The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotrop...

this deals with the harmonic forced vibration of a circular plate surface bonded by two piezoelectric layers, based on the kirchhoff plate model. the form of electric potential field in the piezoelectric layer is assumed such that the maxwell static electricity equation is satisfied. the differential equations of motion are solved analytically for clamped edge boundary condition of the plate. t...

In this paper, we derive a sharp observability inequality for Kirchhoff plate equations with lower order terms in an unbounded domain Ω of lR. More precisely, when the observation is assumed to be located in a subdomain ω such that Ω \ ω is bounded and the observation time T > 0 is sufficiently large, we establish an observability estimate with an explicit observability constant for Kirchhoff p...

Wedge waves are waveguide modes localized near the edge of an elastic wedge and propagating at a speed lower than bulk surface existing in material. These some interest to practice. The purpose this paper is develop calculation methods based on analysis problem for viscoelastic plates, calculate relative phase velocities along wedge-shaped plate. represented as plates variable thickness. basic ...

We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The beams are discretised by the CutFEM technique of letting the basis functions of the plate represent also the beams which are allowed to pass through the...

Abstract The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. interaction between layers is taken into account due to van der Waals forces. investigation based on nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. effect Lorentz force Maxwell’s equations. go...

Abstract We present a new study of linear elasticity for an infinite three-dimensional plate of finite thickness Ω = IR2×(−1, 1). We first caracterize the kernel of the operator of elasticity as polynomials which can be build from the kernel of the classical Kirchhoff-Love model of plate. Using this characterization we get optimal uniform elliptic estimates W , C on the solution as a function o...

natural vibration analysis of plates represents an important issue in engineering applications. in this paper, a new and simplify method for vibration analysis of circular and rectangular plates is presented. the design of an effective robust controller, which consistently attenuates transverse vibration of the plate caused by an external disturbance force, is given. the dynamics of the plate i...

For plate structures, their random parameters can be regarded as a two-dimensional field in the plane. To solve theory considering field, an efficient strategy for stochastic finite element method was adopted. Firstly, used to establish structural model, which characteristics of parameter were considered, and mathematical expression its obtained through Karhunen–Loève expansion; secondly, point...