Transverse Vibration Analysis of Axially Moving Trapezoidal Plates

2021 ◽  
Vol 16 (6) ◽  
pp. 978-986
Author(s):  
Man Zhang ◽  
Ji-Xian Dong
Keyword(s):  
Aspect Ratio ◽  
Transverse Vibration ◽  
Differential Quadrature Method ◽  
Eigenvalue Equation ◽  
Parameter Method ◽  
Complex Eigenvalue ◽  
Complex Frequency ◽  
Discrete Method ◽  
Axially Moving ◽  
Trapezoidal Plate

Transverse vibration of axially moving trapezoidal plates is investigated. The differential equation of transverse vibration for a axially moving trapezoidal plate is established by D'Alembert principle. The original trapezoid region can be replaced by regular square region by the medium parameter method for the convenience of calculation. A generalized complex eigenvalue equation is derived by a discrete method (the differential quadrature method). The complex frequency curve of trapezoidal plate is obtained by calculating the eigenvalue equation. The change of the complex frequencies of the axially moving trapezoidal plates with the dimensionless axially moving speed is analyzed. The effects of the aspect ratio and the trapezoidal angle on instability type of the trapezoidal plate are discussed under different boundary conditions. The results of numerical analysis show that there are two main instability types of axially moving trapezoidal plate: divergence and flutter. The modal orders of the two types of instability are also different, which is related to the trapezoidal angle, aspect ratio and boundary condition of the trapezoidal plate.

scholarly journals Stability of Axially Moving Piezolaminated Viscoelastic Plate Subjected to Follower Force

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yan Wang ◽  
Tao Jing ◽  
Jimei Wu ◽  
Min Xie
Keyword(s):  
Piezoelectric Layer ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Tensile Force ◽  
Viscoelastic Plate ◽  
Follower Force ◽  
Complex Eigenvalue ◽  
Axially Moving ◽  
The Stability ◽  
Moving Speed

The stability of the moving viscoelastic plate with the piezoelectric layer subjected to uniformly distributed tangential follower force is investigated. The force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force. The differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer subjected to uniformly distributed tangential follower force is formulated on the basis of the Kirchhoff thin plate theory and the two-dimensional viscoelastic differential constitutive relation. The complex eigenvalue equations are established by the differential quadrature method. Via numerical calculation, the curves of real parts and imaginary parts of dimensionless complex frequencies versus uniformly distributed tangential follower force and dimensionless moving speed are obtained. The effects of nonconservative force, dimensionless axially moving speed, and dimensionless applied voltages on the stability of axially moving nonconservative viscoelastic plate with piezoelectric layer are analyzed.

scholarly journals Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Tianle Lu ◽  
Zhongmin Wang ◽  
Dongdong Liu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Slenderness Ratio ◽  
Differential Quadrature Method ◽  
Beam Theory ◽  
Complex Eigenvalue ◽  
Complex Frequency ◽  
Growth Trend ◽  
Rotating Beams ◽  
Euler Bernoulli Beam

For the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. Then, introducing dimensionless quantities to differential equations and boundary conditions, the generalized complex eigenvalue equations of the system are obtained by the differential quadrature method. The effects of the slenderness ratio, the viscoelastic ratio, the hub radius-beam length ratio, and dimensionless hub speed and fractional order on the vibration characteristics of fractional derivative viscoelastic rotating beams are discussed by numerical examples. Numerical calculations show that when the dimensionless hub speed is constant, the real part of complex frequency increases with the increase of the fractional order, and the higher-order growth trend is more obvious. Through the study of displacement response at different points on the beam, it can be seen that the closer to the free end, the larger the response amplitude. And, the amplitude of response has been attenuated, which is also consistent with the vibration law of free vibration considering damping.

scholarly journals Nonlinear vibration characteristics and stability of the printing moving membrane

2017 ◽  
Vol 36 (3) ◽  
pp. 306-316 ◽  
Author(s):  
Jimei Wu ◽  
Mingyue Shao ◽  
Yan Wang ◽  
Qiumin Wu ◽  
Ziheng Nie
Keyword(s):  
Aspect Ratio ◽  
Nonlinear Vibration ◽  
Large Deflection ◽  
Initial Conditions ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Complex Frequency ◽  
Weighted Residual Method ◽  
Small Deflection ◽  
Axially Moving

