We investigate the effect of a Steiner type symmetrization on the isotropic constant of a convex body. We reduce the problem of bounding the isotropic constant of an arbitrary convex body, to the problem of bounding the isotropic constant of a finite volume ratio body. We also add two observations concerning the slicing problem. The first is the equivalence of the problem to a reverse Brunn-Min...

We mathematically justify a reduced piezoelectric plate model. This is achieved considering the three-dimensional static equations of piezoelectricity, for a nonhomogeneous anisotropic thin plate, and using the asymptotic analysis to compute the limit of the displacement vector and electric potential, as the thickness of the plate approaches zero. We prove that the three-dimensional displacemen...

The local resonances of a free isotropic elastic plate are investigated using laser ultrasonic techniques. Experimental results are interpreted in terms of zero group velocity Lamb modes and edge mode. At a distance from the edge larger than the plate thickness a sharp resonance is observed at the frequency where the group velocity of the first symmetrical Lamb mode vanishes. Close to the edge ...

the plate girders are used in important structural systems. the earlier design of plate girders was restricted to their critical bukling capacity. experimental and theoretical studies show the plate girders with vertical stiffners can carry load over than their critical buckling loads and then in modern design codes is permitted to use post- buckling capacity of them. in this case the out- of- ...

The present investigation is to study the surface wave propagation at imperfect boundary between an isotropic thermoelastic without energy dissipation half-space and an isotropic elastic layer of finite thickness. The penetration depth of longitudinal, transverse, and thermal waves has been obtained. The secular equation for surface waves in compact form is derived after developing the mathemat...

Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for the stress field, thus satisfying the expectation that stresses should depend on the location of the dislocation loop, but not on the location of surfaces boun...

Elastic waves are guided along finite structures such as cylinders, plates, or rods through reflection, refraction, and mode conversion at the interfaces. Such wave propagation is ubiquitous in the world around us, and studies of elastic waveguides first emerged in the later part of the 19(th) century. Early work on elastic waveguides revealed the presence of backward propagating waves, in whic...

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is Qt i=0(1 + q ) for the types BN , DN , whereas for the case of type CN , more isotro...