We have studied the finite-size effect on the dynamic behavior of graphene resonators and their applications in atomic mass detection using a continuum elastic model such as modified plate theory. In particular, we developed a model based on von Karman plate theory with including the edge stress, which arises from the imbalance between the coordination numbers of bulk atoms and edge atoms of gr...

A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface in R 3 may vary. Besides, originally distributed disclinations are taken into account. For the flat surface, an extended variant of the Edelen-Kadi´c gauge ...

The object of this note is to demonstrate the applicability of the methods of nonlinear functional analysis in the investigation of a complex physical problem. In 1910 T. von Karman [9] introduced a system of 2 fourth order elliptic quasilinear partial differential equations which can be used to describe the large deflections and stresses produced in a thin elastic plate subjected to compressiv...

Mechanical buckling response of isotropic and orthotropic plates using the two variable refined plate theory is presented in this paper. The takes account transverse shear effects parabolic distribution strains through thickness plate; hence it unnecessary to use correction factors. Governing equations are derived from principle virtual displacements. nonlinear strain-displacement Von Karman re...

In this paper, we prove the local exact null controllability of the thermoelastic plate model, in the absence of rotational inertia, and under the influence of the (non-Lipschitz) von Kármán nonlinearity. The plate component may be taken to satisfy either the clamped or higher order (and physically relevant) free boundary conditions. In the accompanying analysis, critical use is made of sharp o...

In this study the centre manifold is applied for reduction and limit cycle calculation of a highly nonlinear structural aeroelastic wing. The limit cycle is arisen from structural nonlinearity due to the large deflection of the wing. Results obtained by different orders of centre manifolds are compared with those obtained by time marching method (fourth-order Runge-Kutta method). These comparis...

The flutter phenomenon is the principal concern in the field of aeroelasticity. In this paper we address the fundamental questions of well-posedness and long-time behavior of the primary mathematical model for a fluttering plate in a panel configuration. Such a system is known as a nonlinear flow-plate interaction. The flow is described by a perturbed wave equation. The plate is modeled by Kirc...

This study is limited to study of buckling analysis of a sandwich cylindrical shell with functionally graded face sheets and homogenous core. High-order sandwich plate theory is improved by considering the in-plane stresses of the core that usually are ignored in the analysis of sandwich structures. Assume that all properties of the face sheets and the core are temperature dependent. Strain com...

In this study, vibration of initially imperfect cracked thick plate has been investigated using the differential quadrature method. The crack modeled as an open crack using a no-mass linear spring. The governing equations of vibration of a cracked plate are derived using the Mindlin theory and considering the effect of initial imperfection in Von-Karman equations. Differential equations are dis...