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.

中文翻译：

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包含微观结构和基础效应的横向各向同性磁电弹性 Timoshenko 梁模型§

摘要 利用基于Hamilton 原理的变分公式，建立了横向各向同性磁电弹性Timoshenko 梁的新模型。扩展的修正偶应力理论和双参数 Winkler-Pasternak 弹性地基模型分别用于描述微观结构和地基效应。同时获得了梁的运动方程和完整的边界条件。新模型包括横向各向同性压电和压磁 Timoshenko 梁模型以及横向各向同性磁电弹性 Bernoulli-Euler 梁模型，所有这些模型都包含微观结构和基础效应，作为特殊情况。为了说明新开发的梁模型，直接应用推导的通式，解析解决了受均匀分布载荷作用的简支横向各向同性磁电弹性梁的静弯曲和自由振动问题。还提供了数值结果，以定性地显示微观结构、基础和磁电弹性耦合对简支梁响应的影响。