A 1D model for the dynamic analysis of magneto-electro-elastic beams with curved configuration

• Derivation of a new model for MEE curved beams.
• The model can be reduced to other previous curved beams and straight beams.
• There are new studies for vibration of MEE curved beams.
• It is a useful model for studies connected with optimization and/or uncertainty quantification due to its inherent low computational cost.

The scope of the present paper is to present some new contributions in the dynamics of curved/straight MEE beams. The structure consists of a curved beam constructed with ceramic/metallic materials whose elastic behavior can be modified by influence of electro-magnetic fields. The problem of coupled elastic, electric and magnetic fields is briefly explained and the motion equations for curved members are introduced. An equivalent model for a MEE curved beam is then deduced appealing to a few constitutive hypotheses that enable the derivation of the electric–magnetic fields acting on the beam in preferential and prescribed directions. The theoretical topics covered in the model include shear flexibility due to bending as well as coupled elastic-electro-magnetic terms, among others. The model can be reduced to other models (straight beams or curved beams) by dropping terms or the magneto-electric fields and/or geometric parameters. Comparisons with the available models (for the reduced case of straight beam) and 2D models evaluated in the context of finite element methodologies are presented as well.