modelQuadratureLobatto3
Extends from Modelica.Icons.Example (Icon for runnable examples).
Information
Technically, this example demonstrates how to utilize a function as input argument to a function in a model.
From a modeling point of view, the example demonstrates in very simplified way the basic approach to model distributed systems with the Ritz method.
The displacement field u(c,t) of a particle (where c is the undeformed position and t is time) is hereby approximated by space-dependent mode shapes Φ(c) and time-dependent modal amplitudes q(t), that is u = Φ(c)*q(t). When inserting this decomposition in the equations of motion and then integrating over all particles, terms such as ∫(Φ(c) dc)*q(t) appear, where the time-invariant integral term can be computed beforehand once with the Lobatto method. By this approach the partial differential equations are transformed to a system of ordinary differential equations.
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Real | A | 1 | Amplitude of integrand of s |
| Real | ws | 2 | Angular frequency of integrand of s |
| Real | wq | 3 | Squared angular frequency of q |
| Real | s | Modelica.Math.Nonlinear.quadratureLobatto(function UtilityFunctions.fun7(A = A, w = ws), 0, 1) | Time-invariant integral value |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Real | q | First-order state variable | |
| Real | qd | Second-order state variable | |
| Real | x | Overall value as product of s and q |