Association des Parents d'Elèves du Conservatoire de musique agréé et de danse de Châlons en Champagne

Application to viscoelasticity

The only application so far of the VFM to viscoelasticity concerns the measurement of the complex stiffness components of thin isotropic vibrating plates. It is a follow up on earlier work on the identification of elastic stiffnesses of thin composite plates using vibration tests (see below).
In the case of vibrations, the principle of virtual work has to take into account the inertial forces. The assumption of linear vibrations is essential to derive this term. The big advantage in this case is that there is no need to measure the applied forces since the inertial forces provide a sort of distributed load cell (if the material density is known, of course). This is also the case for very high strain rate testing, as reported in the high strain rate.
The following slideshow explains how the method works. Application to vibrating plates
There are two main advantages to the proposed procedure. First, both complex stiffnesses are identified simultaneously at a given frequency, ie, the Qxx and Qxy components, but also the two associated loss stiffnesses Bxx and Bxy. Since most of the alternative methods rely on beam specimens, the Bxy parameter cannot usually be measured. The second advantage is that the damping measurements are not affected by dissipation occuring at the support points. Indeed, the method considers a part of the plate that does not contain external forces and writes that the material is at equilibrium (equilibrium between the inertial and viscoelastic forces). This is independent from what happens at the contact zone. For instance, it has been shown that an increase of structural damping (obtained by inserting a rubber washer at the clamping point of the tested plate) did not change the identified parameters (stiffness and damping). Results are shown in the the following document: test with and without rubber washers.
Clearly, it is possible to apply the method to other tests such as heterogeneous creep or relaxation tests although this has not been done yet.