Vibration response, property-parameter

Active vibration-based monitoring method is a classical SHM technique. The main idea behind the method is that structural dynamic characteristics are functions of the physical properties, such as mass, stiffness and damping [22]. Hence, physical property changes due to damages can cause detectable differences in vibration responses. The dynamic characteristic parameters usually used in the technique include frequency, mode shape, power spectrum, mode curvature, frequency response function (FRF), mode flexibility matrix, energy transfer rate (ETR), etc. 

More difficult to calculate are the properties which depend on the response of the solid to an outside influence (stress, electric field, magnetic field, radiation). Elastic constants are obtained by considering the response of the crystal to deformation. Interatomic potential methods often provide good values for these and indeed experimental elastic constants are often used in fitting the potential parameters. Force constants for lattice vibrations (phonons) can be calculated from the energy as a function of atomic coordinates. In the frozen phonon approach, the energy is obtained explicitly as a function of the atom coordinates. Alternatively the deriva-tive, 5 - can be calculated at the equilibrium geometry. 

The popularity of the SOS methods in calculations of non-linear optical properties of molecules is due to the so-called few-states approximations. The sum-over-states formalism defines the response of a system in terms of the spectroscopic parameters, like excitations energies and transition moments between various excited states. Depending on the level of approximation, those states may be electronic or vibronic or electronic-vibrational-rotational ones. Under the assumption that there are few states which contribute more than others, the summation over the whole spectrum of the Hamiltonian can be reduced to those states. In a very special case, one may include only one excited state which is assumed to dominate the molecular response through the given order in perturbation expansion. The first applications of two-level model to calculations of j3 date from late 1970s [93, 94]. The two-states model for first-order hyperpolarizability with only one excited state included can be written as ... 

Fig. 7 illustrates Chapman s treatment of the mechanics of this composite system. The system is treated as a set of zones consisting of fibril and matrix elements. Originally, this was introduced as a way of simplifying the analysis, but, the later identification of the links through IF protein tails makes it a more realistic model than continuous coupling of fibrils and matrix. Up to 2% extension, most of the tension is taken by the fibrils, but, when the critical stress is reached, the IF in one zone, which will be selected due to statistical variability or random thermal vibration, opens from a to P form. Stress, which reduces to the equilibrium value in the IF, is transferred to the associated matrix. Between 2% and 30% extension, zones continue to open. Above 30%, all zones have opened and further extension increases the stress on the matrix. In recovery, there is no critical phenomenon, so that all zones contract uniformly until the initial extension curve is joined. The predicted stress-strain curve is shown by the thick line marked with aiTows in Fig. 6b. With an appropriate. set of input parameters, for most of which there is independent support, the predicted response agrees well with the experimental curves in Fig. 6a. The main difference is that there is a finite slope in the yield region, but this is explained by variability along the fibre. The C/H model can be extended to cover other aspects of the tensile properties of wool, such as the influence of humidity, time dependence and setting.

As in most technical fields, actuators are increasingly designed with the help of computers. The actuator and its surrounding are simulated as a mathematical model by means of commercially available software. Such models are fundamental for the simulation of the system response characteristic in each specific case. In this way, it is possible to find out about all the important properties of the system even before the actuator is built, and the actuators relevant parameters can be optimized to achieve the desired values. This designing strategy is exemplified below with an auxiliary mass damper which is able to withdraw kinetic energy from a host vibrating system. 

The purpose of the present communication is to provide experimental support for the idea that Tp (TTg) are all issued from a unique relaxation kinetics which is primary responsible for the Tg effect The suggestion that Tp is a precursor of Tg is not new 2.4 the idea that T// behaves like a classical kinetic transition, i.e., like a sort of Tg is not new eitfaer. > Frenkel in the USSR suggests that the 7 transition merges with the Tg transition on a log frequency vs. 1/7 plot at a temperature which corresponds to 7//. These observations all concur separately with our own attempt to reconcile into a unique relaxation mechanism the 7 Tg, and Tn "transitions." Atactic polystyrene is chosen here for the experimental data because the physical properties relevant to our discussion are well-documented in the literature for this particular polymer, representative of the class of amorphous polymers. Furthermore, TSC (Thermally Stimulated Current) and DSC results on rheomolded polystyrene samples can be systematically compared since the influence of the rheomolding parameters (frequency of vibration during molding, amplitude of vibration, and post treatment armealing effects) are simultaneously studied and analyzed by both techniques. " ... 

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