On the direct measurement of the dynamic Poisson's ratio

Measurement of the Isotropic Dynamic Young's Modulus in a Seismically Excited Cantilever Beam Using a Laser Sensor

“…The choice of a cantilever beam, i.e., a beam with clamped-free boundary conditions, fastened to the support, is the result of many years of tests. As a matter of fact, at the beginning the tests were carried out with the specimen set as a beam with pinned}pinned boundary conditions, exactly as one of the authors did in a previous work [15] in order to perform a direct measurement of the Poisson ratio of a viscoelastic material. However, such boundary conditions turned out to be inadequate to perform a direct measurement of the dynamic Young's modulus by using the method described in this paper, because the counteracting screws used to realize the pinned}pinned conditions introduced some frictions, which remarkably a!ected the experimental measures.…”

“…Hence, the more the excitation frequency increases, the more the behavior of the specimen is di!erent from that of an ideal beam, to which the theory in this paper refers. For a complete proof of this fact, the interested reader can refer to a previous work of one of the authors [15].…”

A simplified transfer matrix approach for the determination of the complex modulus of viscoelastic materials

“…Several authors have underlined that Poisson's ratio varies slowly with frequency and is real-valued if the sample is analysed in a small deformation regime [5,6]; thus once this parameter has been calculated in advance (for example from a quasi-static test), it is possible to use the proposed methodology to determine the storage and loss moduli of the material. In effect, after simple manipulations we can write the following expression for the velocity transfer function:…”

The elusive and fickle viscoelastic Poisson’s ratio and its relation to the elastic-viscoelastic correspondence principle

“…Unfortunately, these inequalities prevent conversion by the correspondence principle of the extensive elastic formulas developed in [Hahn 1980] and further amplified in [Whitney and McCullough 1990]. However, relations involving only moduli, such as…”

“…In a number of instances [Gottenberg and Christensen 1963;Olesiak 1966;Paulino and Jin 2001a;2001b;Jin and Paulino 2002;Jin 2006;Ko et al 2003;Freudenthal and Henry 1960;Bieniek et al 1981;Librescu and Chandiramani 1989b;1989a;O'Brien et al 2001;Zhu 2000;Shrotriya and Sottos 1998;Zhu et al 2003;Andrianov et al 2004;di Bernedetto et al 2007;Noh and Whitcomb 2003;Klasztorny 2004;Bert 1973;Cowper 1966;Hilton 2009;Therriault 2003], time-independent PR assumptions lead to overdetermined ill-posed problems and cause use of the elasticviscoelastic correspondence principle to become unjustified. In other analyses [Jin and Paulino 2002;Jin 2006;Ko et al 2003;Freudenthal and Henry 1960;Bieniek et al 1981;Librescu and Chandiramani 1989b;1989a;O'Brien et al 2001;Zhu 2000;Shrotriya and Sottos 1998;Zhu et al 2003;Andrianov et al 2004;di Bernedetto et al 2007;Noh and Whitcomb 2003;Klasztorny 2004;Bert 1973;Cowper 1966;Hilton 2009;Therriault 2003;…”