Sizing Optimization for NVH Analyses

Types of Supported Design Responses

All the DRESP quantities are load case dependent.

N implies DRESP is calculated at the node, and thus a single node or group of nodes must be specified.

E implies DRESP is calculated for the element; thus, a single element or a group of elements are specified.


Name of design response	Selection area	Description
`FS_ACCEL_X`	N	Acceleration in x-direction for frequency response.
`FS_ACCEL_Y`	N	Acceleration in y-direction for frequency response.
`FS_ACCEL_Z`	N	Acceleration in z-direction for frequency response.
`FS_COMP`	E	Dynamic compliance for frequency response.
`FS_DBA_PRESSURE`	N	Sound Pressure Level [dBA].
`FS_DB_PRESSURE`	N	Sound Pressure Level [dB].
`FS_DISP_ABS`	N	Absolute amplitude for frequency response.
`FS_DISP_X_ABS`	N	Amplitude in x-direction for frequency Response.
`FS_DISP_Y_ABS`	N	Amplitude in z-direction for frequency response.
`FS_DISP_Z_ABS`	N	Amplitude in z-direction for frequency response.
`FS_PHASE_X`	N	Phase in x-direction for frequency response.
`FS_PHASE_Y`	N	Phase in Y-direction for frequency response.
`FS_PHASE_Z`	N	Phase in Z-direction for frequency response.
`FS_PRESSURE_X`	N	Instantaneous sound pressure [Pa].
`FS_RMS_PRESSURE`	N	Effective sound pressure (RMS) [Pa].
`FS_VELOCITY_X`	N	Velocity in x-direction for frequency response.
`FS_VELOCITY_Y`	N	Velocity in y-direction for frequency response.
`FS_VELOCITY_Z`	N	Velocity in z-direction for frequency response.

Relations for Calculation of Design Responses from Fundamental Quantities


`FS_COMP`	$C_{d y n} = \| {P}_{R}^{T} {u}_{R} - {P}_{c}^{T} {u}_{c}$
`FS_DISP_ABS`	$A = \sqrt{u_{R, x}^{2} + u_{I, x}^{2} + u_{R, y}^{2} + u_{I, y}^{2} + u_{R, z}^{2} + u_{I, z}^{2}}$
`FS_DISP_X_ABS` `FS_DISP_Y_ABS` `FS_DISP_Z_ABS`	$A_{x} = \sqrt{u_{R, x}^{2} + u_{I, x}^{2}}$ , so that $x_{x} = A_{x} \cos (Ω t + α_{x})$ $A_{y} = \sqrt{u_{R, y}^{2} + u_{I, y}^{2}}$ , so that $x_{y} = A_{y} \cos (Ω t + α_{y})$ $A_{z} = \sqrt{u_{R, z}^{2} + u_{I, z}^{2}}$ , so that $x_{z} = A_{z} \cos (Ω t + α_{z})$
`FS_PHASE_X_ABS` `FS_PHASE_Y_ABS` `FS_PHASE_Z_ABS`	$a_{x} = \arctan \frac{u_{I, x}}{u_{R, x}}$ , so that $x_{x} = A_{x} \cos (Ω t + α_{x})$ $a_{y} = \arctan \frac{u_{I, y}}{u_{R, y}}$ , so that $x_{y} = A_{y} \cos (Ω t + α_{y})$ $a_{z} = \arctan \frac{u_{I, z}}{u_{R, z}}$ , so that $x_{z} = A_{z} \cos (Ω t + α_{z})$
`FS_ACCEL_X_ABS` `FS_ACCEL_Y_ABS` `FS_ACCEL_Z_ABS`	${\ddot{A}}_{x} = Ω^{2} \sqrt{u_{R, x}^{2} + u_{I, x}^{2}}$ , so that ${\ddot{x}}_{x} = {- \ddot{A}}_{x} \cos (Ω t + α_{x})$ ${\ddot{A}}_{y} = Ω^{2} \sqrt{u_{R, y}^{2} + u_{I, y}^{2}}$ , so that ${\ddot{x}}_{y} = {- \ddot{A}}_{y} \cos (Ω t + α_{y})$ ${\ddot{A}}_{z} = Ω^{2} \sqrt{u_{R, z}^{2} + u_{I, z}^{2}}$ , so that ${\ddot{x}}_{z} = {- \ddot{A}}_{z} \cos (Ω t + α_{z})$
`FS_VELOCITY_X_ABS` `FS_VELOCITY_Y_ABS` `FS_VELOCITY_Z_ABS`	${\dot{A}}_{x} = Ω \sqrt{u_{R, x}^{2} + u_{I, x}^{2}}$ , so that ${\dot{x}}_{x} = {- \dot{A}}_{x} \sin (Ω t + α_{x})$ ${\dot{A}}_{y} = Ω \sqrt{u_{R, y}^{2} + u_{I, y}^{2}}$ , so that ${\dot{x}}_{y} = {- \dot{A}}_{y} \sin (Ω t + α_{y})$ ${\dot{A}}_{z} = Ω \sqrt{u_{R, z}^{2} + u_{I, z}^{2}}$ , so that ${\dot{x}}_{z} = {- \dot{A}}_{z} \sin (Ω t + α_{z})$
`FS_PRESSURE`	$p$
`FS_RMS_PRESSURE`	$p_{r m s} = \frac{p}{\sqrt{2}}$
`FS_DB_PRESSURE`	$p_{d B} = 10 \log (\frac{p_{r m s}}{p_{0}})$
`FS_DBA_PRESSURE`	$p_{d B A} = 20 \log (\frac{p_{r m s}}{p_{0}})$ $+ 10 \log (\frac{1.562339 Ω^{4}}{(Ω^{2} + {107.65265}^{2}) (Ω^{2} + {737.86223}^{2})})$ $+ 10 \log (\frac{2.242881 \cdot 10^{16} Ω^{4}}{(Ω^{2} + {20.598997}^{2})^{2} (Ω^{2} + {12194.22}^{2})^{2}})$

