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A theoretical method using the linear damping model is proposed to understand the pressure effect.
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The linear damping coefficients of the equivalent linear viscous dampers are calculated taking advantage of modal damping ratios properties of classically damped systems.
Two types of cubic oscillators have been used as examples: the linear damped oscillator f x, xdot) = xdot, and the van der Pol oscillator f x, xdot) = (α − βx2)xdot.
In this study, a new design method of seismic isolation is developed using the linear quadratic algorithm that concurrently provides the terms of stiffness and damping coefficient.
I'm using the linear method".
It is, however, found that in resonance regions the simulation overpredicts response magnitudes, possibly due to the use of the linear damping model and linear elastic constitutive model.
An equivalent linear mechanical model is subsequently developed using an equivalent displacement variable and the linear damping ratio corresponding to the type of excitation being applied to the structure.
Levine [7, 8] first studied the interaction between the linear damping ((q=1)) and source term by using a concavity method.
For this reason, the method is not unlike the familiar decrement method, which can be used to estimate the apparent linear damping.
Moreover, when only the pure cubic order nonlinear damping is used without linear damping, the force or displacement transmissibility is even better.
This suggests that a less significant linear damping together with a strong cubic non-linear damping can be used in MDOF structures to achieve a desired vibration isolation performance.
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