# Periodic Steady-State Simulation

The Periodic Steady-State Simulation serves for the computation of periodic limit cycles of nonlinear and linear systems in dependence of a reference quantity (as, for example the mean angular velocity of a rotational mass). Some important fields of application are:

• oscillation analysis of powertrains with combustion engines
• computation of the describing function of nonlinear dynamical blocks in control systems
• Computation of harmonic distortions of electronic amplifiers and filters in dependence of the amplitude of excitation
• hydraulic and pneumatic test benches for oscillatory long-term stress analysis

The applied periodical approach is supplemented by a linear, time-dependent term to take the steadily growing angles of rotating masses in the oscillation analysis of freely rotating powertrains into account. The following frequency-domain quantities can be displayed for the computed results:

• amplitudes
• fluctuation coefficients
• excitations
• phases
• real parts and imaginary parts

In each of these cases the sum curve, the mean value, and the spectral components (orders) are shown. Furthermore, for the periodical part of the ansatz the signal wave form over one period and the fluctuation are available as typical time-domain results. The steady-state simulation allows the consideration of internal behavioral descriptions in the frequency domain, in particular for those effects, which do not have a time-domain representation. This permits the implementation of frequency-dependent damping models in spring-damper-backlashes instead of the Reid damping models used so far. Frequency-dependent damping was added to the following elements:

• ElasticFriction (Mechanics.Rotation)
• Coupling (PowerTransmission.Couplings)
• DiscClutch (PowerTransmission.Couplings)
• Gear (PowerTransmission.Transmission)
• BeltDrive (PowerTransmission.Transmission)

Each of these elements now features a separate parameter page for steady-state simulation, where the damping model can be selected and the spectral power can be recorded as a result quantity (the real part of the spectral power is the dissipated power loss). The Delay Time with constant delay was implemented in the frequency domain too and will generate correct results in steady-state simulation with continuous-time input signals. You can control the steady-state simulation with the help of the corresponding buttons in the ribbon menu. Before starting the simulation make sure that the combo box for the kind of simulation is set to "Steady State". The following table gives you an overview of the available options:

 Start the simulation (hotkey: F5). Stop the simulation. Reset the simulation back to the start time Expand all available reset options. Progress indicator This dropdown menu lets you select the type of simulation: Choose Transient (default setting) for time domain analyses. Open the Simulation Control options for specific solver parameters (tom improve accuracy, performance, or for model debugging tasks).