Communications in Control Science and Engineering (CCSE) Volume 1 Issue 1, January 2013
www.as-se.org/ccse
Vibration Analysis of the Piezoelectric, Piezomagnetic Materials in Spherical Symmetry Qun Guan Institute of Civil Engineering and Architecture, Hefei University of Technology, Hefei, Anhui, 230009, China grz@hfut.edu.cn Abstract Considering that the piezoelectric, piezomagnetic materials are in the spherical coordinate system and not accounting the body weight, body electric charge and body electric current, from the motion equation, gradient equation and the piezoelectric, piezomagnetic constructive equation, the steady-state solutions of variables such as stress, strain, displacement, electric displacement, electric field intensity, electric potential, magnetic intensity, magnetic potential under additional stimulations are deduced, thereof it can provide good theoretical basement for the dynamic control of the piezoelectric, piezomagnetic materials in the space spherical symmetry. Keywords Piezoelectric; Piezomagnetic; Spherical Symmetry; Steady-state Solution
Introduction Piezoelectric, piezomagnetic materials are receiving increasingly extensive application in the vibration, survey and control fields because of their higher electromechanical conversion efficiency, big stress, high energy density and rapid mechanical response. Piezoelectric, piezomagnetic materials can be used in making instruments of diverse forms and shapes, which generates extension, compression, distortion and such deformations by making use of the variation of additional electric field and magnetic field. These instruments can be utilized for mechanics sensors, which surveys static stress, vibration stress, distortion stress, acceleration and other physics variables, and can also make into slight displacement control machines of simple structure and diverse forms which are extensively used in excessively delicate location, laser tiny process, numeral control machine,
robot, valve control and so on. In recent years, some scholars have studied extensively piezoelectric materials of electromechanical coupling effects. Wang has given the general solutions of space axial symmetry problem in piezoelectric materials, and Yao has given the general solutions of spherical symmetry problem in piezoelectric materials, Wang has also given the state space solutions of the space axial symmetry problem in layered piezoelectric materials, Ding and other scholars have systematically studied the general solutions of transversely isotropic piezoelectric materials. But for the solutions of piezoelectric, piezomagnetic, electromagnetic coupling elastic media, limited study has been done. E.Pan has given the fundamental solutions of static and dynamic analysis about transversely isotropic piezoelectric, piezomagnetic elastic plate with simply supported, and Li has given the steady solutions of the spherical symmetry problem in piezoelectric sphere shell, in addition Zhu has given the three dimensions solutions of the free vibration about the electromagnetic laminated plate, Liu has given the important properties of Green function of two dimensions piezoelectric, piezomagnetic, electromagnetic anisotropic elastic media. This paper considers that piezoelectric, piezomagnetic, electromagnetic coupling elastic medias are in the spherical coordinate system and from the fundamental equations of the linear electromagnetic elastic solid, the steady solutions of stress, strain, displacement, electro-displacement, electric field strength, electric potential, magnetic strength, magnetic potential and other variables under additional stimulations are deduced, therefore they can provide good theoretical basement for the dynamic control of piezoelectric, piezomagnetic materials in the spherical symmetry.
1