Vibration Analysis Of A Cylindrical/Spherical Shell Of Functionally Graded Piezoelectirc-Piezomagnetic Material

As a new type of intelligent composite material,Functionally Graded Piezoelectric Piezomagnetic Material(FGPPM)has been usually used as sensors and brakes in intelligent structure due to its high sensitivity.It is of great significance to optimize the mechanical performance design in smart structures.Although the performance of the material is superior,as an intelligent structural element,deformation and motion will inevitably occur under the action of external excitation load.Therefore the dynamic problem of FGPPM has become a hot research topic.In this paper,the dynamic problems of functionally graded piezoelectric,piezomagnetic hollow cylindrical/spherical shell as sensors and brakes under the action of an external excitation loads are analyzed and studied.In the first chapter,the research background,significance,progress and present situation of FGPPM are described in detail.In the second chapter,the radial vibration problems of piezoelectric and piezomagnetic hollow cylindrical shells with the same gradient index are studied.Firstly,it is assumed that the material parameters of functionally graded piezoelectric and piezomagnetic cylindrical shells vary according to power law along the thickness direction,and the gradient index of density is the same as that of other physical quantities.Then,by using Frobenius series expansion method,the steady state solutions of stress,potential and magnetic potential of cylindrical shell under external excitation are obtained,and the dynamic control problem is analyzed theoretically.Finally,the distribution law of radial stress,circumferential stress,potential and magnetic potential response values along the radial direction is analyzed by numerical examples.In the third and fourth chapters,the radial vibration problems of piezoelectric,piezomagnetic cylindrical and spherical shells with different gradient indexes are studied.Firstly,it is assumed that the material parameters of functionally graded piezoelectric,piezomagnetic cylindrical and spherical shells vary according to the power law along the thickness direction,and the gradient index of density is different from that of other physical quantities.Secondly,by means of the variable substitution technique and the constant change method,the analytical solutions of physical quantities such as the stress,electric potential and magnetic potential of the cylindrical and spherical shells with the Bessel function under the action of external excitation are obtained.Finally,the distribution law of radial stress,circumferential stress,potential and magnetic potential response values along the radial direction is analyzed by numerical examples.