Trigonometric

A trigonometric time series is a sine wave, active over a time window:

$$\lambda (t)=c_{\text{factor}}\sin (\frac{2\pi }{T}(t-t_{\text{shift}}))t_{\text{start}}\le t\le t_{\text{end}}$$

Outside the window the load factor is zero.

🔧 Grasshopper component

Trigonometric Time SeriesAlpaca4d ▸ 04_Time Series

Inputs

TStartNumber0.0Start of the active window, in s.

Before it the factor is zero.

TEndNumberEnd of the active window, in s.

Must be greater than TStart.

PeriodNumberPeriod $T$ of the sine, in s.

Sets the frequency.

ShiftNumber0.0Phase shift $t_{\text{shift}}$, in s.

LoadFactorNumber1.0Amplitude $c_{\text{factor}}$.

Outputs

TimeSeriesTimeSeriesTrigonometric series, for a Load Pattern.

GraphNumberlistThe values over the window, for plotting.

📈 When to use it

Use it when

• The excitation is harmonic with a known frequency — a machine, a rotating unbalance, an idealised sinusoidal base motion.
• You want a set number of cycles: pick Period, then set TEnd - TStart to that many periods.
• You are sweeping frequency to find a resonance.

Do not use it when

• The excitation is irregular — a real earthquake record → Path or Read Time Series.
• The loading is constant or a simple ramp → Constant or Linear.

Note

Sample the response finely enough to see the wave. The analysis time step Dt on Analysis Step should be a small fraction of Period — twenty points per cycle is a reasonable starting point.

🔗 Relation to OpenSees

timeSeries Trig $tag $tStart $tEnd $period -shift $shift -factor $cFactor

Every input maps straight through.