Research on Vibration Control of Thin Plate Based on Pre-Stressing

2018 ◽  
Author(s):  
Cheng Zhang ◽  
Jian-run Zhang ◽  
Xi Lu
Keyword(s):  
Differential Equation ◽  
Stress Distribution ◽  
Tensile Stress ◽  
Vibration Control ◽  
Thin Plate ◽  
Natural Frequencies ◽  
Control Method ◽  
Dynamic Stiffness ◽  
Thin Plates ◽  
Shape Functions

The weak dynamic stiffness of thin plate is one of the important factors that limit the use of thin plate. Improving the dynamic stiffness of thin plate is one of the effective methods for the vibration control of thin plate. In this paper, the influence of pre-stress on the vibration characteristics of thin plate is studied. A vibration control method of thin plate based on pre-stress is proposed. The vibration differential equation of quadrate thin plate under pre-stressing is established. Using the Galerkin principle, the natural frequencies corresponding to the shape functions of the quadrate thin plates under pre-stressing in different distribution forms are obtained. By comparison, it is found that pre-stressing on the thin plate can change the dynamic stiffness of thin plate. In particular, tensile stress can increase the dynamic stiffness of thin plate while compressive stress can reduce the dynamic stiffness of the thin plate. The greater the pre-stress, the more obvious the effect. In the end, the requirements of the pre-stress distribution which can improve the dynamic stiffness of thin plate effectively are derived.

The Method of Successive Decrease and the Concept of Harmonic Wave Filter in Structural Wave Control

1995 ◽  
Author(s):  
Dajun Wang ◽  
Quan Wang ◽  
A. Y. T. Leung
Keyword(s):  
Vibration Control ◽  
Structural Control ◽  
Natural Frequencies ◽  
Control Method ◽  
Harmonic Wave ◽  
Flexible Structures ◽  
Modal Control ◽  
Large Space ◽  
Wave Filter ◽  
Wave Control

Abstract Most of the available vibration control methods for flexible structures are based on the modal control method, which, however, sometimes meets with problems. For examples, the problem of spillover has not been solved adequately. And, for flexible large space structures with closely spaced natural frequencies, it is very difficult to use modal method to treat vibration control problems because the modes corresponding to closely spaced and repeated frequencies can not be computed accurately. In recent years, the method of structural wave control has been developed, but it has not been studied sufficiently. The object of this paper is an attempt to solve some of the existing problems raised due to the application of the modal control method. A wave control method — the method of successive decrease is set up at first, which is aimed at one harmonic wave. Then, a new design method in wave control is proposed, based on the above method. The problem of control spillover is analyzed and the concept of harmonic wave filter is introduced. As an example, the problem of the control of structures with closely spaced natural frequencies is treated by both the method of modal control and the method of successive decrease. The numerical results show that the method of successive decrease is more effective than the method of modal control. It proves that the method of successive decrease and the concept of harmonic wave filter is promising in solving the problems of structural control.

scholarly journals Drying-Induced Strain-Stress and Deformation of Thin Ceramic Plate

2020 ◽  
Vol 4 (1) ◽  
pp. 9 ◽  
Author(s):  
Yoshinori Itaya ◽  
Hiroya Hanai ◽  
Nobusuke Kobayashi ◽  
Tsuguhiko Nakagawa
Keyword(s):  
Tensile Stress ◽  
Thin Plate ◽  
Moisture Transfer ◽  
Electronic Materials ◽  
Maximum Principal Stress ◽  
Thin Plates ◽  
Ceramic Plate ◽  
Air Stream ◽  
Strain Stress ◽  
Drying Conditions

Ceramic thin plates are applied to several industrial purposes including electronic materials and sensors. Drying-induced shrinkage and strain-stress formation of a ceramic thin plate were studied experimentally and theoretically. A kaolin thin plate molded into 10 mm × 30 mm × 1 mm was dried in a hot air stream, and the drying characteristics and deformation were examined. Modeling was also performed to predict the behavior. Heat and moisture transfer conservation equations and constitution equations based on viscoelastic strain-stress were simultaneously solved by a finite element method. A test piece of the thin plate was warped when only one side of the plate was dried, while it was almost flat when both sides were dried. The behaviors of drying and deformation were predicted with a reasonable agreement by the modeling. Parametric analyses by the modeling revealed that the drying conditions with faster drying rate in the beginning period resulted in formation of greater maximum principal stress, and drying on only one side of the plate induced stronger tensile stress in falling rate period than that with both sides drying. The larger thickness of the plate influenced the formation of significantly greater tensile stress but affected maximum compressive stress only a little.

Research on Dynamic Characteristics of Assembled Thin Plates Structure by BEM

2005 ◽  
Vol 297-300 ◽  
pp. 2368-2374 ◽  
Author(s):  
Ying Wu Fang ◽  
Yu Mei Huang ◽  
Guang Peng Zhang
Keyword(s):  
Thin Plate ◽  
Dynamic Characteristics ◽  
High Efficiency ◽  
Natural Frequencies ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Good Precision ◽  
Established Method ◽  
Frequency Scanning ◽  
Boundary Equations

A method of systematic modeling was presented to analyze dynamic characteristics of an assembled thin plates structure. Based on dynamic fundamental solutions of a thin plate, governing boundary equations in the lateral and internal vibration of the thin plate are established by using a boundary element method (BEM). According to assembled conditions on the boundary, dynamic characteristics equations of the assembled thin plates structure are deduced. In order to raise calculating efficiency and avoid complicated programming operation, an approach of frequency scanning is introduced to analyze dynamic characteristics of the assembled thin plates structure. The natural frequencies and modal shapes are obtained fast and effectively. By numerical calculation and experiments given, the established method has not only good precision but also high efficiency.

Free Vibration of Plates of Various Shapes with Intermediate Point Supports by the Hp-Cloud Method and Lagrange Multiplier

2016 ◽  
Vol 16 (09) ◽  
pp. 1550055 ◽  
Author(s):  
Sajad Jamshidi ◽  
Mojtaba Azhari ◽  
Hossein Amoushahi
Keyword(s):  
Lagrange Multiplier ◽  
Natural Frequencies ◽  
Cell Structure ◽  
Ritz Method ◽  
Thin Plates ◽  
Plate Boundaries ◽  
Shape Functions ◽  
Intermediate Point ◽  
Simply Supported ◽  
Kronecker Delta

The Hp-Cloud meshless method was developed to study the dynamic analysis of arbitrarily shaped thin plates with intermediate point supports. By proposing a special pattern for the influence radius of nodes and a polynomial type of enrichment function, the Hp-Cloud shape functions with Kronecker delta property were constructed. They can satisfy the zero deflection conditions for the field nodes at the point supports. The results obtained from these shape functions agree well with the previous ones, showing good accuracy and convergence. For plates with sharp corners, it is not possible to construct the Hp-Cloud shape function with Kronecker delta property. To this end, the Lagrange multiplier method was used for enforcing the boundary conditions. The computations were carried out by the Ritz method, and the cell structure method is refined to improve the speed and accuracy of numerical integration on the subscription surface of clouds intersecting with the plate boundaries. Using the algorithm developed, the natural frequencies of plates of various shapes and support patterns were computed. By increasing the number of point supports on the plate edges, the natural frequencies computed of the plate tend to those of the simply supported plate. Appropriate pattern of point supports distribution was presented for modeling the simply supported plates of various shapes by comparing the corresponding natural frequencies.

Vibration Control Using Connected Control Device for Two Identical Structures Arranged in Parallel

2005 ◽  
Author(s):  
Kiyofumi Fujimura ◽  
Kazuya Makita ◽  
Toru Watanabe ◽  
Kazuto Seto
Keyword(s):  
Optimal Design ◽  
Vibration Control ◽  
Passive Control ◽  
Natural Frequencies ◽  
Control Method ◽  
Dynamic Properties ◽  
Flexible Structures ◽  
Design Strategy ◽  
Control Device ◽  
Supporting Structures

This paper deals with vibration control using the optimal design strategy of the connected control device for flexible structures with same dynamic properties. One of the authors had already proved effectiveness of connected control method for vibration control of flexible structures arranged in parallel. However, its control performance is degraded as the natural frequencies of structures become closer. To overcome this problem, the authors present a modified control mechanism in which the actuators are connected to the structures with differences in its connecting position by using long arms named “supporting structures”. However, the optimal design strategy for vibration control device has not been established yet. In this report, the optimal design strategy of passive control is presented. Computer simulations and the experiments are carried out and the effectiveness of the presented vibration control designed by the connected control device is confirmed.

