Dynamic stability of the double-bonded annular nanocomposite sandwich microplate on viscoelastic foundation

Abstract

In this research, the dynamic stability of the double-bonded annular sandwich microplate is investigated. Face sheets are made from composite materials reinforced by carbon nanotubes in which mechanical properties are obtained by the extended rule of the mixture. Also, the core layer is made from a honeycomb aluminum which is defined by the geometric parameters of the unit cell and mechanical properties of the virgin core material. The equations of motion are derived from Hamilton’s principle and solved by the differential quadrature method (DQM) based on higher order shear deformation theory (HSDT) and modified couple stress theory (MCST). The results are compared with the obtained results by the other literature to examine the accuracy of the present formulation. The dynamic stability of the double-bonded annular sandwich microplate with hexagonal honeycomb core including variations of core thickness, inclined angle, and aspect ratio of the unit cell are discussed. Also, the effects of motion direction of the structure, viscoelastic foundation, material length scale parameter, volume fractions of CNTs in face sheets, and the core thickness to total thickness ratio on dynamic instability region are presented.

Transient nonlinear responses of a sandwich plate with micro-cellular auxetic core based on modified strain gradient theory under impact loads

“…In which, q1(xm) and q2(xm) represent the external forces, while V , M , and Mh denote the boundary shear forces, the classical, and the non-classical (higher-order) moments, respectively. The strain energy of the micro-cell wall is developed by MSGT as follows: 18 Where, mij, pi and τijk are the higher-order stresses. In equation (4), ηijk, χij and γi represent the deviatoric stretch gradient tensor, symmetric rotation gradient tensor, and dilatation gradient vector, respectively, defined as follows: 18 …”

“…The strain energy of the micro-cell wall is developed by MSGT as follows: 18 Where, mij, pi and τijk are the higher-order stresses. In equation (4), ηijk, χij and γi represent the deviatoric stretch gradient tensor, symmetric rotation gradient tensor, and dilatation gradient vector, respectively, defined as follows: 18 …”

Dynamic instability characteristics of graphene‐reinforced cellular sandwich plates using a three‐variable isogeometric approach

“…Also considering the micro-structures, Jalaei and Thai [28] conducted a comprehensive numerical investigation on the dynamic instability for nanoplate structures with porosities. In addition, several significant studies can be also presented here [29][30][31][32][33].…”