* Through product design that incorporates mechanical damping features.
Vibration damping thermoplastic elastomers (VDT), also known as energy dissipating TPEs, can significantly reduce vibration when used in place of non-damping elastomer polymer systems.
The group contribution analysis method is used to calculate theoretical TA values and develop a relation between the contribution of each functional group and damping properties.
where [D.sub.i] is the damping percentage of component i, T[A.sub.i] and T[A.sub.c] are the TA value of component i and composite, and T[A.sub.c,0] is the TA value of composite at 0 wt.% content of component i.
where [alpha] is the mass proportional damping coefficient, M is the mass matrix, [beta] is the stiffness proportional damping coefficient, and K is the stiffness matrix.
where [[omega].sub.i] is the circular frequency of mode i; [alpha] is the coefficient to define the mass proportional Rayleigh damping ratio [[xi].sub.[alpha]]; [beta] is used to define the stiffness proportional Rayleigh damping ratio [[xi].sub.[beta]].
When excited at this resonant frequency, the magnitude of the response is dependent on stiffness and
damping. As
damping changes, the natural frequency changes very little, but the gain's magnitude changes significantly.
Two orders of the reference frequency can be easily and appropriately selected to determine Rayleigh
damping coefficients when the degree of freedom of a structure is low or the dynamic response of this structure is controlled by some low-order modes.
The
damping force adjuster for the semi active damper is composed of a linear solenoid and has a characteristic where the
damping force increases in proportion to the control current i.
(3) Based on the well-known fact that internal and external
damping can be transformed to Rayleigh
damping, it is shown that the
damping coefficients can be effectively determined using proportional
damping and two
damping coefficients can be reasonably estimated for real systems through a parametric study of
damping coefficients in association with flutter loads of Beck's columns.
Figures 4 and 5 are drawn for
damping per period versus wavenumber for fast and slow waves for the same set of values of flow, respectively.
A PSS is added with each synchronous generator to provide an additional
damping torque if system tempts to become unstable for oscillations.
The
damping coefficient is selected so that the vibrational energy it dissipates is equivalent to the energy dissipated in all the
damping mechanisms, combined, present in the actual structure.
[G.sub.p](s) and [G.sub.u](s) are respectively the transfer functions in active power and voltage control loops attached with
damping controllers, then [[DELTA]V.sub.sp] and [[DELTA]V.sub.su] can be written as (3):
