BilinearOilDamper Material

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This command is used to construct a BilinearOilDamper material, which simulates the hysteretic response of bilinear oil dampers with relief valve. Two adaptive iterative algorithms have been implemented and validated to solve numerically the constitutive equations within a bilinear oil damper with a high-precision accuracy.

uniaxialMaterial BilinearOilDamper $matTag $K $Cd <$Fr $p> <$LGap> < $NM $RelTol $AbsTol $MaxHalf>

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$matTag	integer tag identifying material
$K	Elastic stiffness of linear spring to model the axial flexibility of an oil damper (brace and damper portion)
$Cd	Viscous damping coefficient of an oil damper (before relief)
$Fr	Damper relief load (default=1.0, Damper property)
$p	Post-relief viscous damping coefficient ratio (default=1.0, linear oil damper)
$LGap	gap length to simulate the gap length due to the pin tolerance (default=0.0: zero tolerance)
$NM	Employed adaptive numerical algorithm (default value NM = 1; 1 = Dormand-Prince54, 2=adaptive finite difference)
$RelTol	Tolerance for absolute relative error control of the adaptive iterative algorithm (default value 10^-6)
$AbsTol	Tolerance for absolute error control of adaptive iterative algorithm (default value 10^-10)
$MaxHalf	Maximum number of sub-step iterations within an integration step (default value 15)

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Examples:

1. Input parameters:

Assume a bilinear oil damper with axial stiffness K=200.0kN/mm, viscous damping coefficient C=6.0KN/(mm/s), relief load Fr=1000.0KN, p=0.1.

The input parameters for the material should be as follows:

uniaxialMaterial BilinearOilDamper 1 200.0 6.0 1000 0.1

Using these properties, Figure 1c shows the hysteretic response of this damper for sinusoidal displacement increments of 12, 24 and 36mm and a frequency f = 1.0Hz. Figures 1a-1d show the damper hysteresis with varying post-relief viscous damping coefficient ratio (p=1.0, 0.5, 0.1, 0.0).

Figure 1.Oil Damper with various post-relief viscous damping coefficient ratios

Assume a bilinear oil damper with axial stiffness K=200.0kN/mm, viscous damping coefficient C=6.0KN/(mm/s), relief load Fr=1000.0KN, p=0.1 and LGap = 0.5mm due to the pin tolerance at the damper ends.

The input parameters for the material should be as follows:

uniaxialMaterial BilinearOilDamper 1 200.0 6.0 1000 0.1 0.5

Using these properties, Figure 2c shows the hysteretic response of this damper for sinusoidal displacement increments of 0.5, 1 and 1.5mm and a frequency f = 1.0Hz. Figures 2a-2d show the damper hysteresis with varying gap length (LGap = 0.0, 0.2. 0.5. 1.0 mm)

Figure 2.Oil Damper with various gap lengths

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References:

[1]	Akcelyan, S., Lignos, D. G., Hikino, T. (2018). “Adaptive Numerical Method Algorithms for Nonlinear Viscous and Bilinear Oil Damper Models Subjected to Dynamic Loading.” Soil Dynamics and Earthquake Engineering, 113, 488-502. [1].
[2]	Akcelyan, S. (2017). "Seismic retrofit of existing steel tall buildings with supplemental damping devices." Ph.D. Dissertation, McGill University, Canada.

Code Developed and Implemented by : Sarven Akcelyan & Prof. Dimitrios G. Lignos, (McGill University)