multi-support excitation
In this example, we illustrate how to perform response history analysis with multiple support excitations.
The model can be downloaded here.
The multiple support excitation refers to different prescribed motions at various supports. The general discussion of linear elastic systems, as presented in typical textbooks (see for example Chopra's textbook) , is somehow not suitable to numerical implementation.
The implementation in suanPan
converts whatever support excitations applied to prescribed displacements and the displacement controlled algorithm MPDC
is automatically enabled to solve the system.
Thus, support excitations in forms of displacement, velocity and acceleration are supported.
A Simple Model
Here we first create a simple cantilever beam with additional point mass at the free end. The basic geometry related commands are stored in file geometry.sp
.
The analysis setting consists of a dynamic step with Newmark
integrator. Those settings are stored in setting.sp
file.
Apply Excitation On All Nodes
To apply acceleration excitation on all nodes, the boundary conditions need to be assigned in a normal, conventional way so that no rigid body motion is allowed.
It shall be noted $-\ddot{u}_g$ is applied.
Apply Excitation On Support
To apply acceleration excitation on support, the corresponding DoF should not be constrained. Thus, rigid body motions are expected.
Now it is ready to perform the analysis.
Result
Here the displacement of the free end is plotted.
It shall be noted that since rigid body motions are present when excitations are applied to the supports, the relative displacement needs to be obtained by computing the difference between displacements of target DoF and support.
All time integration methods are implemented in such a way that both ways of applying excitations would yield the same results if they are equivalent theoretically. This is done by applying algorithm-aware conversion among displacement, velocity and acceleration excitations.
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