Dynamic Analysis

1. Forced Vibration (Bar)

A single DOF system is subject to a sinusoidal excitation force in the global x-direction in the geometrically linear range. The theoretical solution can be found in the text book by Clough and Penzien, page 53, eq. 4-11 and is displayed in the figure below. The code is contained in the test file __init__.py.

The corresponding FE problem is formulated with 1 or several rod elements in the x-direction in a line. All DOF's except DOF 1 are removed for all nodes. The mass is concentrated at the end node and introduced with a PMASS3 element. The linear dynamic solver is selected, since the problem is linear. Setting the multistep_integration_order to 2 is the sufficient, the numerical damping being dependent on the time step only. Check with the input file r2_tabulated.mdl for the definition of the time step.

The test checks forced vibration defined by the the case option nbc, sfunction defining the excitation function with an expression

   nbc 1 sfunction 'sin(6.6666666666667*t)'

or stabulated with pairs (time, value):

  nbc 1 stabulated [ 0.0 0.0 ... 2.4740042147 -0.707095118523 ]

Both options define the same sinusoidal excitation function of the natural boundary condition. The response is displayed below:

Displacement response.

Figure 72. Displacement response.