mass-spring-dashpot system
Last updated
Last updated
This example is taken from the ABAQUS benchmark manual, see section 2.6.1. The original problem is also reported in the research paper, see 10.1002/nme.1620170902.
The model can be downloaded.
The configuration of the model is shown below.
There are two DoFs in the system, two masses are connected to fixed points via nonlinear elastic springs. In order to do so, we define four nodes.
Here we use unit distance between two adjacent nodes. If the elements used are based on strain and strain rate, the unit distance is the only correct choice. If the elements used are based on displacement and velocity, the unit distance is not a must.
The left spring uses a function. To model it, we use Tanh1D material.
The right spring uses a function. To model it, we use Sinh1D material.
The middle spring is a linear spring, we simply use Elastic1D material.
The dashpot is linear. We use in Viscosity01 material. The viscosity coefficient is .
The springs can be modelled by using either T2D2, which uses strain and strain rate as the basic quantities, or Spring01, which uses displacement and velocity as the basic quantities.
For a linear dashpot, we use Damper01.
In addition to the above, it is necessary to define two mass elements.
The vertical DoFs of all nodes shall be fixed. The horizontal DoFs of the first and last nodes shall be fixed.
The initial condition can be applied to node 2 via
To apply a step load, one shall use tabular amplitude to define the load curve. The following table can be stored in file h.
Then the load can be applied such that
To record response, we define two recorders, one for displacement, one for velocity.
The remaining settings are pretty standard. We use a dynamic step with a default integration scheme (Newmark). If one wishes, other integration schemes can be used.
One could compare the results with the original results in the paper.
