Vibrations of inhomogeneous anisotropic viscoelastic bodies described with fractional derivative models

Generalized fractional derivatives and their applications to mechanical systems

“…Their expressions are given in [11]. For the comparison of the results with those obtained in [11], the plane body shown in Fig. 5 has been analyzed.…”

“…The initial boundary value problem (41), (43) and (45) is solved using the AEM as presented in [11]. This results in the system of 2N semidiscretized equations of motion with respect to the fictitious loads b = {b (1) …”

“…The governing equations in terms of the displacements u(x, y), v(x, y) are obtained using the procedure described in [11], which for homogeneous isotropic material and for the Kelvin-Voigt fractional model read…”

“…The multi-term fractional differential model is employed to describe the response of the viscoelastic material [11] Pσ = CQε…”

BEM for Dynamic Analysis of Plates

“…Eqs. Another important advantage of this method is that it can be readily extended to solve evolution equations of order higher than two, such as those arising from the static or dynamic response of viscoelastic structures described with multi-term differential viscoelastic models [23,24]. In any case the user of these methods should be aware of the applicability of the employed method as well as of its advantages and drawbacks.…”