Dynamics of the elements of the printing device

The schematic diagrams of the printing machine and its elements are presented in [1]. One of the basic components of the printing machine is the printing cylinder. Various types of vibration and wave motions can take place in it. In this paper longitudinal waves in the printing cylinder are analyzed. They are understood as longitudinal from the point of view of the whole cylinder and its axis of symmetry. From the point of view of the surface element of the cylinder they are usually flexural. Another important problem in the analysis of the printing devices is investigation of the dynamics of the printing ink as a viscous fluid. The dynamics of an axisymmetric composite shell problem is analyzed in this paper. The axisymmetric shell is considered to have two external layers of higher stiffness and an internal layer of lower stiffness. The finite element of this axisymmetric shell problem is obtained from the contributions of the three sub-elements. The resulting finite element has six degrees of freedom per node. The eigenmodes are calculated and it is evident that the multiple eigenmodes enable the excitation of wave motion in this system. The analysis is based on [2, 3]. The problem of fluid flow control exploiting the vibrations of a flow boundary is important in the process of design of various engineering devices and optimization of processes of conveyance [10, 9, 7, 6]. Analysis of such a dynamical system requires development of adequate mathematical models and appropriate strategies for numerical modeling [11, 14, 5, 4]. One of the specific precision engineering applications where vibrations play a key role in controlling a fluid flow is dosing and spraying of liquid materials. Particular interest exists for elastic catheter pipe type dosing equipment [9, 7, 12] where the application of piezoelectric actuators for the generation of standing waves in the outlet pipe can produce effects which can be used for the control of dosing process. Definite attention exists for the analysis of tube vibrations induced by internal or external flow [8]. Analysis of such vibrations is very important in many engineering applications including nano-tube vibrations. Nevertheless, analysis of an inverse problem – flow control by forced longitudinal and transverse vibrations of the tube itself is also of interest. Such a vibration based flow control methodology builds ground for the development of new types of liquid material dosing equipment. It is understood that full analysis of such complex problems requires construction of three dimensional models, but the analysis of such models and the interpretations of those results would be quite complicated. A two dimensional model is developed in this paper. The external excitation of the boundary by longitudinal vibrations is encountered through the boundary conditions of the flow of non-Newtonian fluid. Flow excitation by transverse vibrations of the tube is represented through the convective acceleration terms in the equation of dynamic equilibrium of the fluid flow in the cross section of the tube. The excitation velocities are assumed to be equal in the whole cross section area and are the functions of time only. The obtained results provide insight into the process of vibration based control of fluid flow. It is assumed that the boundary (the tube) is a non-deformable rigid body. A FEM model leads to the first order matrix differential equation. The approximate solution is sought using the modal decomposition and numerical integration of the one-dimensional equations in the time domain. The developed procedure is applicable to tubes of various cross sections and the calculations can be effectively carried out for the required values of the parameters. The steady state two dimensional viscous incompressible slow flow is analysed. The element of the type described in [3] is used with the nodal variables being the velocity in the direction of the