Free Vibration analysis of Functionally Graded Lattice Plates in Thermal Environment

In the present study, two analytical and numerical methods have been used for studying and testing of Functionally Graded Latticeplates in thermal environments. In the analytical method, the properties of the Functionally Graded plates are defined as a function oftemperature, and to take account of the properties of Lattice Plates, the stiffness matrix defined by V.V. Vasiliev is used. The governingequilibrium equations are obtained based on the first order shear deformation theory, which includes displacement and rotationalcomponents, and is solved by assuming the boundary conditions that are fully clamped by the energy method. By solving the problemof a special value, the vibrational behavior of the structure in a thermal environment (with the presence of thermal stress) is determined.Analytical and numerical results have been compared and verified with the results of previous works. In the field of free vibration, aFunctionally Graded Lattice plate in a thermal environment has been used to study various parameters such as changing the size of theribs, the distance between the ribs and ... for predicting structural behavior. The results show that when the temperature rises, thenormal frequency in the Functionally Graded Lattice plate decreases with the decrease of the width of the ribs and the increase in thedistance between the ribs.