Parameters

In this page the parameters to classify the comfort level within the app are described.

Peak acceleration

The Peak acceleration is the máximum acceleration registered during the time history. It takes into account positive and negative values, but is given like a single positive value. $$a_{w, pk} = \max \left( |a_{w} (t)| \right)$$

It should be noted that this parameter is dependent on the sampling frequency of the measurement.

Root Mean Square acceleration (RMS)

The Root Mean Square (RMS) acceleration is defined as:

$$a_{w,RMS} = \sqrt{\frac{1}{T} \int_{0}^{T} a_{w}^{2} (t) d t }$$

The weighted Root Mean Square (RMS) acceleration is defined as:

$$a_{w, RMS, \tau} (t_{0}) = \sqrt{\frac{1}{\tau} \int_{t_{0} - \tau}^{t_{0}} a_{w}^{2} (\tau) d \tau }$$

where $t_{0} \in [0, T]$ and $\tau$ is the integration time for running average.

Usually a period of time of $\tau = 1 s$ is used.

Maximum Transient Vibration Value (MTVV)

The Maximum Transient Vibration Value (MTVV) is defined as the maximum weighted Root Mean Square value along the time history serie

$$MTVV = \max \left( a_{w, RMS, 1} (t_{0}) \right)$$

The Maximum Transient Vibration Value is in the order of:

$$\sqrt{2} MTVV = a_{w,pk}$$

that works quite well when the main mode is excited by a resonant load (e.g. the first harmonic of human excitation). This is a usual case in footbridges.

Crest factor (P)

The crest factor is the relationship between the peak acceleration and the rms acceleration obtained from measurements:

$$P = \frac{a_{w,pk}}{a_{w,RMS}}$$

It is used as an indicator to evaluate comfort.

Vibration Dose Value (VDV)

This parameter takes into account magnitude and duration of the vibration

Vibrations behaves as noise, and it becomes uncomfortable when is very high, even a in short time duration or is low but for a long time duration. This parameter takes into account both phenomena.

$$VDV = \int_{0}^{T} \left(a_{w}^{4} dt \right)^{0.25}$$

Response factor (R)

Ratio of the RMS weighted acceleration to a base curve representative of human-induced perception