The Natural Vibration Of Axially Moving Laminated Plate

The composite structures have the characteristics of light weight, high strength, fatigue resistance, good design, easy processing molding etc, and they are applicable in many industrial fields such as aerospace, traffic and transportation, and so on. With the laminates application domain more and more broad, there will be more practical value on the axially moving laminate research. Many complex dynamic characteristics of motor laminations exist under different loads, so the vibration analysis that is studied for the axially moving composite laminate is very necessary. Therefore, there are great practical values and theoretical significance studying the axial movement of composite laminates. This paper is a study of the problem of free vibration of axially moving composite laminates.At the beginning, just considering geometric linear factors, based on the small deflection bending theory and thin plate assumption, the article briefly introduces the geometric and physical equations, the bending stiffness expressions, the relationships between stress and strain of the general and orthogonal anisotropic laminates. Then the expressions of total kinetic energy, potential energy, external force virtual work and their variational form are obtained. The linear vibration equations of axially moving laminated thin plate is derived by using Hamilton principle.Then, based on the conversion relationship existing for the simply supported or under fixed boundary, by using the Galerkin method, the amplitude-frequency equations of the axially moving laminate on simply supported on four sides, the contrast simply supported edge clip and other boundary conditions are derived. On the basis of those equations, we can get the vibration differential equation of different materials, the different thickness of slab. And we can get each order nature frequency through the eigenvalue equations using the Matlab. At last we can get an analysis and discussion of the influence of different parameters on the natural frequency.The last chapter is based on the inter conversion relationship between stress and strain of the partial axial and positive shaft, the changing equations between the positive axis and off-axis modulus are deduced, then the vibration differential equations of general laying angle of fiber and cross ply angle laminate are derived. The last part of the chapter is to simulate the effects of ply angles on natural frequencies by using Matlab.