Vibration control and analysis of Terfenol‐D functional gradient material beams with porosities: Linear and nonlinear perspectives in thermal environments

This paper investigates the vibration characteristics, both linear and non‐linear, of beams made from functional gradient materials (FGMs) with layers of Terfenol‐D attached to the top and bottom surfaces. Given the porosities that can occur during the manufacture of FGMs, the study examines the vibrational behaviour of beams with porosities. Euler–Bernoulli beam theory and the von‐Kármán non‐linear deformation field are used to formulate a fundamental equation predicting the free dynamic vibration of Terfenol‐D FGM structures with porosities. To complete this analysis, the paper also presents the application of two advanced methods. The first method involves employing the generalised finite element method (GFEM) associated with the reduced quadrature finite element method (RQFEM). GFEM offers a versatile and powerful approach, while RQFEM provides a specific method for studying dynamic phenomena. The second method utilises a semi‐analytical approach, the variational iteration method (VIM), which examines and complements the first method. Furthermore, we have demonstrated substantial alignment between the proposed solution and the results of finite element analysis, as well as with the existing literature, underscoring the effectiveness and accuracy of our analytical approach. The study also explores the influences of material property distribution, thermal loading, and porosity volume fraction on the linear and non‐linear behaviour of Terfenol‐D FGM beams. This comprehensive exploration furnishes valuable information on the intricate interplay of factors affecting vibration dynamics and control mechanisms in these advanced composite structures, offering insightful perspectives into the potential application of Terfenol‐D FGM beams in various fields.