Influence of temperature change and humidity condition on free vibration analysis of a nano composite sandwich plate resting on orthotropic Pasternak foundation by considering agglomeration effect

Abstract

This research presents an investigation into the free vibration of a sandwich plate with a transversely flexible polymeric core and two carbon nanotubes reinforced nanocomposite face sheets based on high-order sandwich plate theory. The material properties are considered to be temperature- and moisture-dependent. The mathematical model of the face sheets is developed based on the classical plate theory and modified strain gradient theory. Also, Eshelby–Mori–Tanaka approach is used to estimate the material properties of the face sheets and consider the agglomeration effect of carbon nanotubes. The governing equations of motion which included the size effect as well as hygrothermal effect are derived based on Hamilton’s principle and solved by means of Navier’s solution method. The influence of various parameters such as agglomeration effect and the volume fraction of carbon nanotubes, material length scale parameters, aspect and side ratios, temperature changes, and humidity condition is presented. In addition, orthotropic Pasternak foundation is taken into account to study the influence of orthotropic angle on the vibrational behavior of the sandwich plate, and also a comparison of a symmetric sandwich plate and two types of asymmetric ones is carried out for different values of normal and shear Pasternak foundation modulus. Employing carbon nanotubes reinforced nanocomposite face sheets, orthotropic Pasternak foundation and size-dependent theory leads to an increase in the stiffness of the sandwich structure and considering the temperature and humidity changes and agglomeration effect of carbon nanotubes in the face sheets helps to achieve the results with higher accuracy which can be used in modern engineering applications.