Results

Frequency Response

Bending mode

Frequency [Hz]

Error [%]

Analytical solution

Computed results

1

63.009

62.8796

0.21

Transient Dynamic Response

Time [s]

Point
localization [mm]

Displacement V [mm]

Error [%]

Analytical Solution

Computed results

0.0595

2437.5

2.469

2.467

0.09

To Perform the Test:

The Transient_dynamic_response_beam_inertia.CATAnalysis document presents the complete analysis of the transient dynamic response case.

To compute the case, proceed as follow:

  1. Open the CATAnalysis document.

  2. Compute the Frequency case, and generate an image called Deformed mesh.