The free vibration of isotropic gradient elastic thick non-rectangular microplates is analyzed in this paper. To capture the microstructure-dependent effects microplates, a negative second-order theory with symmetry utilized. related equations motion and boundary conditions are obtained using energy variational principle. A closed-form solution presented for simply supported free-vibrational re...

We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toup...

The subtle but crucial effects of large-scale forcing on the small-scale velocity-gradient (VG) dynamics is examined using direct numerical simulation (DNS) data incompressible turbulence. interplay among forcing, inertia, pressure and viscous characterised as a function local streamline geometry VG magnitude (Frobenius norm). When conditioned topology, forcing: (i) counteracts inertial action ...

In this study, a dynamic Mindlin–Reissner-type plate is developed based on simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations motion and the corresponding boundary conditions are derived using general virtual work variational principle. presented model contains, apart from two classical Lame constants, one additional microstructure material ...