Multiferroic materials are noteworthy for their strong coupling of ferroelectricity, ferromagnetism, and ferroelasticity (Eerenstein et al., 2006; Wang et al., 2010). A large amount of research has been conducted to explore methods for synthesizing and characterizing multiferroics, aiming to achieve a larger magnetoelectroelastic (MEE) coupling effect (Liu et al., 2010; Ramesh and Spaldin, 2007). Most recent studies on multiferroics reported truly remarkable MEE coupling effects (Kirchhof et al., 2013; Kulkarni et al., 2014), which promote the applications of these materials in AC/DC magnetic field sensors, photovoltaic multiferroic solar cells, multiferroic gyrators, and energy harvesting multiferroics (Vopson, 2015). Among these applications, the devices capable of harvesting energy from environmental sources (e.g. air flow, body movements, hydraulic pressure, and ambient vibrations) are of huge commercial values due to their suitability to self-powered systems in portable electronics, environmental condition monitors, structural health monitors, and medical implants (Vopson, 2015; Zhou et al., 2016). Although current energy harvesting devices are mainly based on piezoelectric semiconductors, known as piezoelectric nanogenerators (NGs) (Hu and Wang, 2015; Kim et al., 2014; Wang et al., 2014; Wang and Song, 2006), other approaches for energy harvest based on magnetostrictive materials have been reported in (Erturk et al., 2009; Wang and Yuan, 2008; Zucca et al., 2011). Foreseeably, multiferroic devices combining the piezoelectric and magnetostrictive advantages could result in promising energy harvesters with ultra-high efficiency, as reported in (Challa et al., 2009; Lafont et al., 2012; Li et al., 2015a; Shan et al., 2013). Device development requires systematic optimization for the efficiency of energy conversion and durability of operation, which should be built on deep understanding of the material performance. Recently, a great deal of research on the piezoelectric and magnetostrictive energy harvesters has been conducted for the energy conversion maximization. Several examples are the work by Gu et al. (2012) on structural optimization for flexible fiber energy harvesters, the study by Xu and Qin (2017) about the external force optimization for piezoelectric energy harvesters, the research by Sun and Kim (2010) on the topology optimization for MEE laminate composites, and the optimization by Loja et al. (2014) for several MEE composite structures utilizing differential evolution. However, these works were mainly focused on a static analysis of the piezoelectric or MEE materials, as well as a simplified treatment of the fully coupled piezoelectric/MEE problems. A comprehensive investigation of the dynamic behaviors of multiferroic materials is the first step towards in-depth understanding of the overall responses of the MEE energy conversion.