Original Article 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 Mohammad Sharif Zarei 1 , Mohammad Hadi Hajmohammad 2 , Mostafa Mostafavifar 2 and Mehdi Mohammadimehr 3 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 nanocom- posite 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 nano- tubes. 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 Journal of Sandwich Structures and Materials 0(00) 1–39 ! The Author(s) 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1099636217735118 journals.sagepub.com/home/jsm 1 Faculty of Engineering, Ayatollah Boroujerdi University, Borujerd, Iran 2 Department of Mechanical Engineering, Imam Hossein University, Tehran, Iran 3 Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran Corresponding author: MH Hajmohammad, Imam Hossein University, Tehran 8436113671, Iran. Email: mhajmohammad@ihu.ac.ir