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 a valve relief. 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 $alpha <$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 parameter of oil damper
$alpha	Viscocity exponent
$Fr	Damper relief force (Damper property)
$p	Post-relief damping coefficient ratio (Damper property)
$LGap	gap length to simulate the gap length due to the pin 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^-6)
$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).
Error creating thumbnail: File with dimensions greater than 12.5 MP Oil Damper with various input parameter variations
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)
File:Fig2 OilDampers.pdf

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References:

[1]	Akcelyan, S., and Lignos, D.G. (2015), “Adaptive Numerical Method Algorithms for Nonlinear Viscous and Bilinear Oil Damper Models Under Random Vibrations”, ASCE Journal of Engineering Mechanics, (under review).

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