The dynamic stability of the moving viscoelastic plate with the piezoelectric layer is studied. On the basis of the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer in the Laplace domain is formulated, the equation is suitable for various viscoelastic differential models. Then, the differential equation of motion of the viscoelastic plate with elastic dilatation and Kelvin-Voigt distortion in time domain is derived, with the piezoelectric effect. The complex eigenvalue equations of axially moving viscoelastic plate are established by the differential quadrature method. The generalized eigenvalue equations are solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the axially moving viscoelastic plate. Via numerical calculation, the results for the instability type and the corresponding critical moving speed of viscoelastic plate are presented to show the variations in these factors with respect to the dimensionless moving speed, the dimensionless delay time and the applied voltages. The dynamic stability of the axially moving viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment.
Rotating machinery contains numerous rolling bearings, which are critical for ensuring the normal working position and accurate operation of individual shaft systems. However, damage to rolling bearings can change their damping, stiffness, and elastic force. As a result, fault signals appear nonlinear and nonstationary. Vibration signals thus become difficult to diagnose clearly, especially in the incipient fault stage. To solve this problem, this article proposes an intelligent approach based on variational mode decomposition and the self-organizing feature map for rolling bearing fault diagnosis. First, the intrinsic mode function components of rolling bearing vibration signals are effectively separated by variational mode decomposition. Then, permutation entropy is used to extract feature vectors, which are used as training and testing data for the self-organizing feature map network. Finally, the various fault types of states are clustered on an intuitive visualization map. Clustering results of the experimental signal and the measured signal prove that the proposed method can successfully extract and cluster the rolling bearing faults in engineering applications. The proposed method improves the fault recognition rate to some extent over traditional methods.
Nowadays more and more materials can be manufactured or stored in continuous web form. The vibration of the moving web limits the productivity and quality of the web materials. The active vibration control of the moving web with varying density is considered in this paper. Finite difference method is used to discretize the dynamic equations of the moving web with varying density and derive the state equation of transverse vibration control system for the moving web with varying density. The simulation of the response and decay process of transverse vibration for the moving web with varying density after the implementation of suboptimal control is performed by numerical calculation.
Parametric vibration and dynamic stability of the printing paper web with variable speed were studied. The speed of the moving paper web was regarded as the sum of the constant mean speed and the sine pulse speed. The dynamical model and the transverse vibration differential equation were established. The period coefficient state equation was obtained by discretizing the space variable of the differential equation with the differential quadrature method and imported state vector. The instability region and the stability region of the paper web were determined by the implicit Runge-Kutta method. The relationships of the instability region versus the tension ratio, length-width ratio and the amplitude of the sine pulse speed were analyzed. The results provide a theoretical basis for optimizing the structure of the printing machine and improving the working stability of the paper web.Key words: the moving paper web with variable speed; parameter vibration; differential quadrature method; stability INTRODUCTIONThe printing speed and the production efficiency of web fed printing and gravure presses is becoming faster and higher. It is now being used in volume-production of newspapers, books and packing materials. The transverse vibration along the vertical direction of the tensioned paper web is caused by the eccentricity of the scroll in the printing process. The transverse vibration could affect the paper web's working stability, and thus influence the product quality seriously in paper-making, printing and the packing industry, Furthermore, the improvement of the working speed is restricted. So research into the transverse vibration and stability of moving paper web or membrane is of great important application value, and numerous workers have paid close attention to it.In 2002, Wu [1] studied axisymmetric transversal intrinsic vibrations of annular membranes of varying density with an amended perturbation method and obtained the characteristic equations which determine the transversal intrinsic vibration frequencies. In 2004, Wu [2][3] presented the characteristic equations of transverse intrinsic vibrations of membranes without axial movement in rigid middle supports. The transverse vibration and stability of axial moving membrane were studied by Hou [4]. He focused on the dynamic properties and stability of the membrane at constant speed vs. the length-width ratio and the tension ratio on the border of a rectangular membrane. In 2006, Shina [5] studied the dynamic characteristics of a homogeneous membrane with constant moving speed and obtained the differential equations by using an extended Hamilton principle. In the same year, Marynowski [6] built the elastic and viscoelastic model of viscoelastic cylinder material with axial movement speed by using the 2D-rheology theory. Giannoccaro [7] established a tension control simulation system of the web-fed press and performed simulation experiments. A new shell element has been proposed for geometrically
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