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 T2ω = 0.1s). From transient results, average stiffness and kinetic energies can be calculated by averaging two values obtained at times separated by T2ω/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 T2ω. The range is selected, where t2s = 2000T2ω = 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: