VM-LSDYNA-WB-001
VM-LSDYNA-WB-001
Response of Spring-Mass System to Step Input
Overview
| Reference: | W. T. Thomson. (1965). Vibration Theory and Applications (2nd Printing). Englewood Cliffs, NJ: Prentice-Hall, 98-99. |
| Analysis Type(s): | Explicit Dynamics with Workbench LS-DYNA |
| Element Type(s): |
Solid, Mass, Spring Connection |
| Input Files: | Link to Input Files Download Page |
Test Case
The one-degree-of-freedom system consists of a spring K and mass M. The load is a step function with a rise time as shown. The peak displacement of M from the finite element solution is compared to an analytical result.
| Material Properties | Geometric Properties | Loading |
|---|---|---|
|
M = 1kg K = 100 N/m |
Spring L.C. = 1m |
Applied force, f(t), to the mass in the form shown in the problem sketch, with t1 = 1 second, and Fo = 3 N. |
Analysis Assumptions and Modeling Notes
The magnitude and rise time of the force input were chosen arbitrarily. As outlined in Thomson (1965), for the system in the problem sketch, with the force input shown, the peak response is given by:
where ωn is the system undamped natural frequency in units of radians per second.