Most studies on the membrane vibration are limited to discussing small deflection linear problems, but rarely on the study of nonlinear large deflection problems. In practice, however, membrane deflection is not necessarily far less than the thickness, so it is necessary to research the large deflection vibration problems of moving membrane. In this paper, the large deflection vibration characteristics and stability of the moving printing membrane are analyzed. Large deflection vibration equation of an axially moving membrane is derived by using Von Karman nonlinear plate theory. The large deflection vibration of rectangle moving membrane with four edges fixed boundary is studied by using the Bubnov–Galerkin method which is a semi-analytical-weighted residual method, and the large deflection vibration complex frequency curves along with the change of speed and aspect ratio in the different initial conditions are obtained. The results show that the large deflection nonlinear vibration can be effectively avoided by increasing membrane aspect ratio and decreasing the membrane dimensionless velocity. The study provides theoretical basis for improving the operation stability of the printing equipment.

scholarly journals Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Arun Kumar Gupta ◽  
Shanu Sharma
Keyword(s):  
Temperature Distribution ◽  
Aspect Ratio ◽  
Transverse Vibration ◽  
Thermal Gradient ◽  
Ritz Method ◽  
Linear Temperature ◽  
Varying Thickness ◽  
Free Transverse Vibration ◽  
Trapezoidal Plate ◽  
Taper Constant

The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness inx-direction subjected to linear temperature distribution inx-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant, and aspect ratio for the first two modes of vibrations.

Stability Analysis of Moving Printing Web With Sine Half-Wave Variable Density Based on Differential Quadrature Method

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Jimei Wu ◽  
Mingyue Shao ◽  
Yan Wang ◽  
Qiumin Wu ◽  
Fan Zhao
Keyword(s):  
Flexible Electronics ◽  
Transverse Vibration ◽  
Differential Quadrature Method ◽  
Variable Density ◽  
Differential Quadrature ◽  
Printing Press ◽  
Quadrature Method ◽  
Half Wave ◽  
The Impact ◽  
Density Coefficient

The moving web is widely used to make printing and packaging products, flexible electronics, cloths, etc. The impact of the variable density on printing web dynamic behavior is considered. The density changes in the form of sine half-wave in the lateral direction. Based on the D'Alembert's principle, the transverse vibration differential equation of moving printing web with variable density is established and is discretized by using the differential quadrature method (DQM). The complex characteristic equation is derived. The impacts of the density coefficient and the dimensionless speed on the web stability and vibration characteristics are discussed. The results show that it is feasible to use the DQM to analyze the problem of transverse vibration of printing web with varying density; the tension ratio and the density coefficient have important impacts on the stability of moving printing web. This study provides theoretical guidance and basis for optimizing the structure of printing press and improving the stable working speed of printing press and web.

scholarly journals Flutter and parametric stability analysis of axially moving composite graphene sheets

2019 ◽  
Vol 286 ◽  
pp. 01008
Author(s):  
A. Azrar ◽  
N. Fakri ◽  
A.A. Aljinaidi ◽  
L. Azrar
Keyword(s):  
Harmonic Balance ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Excitation Frequency ◽  
Equation Of Motion ◽  
Graphene Sheets ◽  
Parametric Stability ◽  
Various Boundary Conditions ◽  
Axially Moving ◽  
Fibers Orientation

The dynamic analysis instability of axially moving rectangular composite graphene sheets with visco elastic foundation is modeled and numerically simulated for various boundary conditions based on the differential quadrature method (DQM). The partial differential equation of motion based on the nonlocal elasticity and the Kirchhoff plate theories is given. The Galerkin and harmonic balance methods are used for the linear and parametric vibration analysis. The influences of nonlocal parameter, the fibers orientation and the viscoelastic foundation effects on the dynamic behaviors of the rectangular graphene sheet as well as the instabilities induced by the time dependent axial speed and its excitation frequency are investigated.

scholarly journals Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Qiumin Wu ◽  
Yuan Chen
Keyword(s):  
Density Distribution ◽  
Transverse Vibration ◽  
High Speed ◽  
Differential Quadrature Method ◽  
Variable Density ◽  
Vibration Characteristics ◽  
Lateral Direction ◽  
Vibration Model ◽  
The Stability ◽  
Density Coefficient

The vibration model of moving membrane with variable density distribution is established, and the density distribution of the moving membrane varies along the lateral direction. The transverse vibration differential equations of moving membrane are established based on D’Alembert’s principle and discretized by using the differential quadrature method (DQM). The relationships of the first three dimensionless complex frequencies between dimensionless speed, density coefficient, and tension ratio of the membrane are analyzed by numerical calculation. The effects of the density coefficient and the tension ratio on transverse vibration characteristics of the membrane are investigated. The relationship between density coefficient and critical speed is obtained. The numerical results show that the density coefficient and the tension ratio have important influence on the stability of moving membrane. So the study provides a theoretical basis for improving the working stability of the membrane in the high-speed printing process.

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