Affiliations: [a] School of Mechanical Engineering, Dalian University of
Technology, Dalian, Liaoning, China | [b] School of Mechanical Engineering and Automation,
Northeastern University, Shenyang, Liaoning, China | [c] Department of Flight Theory, Aviation University of
Air Force, Changchun, Jilin, China | [d] Key Laboratory of Health Maintenance for Mechanical
Equipment of Hunan Province, Hunan University of Science and Technology,
Xiangtan, Hunan, China | Doshisha University, Kyoto, Japan | Department of Human and Information Systems, Faculty
of Engineering, Gifu University, Gifu, Japan
Correspondence:
[*]
Corresponding author: Qingkai Han, School of Mechanical
Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China.
E-mail: hanqingkai@dlut.edu.cn
Abstract: Based on the theory of magneto-electro-elastic (MEE) multilayered
plate and by using the state-vector and propagator matrix approach, the natural
characteristics (i.e. modal analyses) of the hard-coating plates are
investigated. The hard-coating plates in this study are composed of a purely
elastic substrate and one magneto-elastic or electro-elastic coating layer of
which the thickness is much smaller compared to the substrate layer. Firstly,
every field variable of the hard-coating multilayered plate is written into one
of the two state vectors, which are related to each other by the form of
matrix-production; Secondly, all the field variables are expanded into the form
of infinite trigonometric series, and then the field variables of two adjacent
layers are connected by the propagator matrix which is the expression of the
unknown natural frequencies; Finally, by applying the boundary conditions at
top and bottom surfaces, the natural frequencies can be exactly solved.
Numerical examples are provided in the last part, and effect of both coating
thickness and coating material properties (with either magnetic or electric
effect involved) on the natural frequencies and mode shapes are discussed. The
results are also compared with some finite element results.
