Vibration Analysis of Laminated Shallow Shells Under Thermal Loading Using Higher Order Shear Deformation Theory

Vibration analysis of orthotropic cross ply laminated shallow shells subjected to thermal loading is studied. The displacement field is evaluated using Reddy’s high-order shear deformation shallow shell theory. The governing equations for a shallow shell with two opposite edges are simply supported and the other two edges are free, clamped, and simply supported are solved using levy type solution. State space technique is applied to find the frequency under thermal load. Effects of some design parameters such as material mechanical properties, geometrical imperfections (shallowness ratio (R/a), thickness ratio (a/h), and aspect ratio (a/b)), and lamination schemes on vibration are studied. The analyses have been done using MATLAB R2023a, and the results are compared with other research methodologies. The natural frequency increases as Young's modulus ratio (E1/E2) increases while it decreases with the increase of shallowness ratio and increasing thermal loads. Thickness ratio (a/h) increases the dimensionless form of natural frequency.