Transverse Vibrations Analysis On Axially Moving Viscoelastic Sandwich Beam

In engineering, axially moving systems have widely application, and they exist in the related industry such as aerospace,electronic,civil,military,machinery. Many engineering system components such as tape,cableway,energy transmission belt,sawblade are typical examples of axially moving systems. Large transverse vibration of these equipments maybe influence work quality, and it also maybe improve work condition. So, it is very important to investigate the vibration characteristics of axially moving systems and its control for designing and improving engineer. The research of axially moving beams are common, however, the research of axially moving sandwich beams are rare. In fact, sandwich structures have been used in engineering structures widely because of their excellent comprehensive performance. So, it is necessary to computer and analysis the mechanical properties for designing sandwich structures. In this paper, the transverse vibration of an axially moving sandwich beam and the related works are studied as follows:Firstly, based on D'Alembert's principle, fourth order partial differential equations of transverse vibration for the axially moving sandwich beam are derived combining material constitutive equations and deformation geometry relations and loading analysis. Euler-Bernoulli beam is employed in modeling without considering the effects of shear deformation and moment of inertia.Secondly, the linear free vibration of the axially moving visco-elastic sandwich beam with simply supported ends boundary is discussed. The fourth order partial differential vibration equations are discreted to ordinary differential equations using Galerkin truncation method. And then the natural frequency equation and modal functions are derived. The dynamic behavior of the axially moving visco-elastic sandwich beam is studied by specific example, and the influence of axially moving speed,thickness ratio,initial axial force on natural frequency and loss factor are investigated, and finally the displacement and phase diagram of transverse vibration are analyzed.Thirdly, the linear forced vibration of the axially moving visco-elastic sandwich beam with simply supported ends boundary and periodic transverse distribution load is investigated. The displacement response is discussed by specific numerical example.Fourth, based on Floquet theory, the parameter vibration of the axially moving visco-elastic sandwich beam is investigated using L-P method.