Plane waves and stability of elastic plates

Achieving control of in-plane elastic waves

We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with 16 spatially varying entries which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [Milton et al., New J. Phys. 8, 248 (2006)]. We numericall...

Degenerate weakly nonlinear elastic plane waves

Weakly nonlinear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically nonlinear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary anisotropic media. The form of the equations obtained depends upon the direction of propagation relative to the crystal axes. A single equation is found for all propag...

Scattering of plane elastic waves by three-dimensional diffraction gratings

Reflection and Transmission of Plane Waves at Micropolar Piezothermoelastic Solids

The present investigation analysis a problem of r­­­eflection and transmission at an interface of two micropolar orthotropic piezothermoelastic media. The basic equations and constitutive relations for micropolar orthotropic piezothermoelastic media for G-L theory are derived. The expressions for amplitude ratios corresponding to reflected and transmitted waves are derived analytically. The eff...

String theory and the Classical Stability of Plane Waves

The presence of fields with negative mass–squared typically leads to some form of instability in standard field theories. The observation that, at least in the light–cone gauge, strings propagating in plane wave spacetimes can have worldsheet scalars with such tachyon–like masses suggests that the supergravity background may itself be unstable. To address this issue, we perform a perturbative a...