B.2. Analysis Assumptions and Modeling Considerations

As in VM90, the spring lengths are selected arbitrarily and used only to define the spring direction.

The end time of the transient analysis is 2.05s and the time step is 5e-3s, so 4100 time points are calculated.

Steady-state is considered established at t = 1.8s. As the period of the harmonic force is Tω = 0.2s, the damping energy (the energy dissipated over a cycle) is obtained by calculating the difference between the value at t = 1.8s and the value at t = 2s. The work done by the external force is calculated in the same way.

Using Equation 14–336 and Equation 14–347, instantaneous stiffness and kinetic energies resulting from harmonic excitation of pulsation ω are cosine waves of pulsation 2ω (period T = 0.1s). From transient results, average stiffness and kinetic energies can be calculated by averaging two values obtained at times separated by T/2 = 0.05s. Times t = 1.95s and t = 2s are selected.

For stiffness or kinetic energies, peak energy is determined by searching for the maximum value around a time that is a multiple of the period T. The range is selected, where t2s = 2000T = 2s.

The amplitude energy is calculated as the sum the average and peak energy.

The phase of the stiffness energy cosine wave is calculated using:

where is the time of maximum cosine waves of stiffness energy in the time range .

The phase of the kinetic energy cosine wave is calculated using:

where is the time of maximum cosine wave of kinetic energy in the time range .

The phase between stiffness energy and kinetic energy cosine waves is calculated using: