scholarly journals Transverse Vibration of a Moving Viscoelastic Hard Membrane Containing Scratches

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Hongmei Zhang ◽  
Qiumin Wu
Keyword(s):  
Differential Equation ◽  
Numerical Calculation ◽  
Transverse Vibration ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Continuity Condition ◽  
Scratch Depth ◽  
Divergence Instability ◽  
Critical Instability ◽  
Calculation Results

The transverse vibration and stability of a moving viscoelastic hard printing membrane containing scratches are investigated. Based on the viscoelastic differential constitutive relation, thin plate theory, and d’Alembert principle, the differential equation of a moving viscoelastic hard membrane with a straight scratch through the surface is derived by using the continuity condition of the scratches. The complex characteristic equation is obtained by using the differential quadrature method. The effects of the scratch depth and scratch position on the critical instability speed of the moving hard membrane were highlighted by solving the differential equation and numerical calculation, and the coupling effects of speed and scratch depth on vibration characteristics of the hard membrane are also analyzed. Numerical calculation results show that the hard membrane experiences divergence instability when the actual printing speed is v=23.2 m/s, and the membrane is stable when v<23.2 m/s. The theoretical guidance and method for scratches detection of the precision coated hard membrane are provided.

scholarly journals Buckling and Vibration of Non-Homogeneous Rectangular Plates Subjected to Linearly Varying In-Plane Force

2013 ◽  
Vol 20 (5) ◽  
pp. 879-894 ◽  
Author(s):  
Roshan Lal ◽  
Renu Saini
Keyword(s):  
Differential Equation ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Material ◽  
Classical Plate Theory ◽  
Simply Supported

The present work analyses the buckling and vibration behaviour of non-homogeneous rectangular plates of uniform thickness on the basis of classical plate theory when the two opposite edges are simply supported and are subjected to linearly varying in-plane force. For non-homogeneity of the plate material it is assumed that young's modulus and density of the plate material vary exponentially along axial direction. The governing partial differential equation of motion of such plates has been reduced to an ordinary differential equation using the sine function for mode shapes between the simply supported edges. This resulting equation has been solved numerically employing differential quadrature method for three different combinations of clamped, simply supported and free boundary conditions at the other two edges. The effect of various parameters has been studied on the natural frequencies for the first three modes of vibration. Critical buckling loads have been computed. Three dimensional mode shapes have been presented. Comparison has been made with the known results.

scholarly journals Thermoelastic Coupling Vibration and Stability Analysis of Rotating Annular Sector Plates

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Yongqiang Yang ◽  
Zhongmin Wang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Transverse Vibration ◽  
Differential Quadrature Method ◽  
Angular Speed ◽  
Thermoelastic Coupling ◽  
Coupling Vibration ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

This study investigates the thermoelastic coupling vibration and stability of rotating annular sector plates. Based on Hamilton’s principle and thermal conduction equation with deformation effect, the differential equation of transverse vibration for a rotating annular sector plate is established. The differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Then, the thermoelastic coupling transverse vibrations under three different boundary conditions are calculated. The change curve of the first three order dimensionless complex frequencies of the rotating annular sector plate with the dimensionless angular speed are analyzed in the case of the thermoelastic coupling and uncoupling. The effects of the dimensionless angular speed, the ratio of inner to outer radius, the sector angle, and the dimensionless thermoelastic coupling coefficient on transverse vibration and stability of the annular sector plate are discussed. Finally, we obtained the type of instability and corresponding critical speed of the rotating annular sector plate in the case of the thermoelastic coupling and uncoupling.

Free transverse vibration analysis of thin rectangular plates locally suspended on elastic beam

2012 ◽  
Vol 227 (7) ◽  
pp. 1515-1524 ◽  
Author(s):  
M Golkaram ◽  
MM Aghdam
Keyword(s):  
Transverse Vibration ◽  
Plate Theory ◽  
Rectangular Cross Section ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Rectangular Plates ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Free Transverse Vibration ◽  
Generalized Differential

Free transverse vibration of thin rectangular plates locally suspended on deformable beam is presented using generalized differential quadrature method. The plate is completely free at all edges except a local region which is attached to a thin beam with rectangular cross section. The other side of the beam is fixed and the whole system is subjected to free transverse vibrations. According to classical plate theory and Euler–Bernoulli beam assumption, two coupled partial differential equations of the system are obtained. The governing equations and solution domain are discretized based on the generalized differential quadrature method and natural frequencies of the plate attached to the beam are obtained. Accuracy of the predictions is investigated using four simplified cases which show reasonably good agreement. For the general case, however, due to lack of data in the literature, predictions are compared with finite element results, which also demonstrate close agreement.

Dynamic Stability of Cracked Viscoelastic Rectangular Plate Subjected to Tangential Follower Force

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Zhong-min Wang ◽  
Yan Wang ◽  
Yin-feng Zhou
Keyword(s):  
Differential Equation ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Viscoelastic Plate ◽  
Equation Of Motion ◽  
Follower Force ◽  
Inverse Transformation ◽  
Complex Eigenvalue ◽  
The Time Domain ◽  
Viscoelastic Rectangular Plate

Based on the thin plate theory and the two-dimensional viscoelastic differential type constitutive relation, the differential equation of motion of a viscoelastic plate containing an all-over part-through crack and subjected to uniformly distributed tangential follower force is established in Laplace domain. Then, by performing the Laplace inverse transformation, the differential equation of motion of the plate in the time domain is obtained. The expression of the additional rotation induced by the crack is given. The complex eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are obtained by the differential quadrature method, and the δ method is adopted at the crack continuity conditions. The general eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force under the different boundary conditions are calculated. The transverse vibration characteristics, type of instability, and corresponding critical loads of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are analyzed.

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.

Static Instability of a Restrained Cantilever Column with a Tip Mass Subjected to a Subtangential Follower Force

2013 ◽  
Vol 345 ◽  
pp. 341-344
Author(s):  
Zhen Chao Su ◽  
Yan Xia Xue
Keyword(s):  
Differential Equation ◽  
Mass Parameter ◽  
Follower Force ◽  
Force Parameter ◽  
Euler Beam ◽  
Numerical Computations ◽  
Divergence Instability ◽  
Static Instability ◽  
Tip Mass

Based on the theory of Bernoulli-Euler beam, the differential equation of a restrained cantilever column with a tip mass subjected to a subtangential follower force is constructed, the solution of the differential equation is found, and the existence of regions of divergence instability of the system is discussed. The influence of the follower force parameter η, the tip mass parameter β and an end elastic end support on the divergence instability of the column is investigated. Several numerical computations of some cases have completed.

scholarly journals COMPARISON OF THREE CALCULATION METHODS OF ENERGY PERFORMANCE CERTIFICATES IN SLOVENIA

2018 ◽  
Vol 13 (1) ◽  
Author(s):  
Wadie Kidess
Keyword(s):  
Numerical Calculation ◽  
Energy Performance ◽  
Heat Losses ◽  
Calculation Methods ◽  
The Third ◽  
Simplified Method ◽  
Calculation Results ◽  
Thermal Bridges ◽  
Simplified Calculation ◽  
Family House

In order to get the authorization for issuing energy performance certificates in Slovenia, the expert candidate has to attend the prescribed course and pass the exam. The simplified method for heat losses calculation that is taught at this course neglects the thermal bridges, raising concerns whether the calculation results are reliable. In this paper we have compared three methods for calculation of thermal losses for a “typical” family house. The first is the above mentioned simplified calculation using a correctional factor; the second takes into account the thermal bridges, using linear thermal transmittances obtained by numerical calculation, and the third takes into account the thermal bridges, using default values for linear thermal transmittances. Noting that the second method returns the most exact values, we have found that the first method results are too large, yet still smaller than the third method results.

scholarly journals Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 575 ◽  
Author(s):  
Aymen Jallouli ◽  
Najib Kacem ◽  
Joseph Lardies
Keyword(s):  
Differential Equations ◽  
Dynamic Behavior ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Ultrasonic Transducers ◽  
Initial Deflection ◽  
Geometric Imperfections ◽  
Resonance Frequencies

In order to investigate the effects of geometric imperfections on the static and dynamic behavior of capacitive micomachined ultrasonic transducers (CMUTs), the governing equations of motion of a circular microplate with initial defection have been derived using the von Kármán plate theory while taking into account the mechanical and electrostatic nonlinearities. The partial differential equations are discretized using the differential quadrature method (DQM) and the resulting coupled nonlinear ordinary differential equations (ODEs) are solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). It is shown that the initial deflection has an impact on the static behavior of the CMUT by increasing its pull-in voltage up to 45%. Moreover, the dynamic behavior is affected by the initial deflection, enabling an increase in the resonance frequencies and the bistability domain and leading to a change of the frequency response from softening to hardening. This model allows MEMS designers to predict the nonlinear behavior of imperfect CMUT and tune its bifurcation topology in order to enhance its performances in terms of bandwidth and generated acoustic power while driving the microplate up to 80% beyond its critical amplitude.

Sign in / Sign up

Export Citation Format

Share Document