Dynamic analysis of porous FGM viscoelastic sandwich beams using differential transform method (DTM)

The differential transformation method (DTM) is applied to investigate free vibration of FGM sandwich beams with viscoelastic nonlinear material behaviour. . In the analytical formulation, both normal and shear deformations are considered in the core by using the higher-order zig-zag theories. The governing equations for viscoelastic damped sandwich beams are derived using the virtual displacement principle. In this study, the core layer is modelled as frequency-dependent, resulting in a nonlinear eigenvalue problem. This problem is solved iteratively using the Differential Transformation Method (DTM) until the required convergence criteria are met. Within the framework of the Differential Transformation Method (DTM), variations in the first three natural frequencies and their corresponding loss factors are analyzed. A detailed numerical study is conducted to investigate the effects of the porosity coefficient, various thickness and geometric ratios, as well as material properties on the fundamental frequencies and loss factors of the sandwich beam. The results show excellent agreement with previous studies and underscore the accuracy and computational efficiency of DTM as a reliable method for the analysis, design, and optimization of FGM sandwich beams with nonlinear viscoelastic cores.