Importance of Specifying Damping Parameters

Important:

It is always recommended to have some kind of damping, either viscous damping or structural damping.
It is recommended to have more damping than might be present in correct physical system. The increase of damping enforces the peaks in the spectra to be wider. Thus, the chance for ending in a local minimum is less likely.

The relationship between the viscous damping $α, β$ and the fraction of critical damping $ξ$ , at frequency $ω$ is given by the following equation:


$ξ = \frac{1}{2} (\frac{α}{ω} + β ω)$

The critical damping indicates the switch from oscillatory response to $ξ = 1$ nonoscillatory. For normal application the damping is around 0.5% (0.005) to around 15% (0.15).

If the damping is unknown, a recommendation is to use the following numbers for the viscous damping:


$α \approx 0, 03 ω \approx 0, 13 f$ $β \approx \frac{0, 03}{ω} \approx \frac{0, 006}{f}$

The relationship between the structural damping and the fraction of critical damping $ξ$ at frequency $ω$ is given by the following equation:


$ξ = \frac{1}{2} (\frac{α_{Ω}}{ω^{2}} + β_{Ω})$

Stiffness-proportional damping more effectively damps higher modes of the domain. If the optimization includes the first peaks in the spectrum and only structural damping is applied, then apply a high damping (>10%) for not creating too narrow peaks. Alternatively, use more sampling points in the frequency response range, especially around the eigenfrequencies.

The user must always define the damping for the design elements and the elements included in the manufacturing constraints using OPT_PARAM.
The design elements and the elements included in the manufacturing constraints should all have the same damping.

Important:

Generally, all damping appearances being independent on eigenfrequencies are allowed.
Damping depending on the eigenfrequencies and eigenmodes are not allowed.
Consequently, modal damping is not allowed in the finite element input file for the frequency response. All kind of discrete damping elements and other kind of damping are allowed outside the design domain.
During the designing the eigenfrequencies change significantly and, thus, will the modal damping also change significantly. The damping of the elements in the design domain must be defined in the parameter file.


Viscous Damping	Structural Damping
Viscous damping for design elements (Rayleigh damping) where the damping matrix is assumed to be proportional to the mass and the stiffness matrices. The damping matrix is defined as $[C] = α [M] + β [K]$ The viscous damping for the elements in the design domain should always be defined using the OPT_PARAM command, where A stands for viscous damping scaled with mass matrix and B stands for the viscous damping scaled with stiffness matrix, as shown below: `OPT_PARAM ... DAMP_VISCOUS_MASS = A DAMP_VISCOUS_STIFF = B ... END_`	Structural damping for design elements where the damping matrix is assumed to be proportional to the mass and the stiffness matrices divided by the excitation and defined as $[C] = (α_{Ω} / Ω) [M] + (β_{Ω} / Ω) [K]$ The structural damping for the elements in the design domain should always be defined using the OPT_PARAM commend, where A stands for structural damping scaled with mass matrix and B stands for structural damping scaled with stiffness matrix, like the following: `OPT_PARAM ... DAMP_STRUCTURAL_MASS = A DAMP_STRUCTURAL_STIFF = B ... END_`

Important:

Concentrated and discrete dampers (often viscous) and other types of damping elements outside the design domain are all allowed.

Warning:

Modal damping (also called fraction of critical damping) in all forms is prohibited.