Resonant damping treatments

Resonant Damping Treatments. Where damping is required over a more-or-less limited range of frequency, resonant damping treatments can be of use (Ji, Z). Figure 13 shows examples of resonant or tuned dampers that use viscoelastic materials as the lumped elastic element in combination with an appropriate mass. The viscoelastic element can have its principal deformation either in extension or in shear, depending on the geometry chosen. 

In this section we shall give the connections between the nonadiabatic and damped treatments of Fermi resonances [53,73] within the strong anharmonic coupling framework and the former theory of Witkowski and Wojcik [74] which is adiabatic and undamped, involving implicitly the exchange approximation (approximation later defined in Section IV.C). 

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

We shall give here a brief summary of our previous work [71,72] that was concerned with the introduction of the relaxation phenomenon within the adiabatic treatment of the Hamiltonian (77), as was done in the undamped case by Witkowski and Wojcik [74]. Following these authors, we applied the adiabatic approximation and then we restricted the representation of the Hamiltonian to the reduced base (89). Within this base, the Hamiltonian that describes a damped H bond involving a Fermi resonance may be split into effective Hamiltonians whose structure is related to the state of the fast and bending modes ... 

Finally, we should mention the possibility of coherent excitation transfer when the donor-acceptor interaction is strong, but the coupling of the system to the thermal bath is weak. The resulting two-level weakly damped system lends itself to the time-dependent density-matrix approach [33], which is essentially identical to the familiar spin-1/2 treatment in magnetic resonance. Under certain circumstances, coherence effects can be important for singlet energy transfer, because the donor states are populated instantaneously by direct photoexcitation. With a sufficient band width of the excitation source (e.g., ultrashort femtosecond pulses), quantum superposition states can be prepared in a coherent fashion even in condensed media at room... 

The rate equations (147) and (148), which account for all the previously derived dynamical features of creation and evolution of the molecular excitations, are useful because they establish a connection with the standard Liouville equation formalism for rate processes in quantum statistical systems. It should be noted that they are submitted to the same assumptions as the treatment in Section II,A of the molecular resonant states. Collisional damping is described in the framework of impact approximation and weak... 

In the peptide-silica solution, the resonant frequency shift is twice as large as the one measured in the peptide-carbon solution. In addition, the damping coefficient is about 3.5 times larger in the peptide-silica solution than in the peptide-carbon solution. As the accuracy of the experimental data does not allow seeing differences on the values of the plateau between wetting and receding of the liquid surface, the data treatment is based on a resonant frequency shift that remains nearly constant over the whole process. 

Moreover, in considering the effects of the size in the optical response of a metallic nanoparticle, we must put in evidence that in the case of particles with dimensions comparable or smaller than the mean free path of its oscillating electrons (i.e. for gold and silver particles of radius o < 10 nm) the dielectric function of the particles becomes strongly size-dependent and the additional surface damping must be considered for a correct treatment of the resonances intensity. 

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