ANSYS与ANSYS WORKBENCH阻尼分析：深入理解仿真原理

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一、ANSYS 中的阻尼

1.ANSYS中不同分析类型中用到的阻尼

（2）. Damping is used only for mode combination and not for computation of mode coefficients

（3）. Includes superelement damping matrix

（4）. If converted to modal damping by expansion of modes

（5）. If specified, an effective damping ratio is calculated for subsequent spectrum analyses

（6）. The QR damped eigensolver supports damping that may be present in the system (applied via the various damping specification methods available in ANSYS). However, the damping must be applied in the modal analysis portion of the mode-superposition analysis.

（7）. Only the QR damped method supports the constant material damping coefficient application in a downstream mode-superposition harmonic analysis

Alpha damping and Beta damping are used to define Rayleigh damping constants α and β. The damping matrix (C) is calculated by using these constants to multiply the mass matrix (M) and stiffness matrix (K):

(C) = α(M) + β(K)

The ALPHAD and BETAD commands are used to specify α and β, respectively, as decimal numbers. The values of α and β are not generally known directly, but are calculated from modal damping ratios, ξi. ξi is the ratio of actual damping to critical damping for a particular mode of vibration, i. If ωi is the natural circular frequency of mode i, α and β satisfy the relation

ξi = α/2ωi + βωi/2

In many practical structural problems, alpha damping (or mass damping) may be ignored (α = 0). In such cases, you can evaluate β from known values of ξi and ωi, as

β = 2 ξi/ωi

Only one value of β can be input in a load step, so choose the most dominant frequency active in that load step to calculate β.

To specify both α and β for a given damping ratio ξ, it is commonly assumed that the sum of the α and β terms is nearly constant over a range of frequencies . Therefore, given ξ and a frequency range ωi to ωj, two simultaneous equations can be solved for α and β.

2. 用不同阻尼系数构建阻尼矩阵

3. 阻尼矩阵

二、ANSYS WORKBENCH的阻尼（注：比ANSYS多了一个数值阻尼[Numerical damping ]）

Damping is present in most systems and should be specified in a rigid dynamic, flexible dynamic, harmonic response or random vibration analysis. The following forms of damping are available in the program:

Alpha and Beta Damping (Rayleigh Damping). Beta damping defines the stiffness matrix multiplier for damping. You can input the value of beta damping directly or the value can be computed from a damping ratio at a specified frequency. You define beta damping in the Details View of the Analysis Settings object.

The value of β is not generally known directly, but is calculated from the modal damping ratio, ξi. ξi is the ratio of actual damping to critical damping for a particular mode of vibration, i. If ωi is the natural circular frequency, then the beta damping is related to the damping ratio as β = 2 ξi/ωi . Only one value of β can be input in a step, so choose the most dominant frequency active in that step to calculate β.

Material-Dependent Damping. You define material-dependent damping as a material property in theEngineering Data module.

Constant Material Damping Coefficient - only applicable for Harmonic Response analyses. You define the constant material damping coefficient as a material property in the Engineering Data module.

Constant Damping Ratio - only applicable for Harmonic Response and Random Vibration analyses. This is the simplest way of specifying damping in the structure. If you set this in conjunction with beta damping, the effects are cumulative. You define the constant damping ratio in the Details View of the Analysis Settings object.

Element Damping from Spring elements – only applicable for rigid dynamic, flexible dynamic, and harmonic response analyses. You define the element damping from spring elements in the Details View of the Springobject.

Numerical damping, also referred to as amplitude decay factor (γ), controls numerical noise produced by the higher frequencies of a structure. Usually the contributions of these high frequency modes are not accurate and some numerical damping is preferable. A default value of 0.1 is used.

You can specify more than one form of damping in a model. The program will formulate the damping matrix as the sum of all the specified forms of damping.