A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment

This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.

Тестирование на изгиб наноразмерных консолей в атомно-силовом микроскопе

Consoles and bridges of MgNi2Si2O5(OH)4 nanoscrolls were tested for bending in atomic force microscope. Using test data, we analyze how the consoles or bridges were fixed, and took this information into account when calculating the Young's modulus of the nanoscrolls. The results on the consoles are in good agreement with the results on the bridges when modeling the latter as three-span beams, and the former as beams on an elastic foundation with a suspended console.

Strip on elastic foundation described by different models, loaded by evenly distributed load

The problem of changing the size of the reactive pressures perceived by a strip at use of various models of the soil foundation and at various indicators of flexibility of the “strip-soil” system is investigated. The aim of the work is to obtain the form of plots of reactive pressures produced by the soil foundation on a strip loaded along its entire length with a uniformly distributed load. In determining the values ​​of reactive pressures and values ​​of bending moments, the data of a previously published work of one of the authors of the article, based on V.N. Zhemochkin method, is used. Analysis of the obtained calculation results showed that the shape of the plot of reactive pressures largely depends on both the index of flexibility of the foundation and the index of flexibility of the “strip-soil” system. The novelty of the research is that the calculation results are obtained using the traditional method of calculation (i.e., without taking into account the joint work of the “strip-soil” system and using 3 models of the soil base: linearly deformable half-plane, linearly deformable layer of finite thicknesses and the Winkler model. The obtained results of calculation will allow to design ground structures on the elastic foundation.

Active control of a sandwich plate with reinforced magnetostrictive faces and viscoelastic core, resting on elastic foundation

The current study presents a vibration investigation of a laminated plate considering a viscoelastic core with embedded magnetostrictive layers. The simply-supported plate is supported via Pasternak’s substrate medium. Based on different plate theories and employing Hamilton’s principle, the system of governing differential equations is derived. The mechanical properties of the viscoelastic core are described depend on the time varies based on Kelvin–Voigt model. Actuating magnetostrictive layers are utilized to control the vibration damping process of the system with the assistance of feedback and constant gain distributed control. The analytical solution is obtained to investigate the influence of half wave numbers, thickness ratios, core thickness, aspect ratios, lamination schemes, elastic foundation parameters, damping coefficient, feedback coefficient magnitude, magnetostrictive layers location, on the vibrational behavior of laminated plate. Some observations about the vibration damping process of the present plate are displayed. The results refer to that the vibration suppression rate depends on the thickness of the plate, the feedback control value, the foundation constants, and the viscoelastic structural damping significantly. Moreover, the study can be providing benchmark tests to validate future contributions on the viscoelastic smart structural issues and developing the design of smart viscoelastic structures and control of their vibrations.