A transversely isotropic magneto-electro-elastic Timoshenko beam model incorporating microstructure and foundation effects. (October 2020)

• Record Type: Journal Article
• Authors: Zhang, G.Y.; Qu, Y.L.; Gao, X.-L.; Jin, F.
• Is Part Of: Mechanics of materials. Volume 149(2020)
• Publication Date: 2020-10
• Subjects: Timoshenko beam -- Magneto-electro-elastic beam -- Microstructure effect -- Modified couple stress theory -- Hamilton's principle -- Beam vibration; Strength of materials -- Periodicals; Mechanics, Applied -- Periodicals; Résistance des matériaux -- Périodiques; Mécanique appliquée -- Périodiques; Mechanics, Applied; Strength of materials; Periodicals; Electronic journals; 620.11
• DOI: 10.1016/j.mechmat.2020.103412
• Languages: English
• ISSNs: 0167-6636

Abstract

Abstract: A new model is developed for transversely isotropic magneto-electro-elastic Timoshenko beams by using a variational formulation based on Hamilton's principle. An extended modified couple stress theory and a two-parameter Winkler-Pasternak elastic foundation model are applied to describe the microstructure and foundation effects, respectively. The equations of motion and complete boundary conditions for the beam are simultaneously obtained. The new model includes the models for transversely isotropic piezoelectric and piezomagnetic Timoshenko beams and the model for transversely isotropic magneto-electro-elastic Bernoulli–Euler beams, all incorporating the microstructure and foundation effects, as special cases. To illustrate the newly developed beam model, the static bending and free vibration problems of a simply supported transversely isotropic magneto-electro-elastic beam subjected to a uniformly distributed load are analytically solved by directly applying the general formulas derived. Numerical results are also provided to qualitatively show the microstructure, foundation and magneto-electro-elastic coupling effects on the responses of the simply supported beam.