VM-LSDYNA-WB-004
VM-LSDYNA-WB-004
Undamped Vibration Absorber
Overview
| Reference: | Meirovitch, L. (1986). Elements of Vibration Analysis (2nd Edition). New York: NY: McGraw-Hill Book College Division.131-134. |
| Analysis Type(s): | Explicit Dynamics with Workbench LS-DYNA |
| Element Type(s): |
Solid, Spring Connection |
| Input Files: | Link to Input Files Download Page |
Test Case
A sinusoidal force is applied to the main mass M1 (C, in the figure below) of the undamped system with a dynamic vibration absorber. The response of the main mass is zero for the case of a tuned main system/absorber system at steady state. The absorber system consists of a spring K2 and an absorber mass M2 (A, in the figure below).
| Material Properties | Geometric Properties | Loading | ||||
|---|---|---|---|---|---|---|
|
Main Mass
Main Spring
Absorber Mass
Absorber Spring
|
Spring Length of Springs = 1 m |
Force of Main Mass = 1.0 sin (10t) (entered as discrete values in an array) Initial Absorber Mass Velocity = -0.1 m/s |
Analysis Assumptions and Modeling Notes
As outlined in Meirovitch (1986), if a sinusoidal force of the form 
, acts on the main mass of a system with a vibration absorber, and if the
forcing frequency equals the natural frequency of the absorber system alone:
then at steady state, the main mass motion, 
, is zero, and the absorber mass motion, 
, is given by:
To approximate a sinusoidal force of unit amplitude in the analysis, discrete values are entered in an array, and the array is specified in the dynamic load definition. An initial velocity is assigned to the absorber mass, corresponding to the steady state condition. The resulting motion agrees with the theory of the vibration absorber. The system parameters were selected arbitrarily, resulting in a natural frequency for the absorber system alone of 10 rad/s. This is the required absorber natural frequency for eliminating main mass motion if the input frequency is also 10 rad/s. Also, the chosen parameters result in a steady-state absorber mass response amplitude of 0.01 m.