Abstract A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation used to simulate the interaction between elastic medium. exact solutions frequency critical load 2D QC are obtained by solving eigensystem using propagator matrix method. present three-dimensional (3D) soluti...

The three-dimensional linearized theory of elastodynamics mathematical formulation of the forced vibration of a prestretched plate resting on a rigid half-plane is given. The variational formulation of corresponding boundary-value problem is constructed. The first variational of the functional in the variational statement is equated to zero. In the framework of the virtual work principle, it is...

Abstract We propose a new kind of compound optical vortex (COV) generator in this paper. The device consists an inner spiral phase plate (SPP) and outer annular plate. There is opaque band between two SPPs. Under the flat-top beam irradiation, concentric multi-ring COV rings with different topological charges radial radii can be generated. theoretical analysis lays foundation for design generat...

We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work provides a more rigorous physical foundation that connects the numerical code to the physics of attachment kinetics and diffusion dynamics. We then apply these a...

In this paper we continue the study begun by Kawohl and Sweers of the precise constant at which the elastic foundation supporting a bending plate can allow lift-off in the case of downward loading. We provide a number of numerical results and a rigorous result on a different counterexample than the one suggested in Kawohl and Sweers (2002). Important open problems are summarized at the conclusion.