15.1. Acoustics Overview

RecurDyn/Acoustics is a post analysis toolkit. If the user’s model has any flexible bodies (FFlex and/or RFlex) and loaded an animation file, then the Acoustics analysis can be used. The main function of the Acoustics toolkit is computing the ERP (Equivalent Radiation Power) values.

The ERP are defined as following equation.

(15.1)\[{{e}_{ERP}}={{f}_{RLF}}\frac{1.0}{2.0}C\rho \sum{({{A}_{i}}v_{i}^{2})}\]
Where,
\({{f}_{RLF}}\) is Radiation Loss Factor and a dimensionless number.
\(C\) is a sound velocity. [L/T]
\(\rho\) is a density of a target material which is transferred the noise(sound) or vibration like as an air. [M/L/L/L]
\({{A}_{i}}\) is a area on an i-th flexible patch. [L*L]
\({{v}_{i}}\) is a face normal velocity on an i-th flexible patch. [L/T]

Unit of the ERP is [(M*L/T/T)*L/T]. (Where, M, L, and T are Mass, Length and Time units of the RecurDyn.) If MKS unit system is used, then the ERP unit is [W] (=[N*m/s]).

The ERP density on a i-th flexible patch is defined as following equation. In the ERP density, the patch area is not considered.

(15.2)\[{{e}_{ERP\_\rho i}}={{f}_{RLF}}\frac{1.0}{2.0}C\rho v_{i}^{2}\]

The reported ERP density of the RecurDyn/Acoustics toolkit is defined as followings equation.

(15.3)\[{{e}_{ERP\_\rho }}=\sum{{{e}_{ERP\_\rho i}}}={{f}_{RLF}}\frac{1.0}{2.0}C\rho \sum{v_{i}^{2}}\]

Unit of the ERP density is [(M*L/T/T)*L/T/L/L] (=[M/T/T/T]). If MKS unit system is used, then ERP density unit is [W/m/m].

Acoustics Algorithms

  • Velocity Evaluation

    Acoustics is a post analysis toolkit. It means that the animation data is needed to compute the ERP. And the animation data is written only position level data. Therefore, the velocity is computed from position data of all flexible nodes. The velocity data is computed following equation.

    (15.4)\[\begin{split}\begin{aligned} {\mathbf{v}}_{i,0} &= \mathbf{0}, && j=0 \\ {\mathbf{v}}_{i,j} &= \cfrac{{\mathbf{p}}_{i,j}-{\mathbf{p}}_{i,j-1}}{{t}_{j}-{t}_{j-1}}, && j>0 \end{aligned}\end{split}\]
    Where,
    \({{j}}\) is a simulation time step from 1 to the number of selected animation frames.
    \({{t}_{j}}\) is a j-th simulation time.
    \({{\mathbf{v}}_{i}}\) is a velocity vector of a i-th node.
    \({{\mathbf{p}}_{i}}\) is a position vector of a i-th node with respect to the inertia reference frame.

    Therefore, if the simulation time step is used small value, then the ERP can be more accurate result.

  • The accuracy of FFT (Fast Fourier Transform) Data

    Linear interpolation is used before computing FFT. And the number of FFT data is defined as an odd number. (If user set 24 animation frames, then the scope data is 25 data.)
    Therefore, following two cases is recommended in order to get more accuracy results.
    The animation result should be simulated with constant and small-time interval.
    And select an odd number of animation frames for computing the ERP.

  • Modal ERP Data

    If the selected patch is a RFlex’s and some modes are also selected for Modal ERP, then the Modal ERP data is computed. The computing algorithm is already shown.
    All input data is defined on the RFlex Body Reference Frame and one modal configuration on the each selected modes is only used for the Modal ERP.

Step to Acoustics Analysis

  1. Acoustics needs a model including flexible bodies. And the animation file (RAN) must be loaded.

  2. Define Acoustics parameters and calculate. Or set previous Acoustics result.

  3. See the result with Contour or Scope.