Free Vibration Analysis Of An Elastically Connected Double-plate System With Moderately Thickness And Supper Elliptic Geometric Shape

In the field of engineering, plates has many applications, there are a lot of plates exist in various building, construction and spacecraft.Plate structural element can reduce material losses, increases the effective load and provide effective support.With the development and popularity of high-speed computers, theoretical analysis is often used to solve problems in engineering practice. In many problems, an elastically connected double plate vibration problems has a great of significance in both theory and practice. Many important structural elements can be simplified modeling of elastically connected double-plate vibration system. The system can also be used to analyze the walls or floor vibrations.But study on the plate, is basically based on the typical thin plate theory and the effect of shear deformation theory is ignored. Meanwhile, double plate boundary condition limited to simply supported edges. As known to all, when thickness of plate is not enough thin, plate of shear deformation and support conditions will effect on mechanical behavior of plate.Compared to rectangular plate, Circular plate is very little, and quite a few are focus in the polar plate; Study on round plates, namely, super-ellipse plates, only a few researchers have published more than 10 related papers. Most of the research based on Kirchhoff-Love plate theory,This paper mainly focus on the research of free vibration of moderately thick plate of double plate system, and double ellipse Plate and double super ellipse Plate of free vibration, using first order shear deformation theory of Mindlin plate and pb-2Ritz method for calculation method, derived out the stiffness matrix of free vibration of thick double plate system, transformed into a mathematical solution of eigenvalue problem, eventually. Then use Matlab programming, through numerical calculation,get frequency and vibration mode of double plate system.pb-2Ritz method in solving the issue with good convergence and stability was proved through some circular and elliptical plate numerical examples. Discussed free vibration of the double circular plate system in detail, and proved in the case of small thickness have a good precisionHowever, with the increase of thickness, it highlights its limitations, it illustrates that shear deformation and rotatory inertia have growing influence of the natural frequency of the system with increasing thickness of the system, which proved moderately thick plate theory have good versatility and accuracy; By numerical calculation, the natural frequency and vibration mode of double plate system has no connection with scale On a macro scale,when the high-span ratio is a constant,. Through large amounts of data, get variation of non-isometric and isometric of free vibrations of super-elliptic plates with thickness,under the clamed support:When n = 2, the natural frequency of double isometric super-ellipse plate can be greatly reduced, with respect to the circular plate. Each order frequency decreased more; when the value of n greater than 2, the natural frequency of isometric super-ellipse plate decreased slightly, that is, when n is greater than 2, super-ellipse geometry boundary changes, small changes in its natural frequency,it illustrates that the super-ellipse plate have superiority in engineering fields.Many analysis data can help to design and research staff.