for the nonlinear initial boundary value problem of Kirchhoff equation $$ \displaylines{ u_{tt}+\Delta^2 u + M(\|\nabla u\|^2)(-\Delta u) u_{t}= \ln |u|^2,\text{ in }\Omega\times (0,T), \cr u(x,0) = u_0(x), \quad u_{t}(x,0)=u_1(x),\quad x \in \Omega, u(x,t) \frac{\partial u}{\partial \eta}(x,t)=0, \partial \Omega,\; t\geq 0, }$$ where (\Omega;\)is a bounded domain \(R^2\) with smooth \(\partial...

Asymptotic expansions are constructed for the eigenvalues of the Dirichlet problem for the biharmonic operator in a domain with highly indented and rapidly oscillating boundary (the Kirchhoff model of a thin plate). The asymptotic constructions depend heavily on the quantity γ that describes the depth O(εγ) of irregularity (ε is the oscillation period). The resulting formulas relate the eigenva...

in this paper, the effect of different boundary conditions on the free vibration analysis response of a sandwich plates is presented using higher order shear deformation theory. the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (fsdt) based on rissners-mindlin (rm) kinematics field. based on energy method and hamilton's principle, the ...

We revisit a classic design problem for a plate of variable thickness under the model of Kirchhoff. Our main contribution has two goals. One is to provide a rather general existence result under a main assumption on the structure of the tensor of material constants. The other focuses on providing a minimal number of additional design variables for a relaxation of the problem when that assumptio...

A general framework of constructing C discontinuous Galerkin (CDG) methods is developed for solving the Kirchhoff plate bending problem, following some ideas in [10, 12]. The numerical traces are determined based on a discrete stability identity, which lead to a class of stable CDG methods. A stable CDGmethod, called the LCDGmethod, is particularly interesting in our study. It can be viewed as ...

The scattered field arising from diffraction of a plane flexural wave by a semi-infinite crack in an orthotropic Kirchhoff thin plate is analysed. The crack is aligned with a principal direction of the material, so that two of the plate’s three planes of symmetry are preserved. An asymptotic approximation is derived via the method of steepest descents, and explicit expressions are given for the...

A theoretical model is developed to describe the interferometric coherency between pairs of SAR images of rough soil surfaces. The model is derived using a dyadic form for surface reflectivity in the Kirchhoff approximation. This permits the combination of Kirchhoff theory and spotlight synthetic aperture radar (SAR) image formation theory. The resulting model is used to describe the interferom...

In this paper, the thermal buckling analysis of a circular plate made of FGM materials with actuator/actuator piezoelectric layers based on neutral plane, classical plate theory and first order shear deformation plate theory is investigated. Reddy's model is assumed for material properties of FGM plate. Plate under the thermal loading, nonlinear temperature rise through the thickness and clampe...