A DYNAMIC STIFFNESS METHOD FOR DETERMINING NATURAL FREQUENCIES OF BEAMS WITH ALLOWANCE FOR DEAD LOAD

2009 ◽  
Vol 09 (04) ◽  
pp. 777-790 ◽  
Author(s):  
JING ZHANG ◽  
WEI-XIN REN
Keyword(s):  
Differential Equation ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Initial Stresses ◽  
Single Element ◽  
Dead Load ◽  
Load Effect ◽  
Dynamic Stiffness Matrix ◽  
Governing Differential Equation

The initial stresses due to dead loads have an influence on the natural frequencies of bridges. In this paper, a dynamic stiffness-based method is proposed for determining the natural frequencies of uniform elastic beams with allowance for the dead load effect. Firstly, the governing differential equation including the effect of dead loads is derived. Next, the analytical dynamic stiffness matrix is obtained by applying the displacements and forces boundary conditions at the ends of the beam. In order to solve analytically the governing differential equation, the modified dynamic stiffness matrix is defined by converting the governing quasi-static boundary value problem into an equivalent set of initial value problems. Finally, the Wittrick–Williams algorithm is implemented to extract the natural frequencies from the modified dynamic stiffness matrix. Numerical examples are presented and corresponding parameter studies have been performed to illustrate the applicability and reliability of the proposed method. It is demonstrated that the proposed dynamic stiffness matrix-based method is effective even though the beam is considered as a single element without adding additional nodes.

Instability Analysis of the Bipolar Plate for Welding Fuel Cell

2012 ◽  
Vol 152-154 ◽  
pp. 568-573
Author(s):  
Yu Xin Yao ◽  
Chun Yuan Shi
Keyword(s):  
Fuel Cell ◽  
Stress Distribution ◽  
Tensile Stress ◽  
Compressive Stress ◽  
Thin Plate ◽  
Bipolar Plate ◽  
Maximum Compressive Stress ◽  
Heating And Cooling ◽  
Instability Theory ◽  
The Difference

The instability of the bipolar plate for welding fuel cell was analyzed taking the bipolar plate as thin plate. The minimum compressive stress is calculated based on thin plate instability theory caused by longitudinal compressive stress. The simplified thermal stress distribution function is determined using the analytical solution of the plane heat conduction equation. The maximum compressive stress is determined through the analysis of the longitudinal stress distribution of the cross section passing through the solder point during heating and cooling process. The results are used to obtain the pre-tensile stress controlling the instability of the bipolar plate for welding fuel cell, and the minimum pre-tensile stress is the difference between the maximum compressive stress and the minimum compressive stress as the thin plate loses instability.

scholarly journals A Variable Parameter Ambient Vibration Control Method Based on Quasi-Zero Stiffness in Robotic Drilling Systems

Machines ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 67
Author(s):  
Laixi Zhang ◽  
Chenming Zhao ◽  
Feng Qian ◽  
Jaspreet Singh Dhupia ◽  
Mingliang Wu
Keyword(s):  
Vibration Control ◽  
Vibration Isolation ◽  
Control Method ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Variable Parameter ◽  
Harmonic Balance Method ◽  
Variable Stiffness ◽  
Ambient Vibration ◽  
Robotic Drilling

Vibrations in the aircraft assembly building will affect the precision of the robotic drilling system. A variable stiffness and damping semiactive vibration control mechanism with quasi-zero stiffness characteristics is developed. The quasi-zero stiffness of the mechanism is realized by the parallel connection of four vertically arranged bearing springs and two symmetrical horizontally arranged negative stiffness elements. Firstly, the quasi-zero stiffness parameters of the mechanism at the static equilibrium position are obtained through analysis. Secondly, the harmonic balance method is used to deal with the differential equations of motion. The effects of every parameter on the displacement transmissibility are analyzed, and the variable parameter control strategies are proposed. Finally, the system responses of the passive and semiactive vibration isolation mechanisms to the segmental variable frequency excitations are compared through virtual prototype experiments. The results show that the frequency range of vibration isolation is widened, and the stability of the vibration control system is effectively improved without resonance through the semiactive vibration control method. It is of innovative significance for ambient vibration control in robotic drilling systems.

scholarly journals The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 799
Author(s):  
Xiangli Pei ◽  
Ying Tian ◽  
Minglu Zhang ◽  
Ruizhuo Shi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Model ◽  
Control Method ◽  
System Modeling ◽  
Working Environment ◽  
Partial Differential ◽  
External Interference ◽  
Differential Control ◽  
Differential Control Method

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.

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