VM156
VM156
Natural Frequency of a Nonlinear Spring-Mass System
Overview
Test Case
A mass is supported from a spring having the nonlinear characteristics shown. The mass is displaced an amount δ from its equilibrium position and released (with no initial velocity). Find the corresponding period of vibration τ.
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Analysis Assumptions and Modeling Notes
The problem is solved using the nonlinear spring element (COMBIN39).
For the nonlinear spring element (COMBIN39), the nonlinear spring constant is converted to eleven discrete force-deflection points by F = kδ for δ = 0.0 to 1.0 in steps of 0.1 in.
The IC command is used to impose the initial displacement and velocity configuration. The first load step is defined over a very small time step (.0002 sec) to allow the initial step change in acceleration to be attained. The integration time step for the second load step is based on 1/30 of the period to produce a fine resolution for the theoretical comparison. A final time of 0.18 sec is arbitrarily selected.
The nodes for the nonlinear spring element (COMBIN39) are defined as coincident but are shown apart in the model for clarity.
POST26 is used to extract results from the solution phase. The period is determined by the time when the mass is closest to the original released position after it passes through the spring's equilibrium position.