/PROP/TYPE27 (SPR_BDAMP)

Block Format Keyword Describes a damper spring property with one translational DOF. Damper force is bounded by stiffness force.

Format

(1)	(2)	(3)	(5)	(6)	(7)	(8)	(9)	(10)
/PROP/TYPE27/`prop_ID`/`unit_ID` or /PROP/SPR_BDAMP/`prop_ID`/`unit_ID`
`prop_title`
`Mass`				`sens_ID`	`I`_sflag	`I`_leng	`I`_tens	`I`_fail
`K`		`C`	`n`		$δ_{\min}^{1}$		$δ_{\max}^{1}$
`gap`						`F`_smooth	`F`_cut
`fct_ID`₁	`fct_ID`₂	`Ascale`₁	`Fscale`₁		`Ascale`₂		`Fscale`₂

Definition

Field	Contents	SI Unit Example
`prop_ID`	Property identifier. (Integer, maximum 10 digits)
`unit_ID`	(Optional) Unit Identifier. (Integer, maximum 10 digits)
`prop_title`	Property title. (Character, maximum 100 characters)
`Mass`	Mass. (Real)	$[kg]$ (`I`_leng = 0) $[\frac{kg}{m}]$ (`I`_leng = 1)
`sens_ID`	Sensor identifier. = 0 Spring is active. (Integer)
`I`_sflag	Sensor flag. = 0 Spring element activated when `sens_ID` activates and cannot be deactivated. = 1 Spring element deactivated when `sens_ID` activates and cannot be activated. = 2 Spring element activated or deactivated state matches the sensor state and can switch back and forth. The spring initial length ( $l_{0}$ ) is based on the spring length at the activation time. (Integer)
`I`_leng	Input per unit length flag. = 0 Spring properties are input as explained in the definition table. = 1 Some inputs are per unit length. (Integer)
`I`_tens	Tensile behavior flag. = 0 The spring only works in compression. No stiffness or damping in tension. = 1 The spring also works in tension with the defined stiffness and damping. (Integer)
`I`_fail	Failure model flag. =1 Displacement criterion (`I`_leng = 0). Strain criterion (`I`_leng = 1). = 2 Force criterion. (Integer)
`K`	Linear loading and unloading stiffness. (Real)	$[\frac{N}{m}]$ (`I`_leng = 0) $[\frac{N}{m^{2}}]$ (`I`_leng = 1)
`C`	Linear damping coefficient. Default = 0.0 (Real)	$[\frac{Ns}{m}]$ (`I`_leng = 0) $[\frac{N s}{m^{2}}]$ (`I`_leng = 1)
`n`	Exponent for nonlinear stiffness force. Default = 1.0 (Real)
$δ_{\min}^{1}$	Negative failure limit. Default = -10²⁰ (Real)
	`I`_fail = 1: Failure displacement (`I`_leng = 0) Failure strain (`I`_leng = 1)	$[m]$ (`I`_leng = 0)
	`I`_fail = 2: Failure force.	$[N]$
$δ_{\max}^{1}$	Positive failure limit. Default = 10²⁰ (Real)
	`I`_fail = 1: Failure displacement (`I`_leng = 0) Failure strain (`I`_leng = 1)	$[m]$ (`I`_leng = 0)
	`I`_fail = 2: Failure force.	$[N]$
`gap`	Minimum gap before activation. Default = 0.0 (Real)	$[m]$ (`I`_leng = 0)
`F`_smooth	Spring force filtering flag. = 0 No filtering. = 1 Spring force is filtered using the cutoff frequency `F`_cut. (Integer)
`F`_cut	Cutoff frequency for spring force filtering. Default = 100 kHz (Real)	$[Hz]$
`fct_ID`₁	Nonlinear stiffness force function identifier: `I`_leng = 0 A function of spring elongation $f (δ)$ . `I`_leng = 1 A function of engineering strain $f (ε)$ . (Integer)
`fct_ID`₂	Damping force function identifier: `I`_leng = 0 A function of spring velocity $g (\dot{δ})$ . `I`_leng = 1 A function of strain rate $g (\dot{ε})$ . (Integer)
`Ascale`₁	`I`_leng = 0 Elongation scale factor for the stiffness function $f$ . `I`_leng = 1 Engineering strain scale factor for the stiffness function $f$ . Default = 1.0 (Real)	$[m]$ (`I`_leng = 0)
`Fscale`₁	Ordinate scale factor for the stiffness function $f$ . Default = 1.0 (Real)	$[N]$
`Ascale`₂	`I`_leng = 0 Velocity scale factor for the damping function $g$ . `I`_leng = 1 Strain rate scale factor for the damping function $g$ . Default = 1.0 (Real)	$[\frac{m}{s}]$ (`I`_leng = 0) $[\frac{1}{s}]$ (`I`_leng = 1)
`Fscale`₂	Ordinate scale factor for the stiffness function $g$ . Default = 1.0 (Real)	$[N]$

Comments

The spring has one translational degree of freedom in the local x direction which is defined between node N1 and N2 of the spring.
Force computation is activated by default in compression ( δ < 0), and in tension only if I_tens = 1. The spring force value is obtained as follows, where I_leng = 0:
- Stiffness part:
  ${\begin{matrix} F_{K} (δ) = s i g n (δ) \cdot K \cdot {| δ |}^{n} & if & f c t_I D_{1} = 0 \\ F_{K} (δ) = F s c a l e 1 \cdot f (\frac{δ}{A s c a l e 1}) & otherwise \end{matrix}$
  
  Where, $n \geq 1$ .
- Damping part:
  ${\begin{matrix} F_{D} (\dot{δ}) = C \cdot \dot{δ} & if & f c t_I D_{2} = 0 \\ F_{D} (\dot{δ}) = F s c a l e 2 \cdot g (\frac{\dot{δ}}{A s c a l e 2}) & otherwise \end{matrix}$
- Global force:
  ${\begin{matrix} F (δ, \dot{δ}) = F_{K} (δ) + F_{D} (\dot{δ}) & if & | F_{D} (\dot{δ}) | < | F_{K} (δ) | \\ F (δ) = 2 \cdot F_{K} (δ) & otherwise \end{matrix}$
If the I_leng flag is activated (I_leng = 1), the above computations become:
- Stiffness part:
  ${\begin{matrix} F_{K} (ε) = s i g n (ε) \cdot K \cdot {| ε |}^{n} & if & f c t_I D_{1} = 0 \\ F_{K} (ε) = F s c a l e 1 \cdot f (\frac{ε}{A s c a l e 1}) & otherwise \end{matrix}$
- Damping part:
  ${\begin{matrix} F_{D} (\dot{ε}) = C \cdot \dot{ε} & if & f c t_I D_{2} = 0 \\ F_{D} (\dot{ε}) = F s c a l e 2 \cdot g (\frac{\dot{ε}}{A s c a l e 2}) & otherwise \end{matrix}$
- Global force:
  ${\begin{matrix} F (ε, \dot{ε}) = F_{K} (ε) + F_{D} (\dot{ε}) & if & | F_{D} (\dot{ε}) | < | F_{K} (ε) | \\ F (ε) = 2 \cdot F_{K} (ε) & otherwise \end{matrix}$
You can define a compression gap activation as defined on the following scheme:

Figure 1.

If the gap is defined (gap ≠ 0.0) the force computation is activated once the spring compression is bigger than the specified gap.(1)
${\begin{matrix} F (δ + | g a p |, \dot{δ}) \neq 0 & if & δ < - | g a p | \\ F (δ + | g a p |, \dot{δ}) = 0 & otherwise \end{matrix}$

Note: Defining a gap value implies that the spring only works in compression and thus, I_tens = 0, if the gap is defined. If I_leng = 1, the gap is homogeneous to a compressive strain.
The switching between the two forces computation’s formula can lead to a noisy spring response. To address this issue, you can use filtering on the spring force computation, allowing a smooth transition between the two spring states (damped and undamped). To do so, the force filtering flag F_smooth and the cutoff frequency F_cut can be used as:
- If F_cut ≠ 0.0, the filtering is activated (F_smooth is automatically set to 1), and the filtering uses the cutoff frequency provided by you.
- If F_smooth =1 and F_cut = 0.0, the filtering is activated and a default cutoff frequency of 100 kHz is used.
- If F_smooth =0 and F_cut = 0.0, no filtering is used.
If the filtering is activated, the spring force is computed as:(2)
$F_{n}^{f i l t e r} = α F_{n} + (1 - α) F_{n - 1}$

Where, $\begin{matrix} α = 2 π \cdot Δ t \end{matrix} \cdot F c u t$