An Influence Analysis of Second-Order Effect to the Vibration Control of Piezoelectric Beam by the Spline Finite Point Method

2012 ◽  
Vol 166-169 ◽  
pp. 3124-3130 ◽  
Author(s):  
Shuang Bei Li ◽  
Lin Jie Jiang ◽  
Chun Xia Gu ◽  
Rong Qin
Keyword(s):  
Control Theory ◽  
Vibration Control ◽  
Axial Force ◽  
Natural Frequencies ◽  
Order Effect ◽  
Second Order ◽  
Modal Control ◽  
Finite Point ◽  
Axial Forces ◽  
Piezoelectric Beam

The field functions of the spline finite point (SFP) method were constructed by the linear combination of B-spline basis function, and the higher-precision results would be obtained with less discrete nodes by the SFP method. In this paper, based on Reddy's third order beam theory, a motion equation was developed by the SFP method to analyze the first five natural frequencies of piezoelectric laminated beam under different axial forces. The influence of second-order effect caused by the axial force on vibration control was discussed based on the modal control theory and the Linear Quadratic Regulator (LQR) optimal control method. It can be concluded that the SFP method is suitable for the dynamic analysis of piezoelectric beam which needs less computational cost and has high accuracy. The vibration of the structure can be effectively inhibited by the LQR method and modal control theory. And the axial force has significant impact on the natural frequencies and control voltage of piezoelectric beam.

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 Modelling and Testing of the Piezoelectric Beam as Energy Harvesting System

2016 ◽  
Vol 10 (4) ◽  
pp. 291-295 ◽  
Author(s):  
Andrzej Koszewnik ◽  
Krzysztof Wernio
Keyword(s):  
Energy Harvesting ◽  
Modal Analysis ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Piezo Actuator ◽  
Experimental Investigations ◽  
Modal Control ◽  
Piezoelectric Beam ◽  
Energy Harvesting System ◽  
Control Forces

Abstract The paper describes modelling and testing of the piezoelectric beam as energy harvesting system. The cantilever beam with two piezo-elements glued onto its surface is considered in the paper. As result of carried out modal analysis of the beam the natural frequencies and modes shapes are determined. The obtained results in the way mentioned above allow to estimate such location of the piezo-actuator on the beam where the piezo generates maximal values of modal control forces. Experimental investigations carried out in the laboratory allow to verify results of natural frequencies obtained during simulation and also testing of the beam in order to obtain voltage from vibration with help of the piezo-harvester. The obtained values of voltage stored on the capacitor C0 shown that the best results are achieved for the beam excited to vibration with third natural frequency, but the worst results for the beam oscillating with the first natural frequency.

scholarly journals Dynamic Behavior of Externally Prestressed Continuous Beam considering Second-Order Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
De-Ping Fang
Keyword(s):  
Analytical Solution ◽  
Dynamic Behavior ◽  
Energy Method ◽  
Natural Frequencies ◽  
Order Effect ◽  
Second Order ◽  
Influence Coefficient ◽  
Continuous Beam ◽  
Order Deformation ◽  
Zero Effect

Considering precisely the second-order deformation of external tendon, the analytical solution of natural frequencies of 2-span externally prestressed continuous beam was obtained by the energy method. The effect of external prestress compression softening is between the zero effect of unbonded prestress compression and the effect of axial outside compression and is determined by the influence coefficient ranging within 0∼1. The influence coefficient is mainly related to the number of deviators and slightly related to tendon layout. Without deviator, the influence coefficient is 1, and the effect of external prestress compression softening is the same as the effect of axial outside compression. As the number of deviators increases, the influence coefficient gradually decreases from 1 to near 0, and the effect of external prestress compression softening is close to zero effect of unbonded prestress compression. With one or more deviators, the effect of external prestress compression softening is negligible. As the eccentricity and area of tendon increase, only the first symmetric frequency increases obviously, and other frequencies almost remain unchanged. The influence of tendon layout linear transformation on the frequency is negligible.

Study on Frequency Tuning of Parallel Mechanism for Reducing Vibration

2013 ◽  
Vol 275-277 ◽  
pp. 905-908
Author(s):  
Feng Yang ◽  
Jun Chuan Niu ◽  
Kun Peng Li ◽  
Yong Li
Keyword(s):  
Vibration Control ◽  
Parallel Mechanism ◽  
Natural Frequencies ◽  
Frequency Tuning ◽  
Vibration Reduction ◽  
Kinematics And Dynamics

To reduce the multi-dimensional vibration which exist in some vibrating machines or equipments such as running ambulances, a parallel mechanism with 3-translation DOFs was presented and introduced into the ambulance stretcher, then a three-translation vibration reduction platform was developed. The kinematics and dynamics equations of the presented vibration reduction platform were deduced. And then the workspace, tuning principles and dynamics characteristics were studied. The simulations show that the presented parallel mechanism or vibration reduction platform is valid for reducing vibration and the system has different natural frequencies in case that the upper platform of the mechanism works on some specific positions, so it can be used to achieve tunable vibration control.

Electromagnetism as a second order effect

1961 ◽  
Vol 3 (1) ◽  
pp. 28-44 ◽  
Author(s):  
W. G. V. Rosser
Keyword(s):  
Order Effect ◽  
Second Order

Advances In The Modeling And Dynamic Simulation of Reeving Systems Using The Arbitrary Lagrangian-Eulerian Modal Method

2021 ◽  
Author(s):  
José L. Escalona ◽  
Narges Mohammadi
Keyword(s):  
Finite Elements ◽  
Axial Force ◽  
Axial Direction ◽  
Rotary Inertia ◽  
Arbitrary Lagrangian Eulerian ◽  
Original Formulation ◽  
Absolute Position ◽  
Axial Forces ◽  
Modal Coordinates ◽  
Modal Method

Abstract This paper presents new advances in the arbitrary Lagrangian-Eulerian modal method (ALEM) recently developed for the systematic simulation of the dynamics of general reeving systems. These advances are related to a more convenient model of the sheaves dynamics and the use of axial deformation modes to account for non-constant axial forces within the finite elements. Regarding the sheaves dynamics, the original formulation uses kinematic constraints to account for the torque transmission at the sheaves by neglecting the rotary inertia. One of the advances described in this paper is the use of the rotation angles of the sheaves as generalized coordinates together with the rope-to-sheave no-slip assumption as linear constraint equations. This modeling option guarantees the exact torque balance the sheave without including any non-linear kinematic constraint. Numerical results show the influence in the system dynamics of the sheave rotary inertia. Regarding the axial forces within the finite elements, the original formulation uses a combination of absolute position coordinates and transverse local modal coordinates to account for the rope absolute position and deformation shape. The axial force, which only depends on the absolute position coordinates, is constant along the element because linear shape functions are assumed to describe the axial displacements. For reeving systems with very long rope spans, as the elevators of high buildings, the constant axial force is inaccurate because the weight of the ropes becomes important and the axial force varies approximately linearly within the rope free span. To account for space-varying axial forces, this paper also introduces modal coordinates in the axial direction. Numerical results show that a set of three modal coordinates in the axial direction is enough to simulate linearly varying axial forces.

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.

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