Abstract In this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations problem based on von Kármán plate theory Kirchhoff–Love hypothesis. small-size effect is taken into account due nonlocal elasticity theory. formulation mixed employs Airy stress function. two-mode approximation deflection application Bubno...

Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis nonlocal theory elasticity. The upper part spectrum with wavelength comparable to internal characteristic dimension a nanorod is examined. An equations in integral form Helmholtz kernel, incorporating both local and phases, used as constitutive one. original integro-differential equation reduc...

We are interested in the mathematical modeling of the deformation of the human lung tissue, called the lung parenchyma, during the respiration process. The parenchyma is a foam–like elastic material containing millions of air–filled alveoli connected by a tree– shaped network of airways. In this study, the parenchyma is governed by the linearized elasticity equations and the air movement in the...

This paper first considers the approximation of peridynamics by strain-gradient models in the linear, one-dimensional setting. Strain-gradient expansions that approximate the peridynamic dispersion relation using Taylor series are compared to strain-gradient models that approximate the peridynamic elastic energy. The dynamic and energetic expansions differ from each other, and neither captures ...

Abstract Parametric vibrations of the single-layered graphene sheet (SLGS) are studied in presented work. The equations motion govern geometrically nonlinear oscillations. appearance small effects is analysed due to application nonlocal elasticity theory. approach developed for rectangular simply supported small-scale plate and it employs Bubnov–Galerkin method with a double mode model, which r...

in this research, the buckling and bending behaviour of smart nanocomposite plate reinforced by single- walled carbon nanotubes (swcnts) under electro-magneto-mechanical loadings is studied. the extended mixture rule approach is used to determine the elastic properties of nanocomposite plate. equilibrium equations of smart nanocomposite plate are derived using the hamilton’s principle based on ...

We study the spatiotemporal dynamics of a crack front propagating at the interface between a rigid substrate and an elastomer. We first characterize the kinematics of the front when the substrate is homogeneous and find that the equation of motion is intrinsically nonlinear. We then pattern the substrate with a single defect. Steady profiles of the front are well described by a standard linear ...

The effect of central opening on the buckling and nonlinear post-buckling response of carbon nanotubes (CNTs) reinforced micro composite plate embedded in elastic medium is considered in this paper. It is assumed that the system is surrounded by elastic medium, therefore; the influence of Pasternak foundation on buckling and post-buckling behavior are analyzed. In order to derive the basic form...