Equivalent damping coefficient

Here pv and Cy are the equivalent mass per unit length and the equivalent damping coefficient of IPMC in the fluid, respectively ... 

Preliminary design was performed assuming 25% damping ratio on the first mode assuming one damper placed at every story unit (uniform distribution), therefore the fictitious lateral stiffness at a given story is k =34000 kN/m, while the equivalent damping coefficient is c =3588.7 kN s/m. 

Note that c is the equivalent damping coefficient due to the velocity-dependent friction and it becomes negative if < 0. The eigenvalues of the Jacobian matrix... 

A commonly used maximum closedloop log modulus specification is 4 2 dB. The controller parameters are adjusted to give a maximum peak in the closedloop servo log modulus curve of -1-2 dB. This corresponds to a magnitude ratio of 1.3 and is approximately equivalent to an underdamped system with a damping coefficient of 0.4,... 

All three are completely equivalent. The time constant and the damping coefficient for the system are... 

A process has the openloop transfer function Gm = K,/[s(t,s -i- 1)]. A proportional-only controller is used. Calculate analytically the closedloop damping coefficient that is equivalent to a phase margin of 45°. What is the maximum closedloop log modulus vdien the controller gain that gives a 45 phase margin is used ... 

The coherence with the reference spectrum has to be verified on the basis of the comparison with spectral ordinates of the accelerograms, for an equivalent viscous damping coefficient of 5%. 

Gluck et al. (1996) adapted optimal control theory (OCT) to the damper placement problem. OCT is used to minimise the performance objective by optimising the location of linear passive devices. Since passive dampers cannot provide feedback in terms of optimal control gains, three approaches (response spectrum approach, single mode approach, and truncation approach) are proposed to remove the off-diagonal state interactions within the gain matrix and allow approximation of floor damping coefficients. Combination of these methods with OCT and passive devices achieves an equivalent effect compared to active control. 

All linear analysis methods for structures equipped with rate-dependent passive dampers involve a simplified calculatirm of the supplemental (equivalent) damping ratio, For example, given the damping coefficients C, at each story i of a building and by assuming linear fluid viscous dampers (a = 1 in Eq. 1) positioned in a horizontal configuration, eq at the fundamental period of vibration Tj under elastic conditions can be estimated as (Whittaker et al. 2003) ... 

For an SP system with friction coefficient of 0.06 and a peak base shear coefficient of 0.25, the equivalent damping can easily computed as... 

It is useful to define damping coefficient, Cd the total supported mass of the isolation system. From the equation for equivalent viscous damping, the equivalent damping for an isolation system with viscous dampers is given by... 

The value assumed for the equivalent viscous damping ratio is Co = c/Ccrit = 0.02, being Ccrit = 2 /to the viscous damping coefficient for a critically damped system. Even though quite small, this value of Co is reasonable for an undamaged structure within the linear-elastic range. 

As with BDF, the simpler second-order scheme appears about optimal. This method also shows the same smooth and damped error response of Laa-sonen, with the accuracy of CN. The drawback is that for every step, several calculations must be performed in the case of second-order extrapolation, three in all (see Sect. 4.9). This also implies an extra concentration array, for the final application of the formula, for example the vector equivalent of (4.31), requiring the result of the first, whole step, and then the result of the two half-steps. Discretisation for extrapolation is the same as for Laa-sonen (coefficients as in (8.12)), but using two different values of 6T. There are example programs using extrapolation (COTT EXTRAP and C0TT EXTRAP4) referred to in Appendix C. 

Figure 5 Solvent suppression pulse sequences based on filtering methods. Method (A) uses a 7, filter to discriminate resonances of solvent and solutes. The difference in molecular diffusion coefficients is used in method (B). is the spin-echo time. (C) Double-quantum filtering COSY, which uses the fact that there is no J-coupling between the two equivalent protons in water molecules and thus it cannot be excited to higher quantum coherence. The PFG pulses in (A) and (B) are used to attenuate radiation damping effects and dephase any transverse magnetization. They are used for the desired coherence selection in (C).

---