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Test case, hanging chain

Purpose

The purpose of this test case is to verify that the simulation model gives second order accuracy for the general alpha time integration, see Theory, applied on a hanging chain (balance between inertia, gravity and axial line force). Standing oscillations of a hanging chain have been computed numerically. Comparisons are made with the analytically calculated exact frequencies and displacements of oscillation. The numerical calculation was done for a chain fixed in the upper end and oscillating in the lower frequency modes.

Results

Click on graph below to start animation.

The relative potential and kinetic energies for one period of an oscillation are presented below

The relative error norm versus no of spatial grid divisions is presented below verifying second order error decay.