Vibration Analysis and Control of a Rotating Flexible Arm With ACLD Treatment

2002 ◽  
Author(s):  
E. H. K. Fung ◽  
D. T. W. Yau
Keyword(s):  
Vibration Suppression ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Gravitational Effect ◽  
Transverse Displacement ◽  
Complex Eigenvalue ◽  
Constrained Layer Damping ◽  
Rotating Speed ◽  
Centrifugal Stiffening ◽  
And Control

In this paper, the vibration behavior and control of a clamped-free rotating flexible cantilever arm with fully covered Active Constrained Layer Damping (ACLD) treatment is investigated. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The stress-strain relationship for the viscoelastic material (VEM) is described by a complex shear modulus while the shear deformations in the two piezoelectric layers are neglected. Hamilton’s principle in conjunction with finite element method (FEM) is used to derive the nonlinear coupled differential equations of motion and the associated boundary conditions that describe the rigid hub angle rotation, the arm transverse displacement and the axial deformations of the three-layer composite. This refined model takes into account the effects of centrifugal stiffening due to the rotation of the beam and the potential energies of the VEM due to extension and bending. Active controllers are designed with PD for the piezo-sensor and actuator. The vibration frequencies and damping factors of the closed-loop beam/ACLD system are obtained after solving the characteristic complex eigenvalue problem numerically. The effects of different rotating speed, thickness ratio and loss factor of the VEM as well as different controller gain on the damped frequency and damping ratio are presented. The results of this study will be useful in the design of adaptive and smart structures for vibration suppression and control in rotating structures such as rotorcraft blades or robotic arms.

Passive Control of Vibration of Elastically Supported Beams Subjected to Moving Loads

2005 ◽  
Author(s):  
D. Younesian ◽  
E. Esmailzadeh ◽  
M. H. Kargarnovin
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Compressive Force ◽  
Moving Loads ◽  
Axial Compressive Force ◽  
Before And After ◽  
Elastically Supported

Vibration suppression of elastically supported beams subjected to moving loads is investigated in this work. For a Timoshenko beam with an arbitrary number of elastic supports, subjected to a constant axial compressive force, and having a tuned mass damper (TMD) installed at the mid-span, the equations of motion are derived and using the Galerkin approach the solution is sought. The optimum values of the frequency and damping ratio are determined both analytically and numerically and presented as some design curves directly applicable in the TMD design for bridge structures. To show the efficiency of the designed TMD, computer simulation for two real bridges, subjected to a S.K.S Japanese high-speed train, is carried out and the results obtained are compared for before and after the installation of the TMD system.

DYNAMIC ANALYSIS OF ROTATING ELECTRORHEOLOGICAL COMPOSITE BEAMS

2005 ◽  
Vol 19 (07n09) ◽  
pp. 1236-1242 ◽  
Author(s):  
KEXIANG WEI ◽  
GUANG MENG ◽  
HONGQUAN LU ◽  
SHISHA ZHU
Keyword(s):  
Electric Fields ◽  
Composite Beam ◽  
Loss Factor ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Resonant Frequencies ◽  
Rotating Speed ◽  
Vibration Properties ◽  
Er Fluids ◽  
Elastic Layers

The modeling and vibration properties of rotating electrorheological (ER) sandwich beams are discussed. The proposed beam is composed of three layers with ER fluids sandwiched between two elastic layers. Based on the Hamilton's principle and finite element method (FEM), the equations of motion of ER beam are derived. The effects of different electric fields, rotating speed and thickness ration on the resonant frequencies and modal loss factors are presented. The results of numerical simulation show that the model loss factor of rotating ER beam can be substantially increased when applied an electric field. The ER materials have a significant effect on the vibration suppression of rotating composite beam.

Vibration Control of a Space Flexible Robot Manipulator Using PZT Actuators

2011 ◽  
Vol 66-68 ◽  
pp. 1142-1148 ◽  
Author(s):  
Jun Qiang Lou ◽  
Yan Ding Wei
Keyword(s):  
Control Strategy ◽  
Vibration Suppression ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
System Stability ◽  
Flexible Manipulator ◽  
Flexible Robot ◽  
Simulation Results ◽  
And Control ◽  
And Robotics

The dynamic analysis and control of flexible robot manipulators have been the main concerns of many recent studies in aeronautics and robotics. Moreover, the complexity of this problem increases when a flexible manipulator carries a payload. In this paper, we proposed a space two-link flexible manipulator with tip payload featuring surface-bonded piezoelectric torsional actuator and shear actuator. The equations of motion for the system are obtained using Hamilton’s principle. A Lyapunov-based controller is proposed to suppress the vibration of the system. Stability of the system is also investigated. The simulation results demonstrate the proposed control strategy is well suited for active control of vibration suppression on flexible manipulators.

scholarly journals Free Vibration and Damping of Rotating Composite Shaft with a Constrained Layer Damping

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Ren ◽  
Yuhuan Zhang
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Constrained Layer Damping ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Damping Characteristics ◽  
Reinforced Composite ◽  
Composite Shaft ◽  
Passive Constrained Layer Damping

The free vibration and damping characteristics of rotating shaft with passive constrained layer damping (CLD) are studied. The shaft is made of fiber reinforced composite materials. A composite beam theory taking into account transverse shear deformation is employed to model the composite shaft and constraining layer. The equations of motion of composite rotating shaft with CLD are derived by using Hamilton’s principle. The general Galerkin method is applied to obtain the approximate solution of the rotating CLD composite shaft. Numerical results for the rotating CLD composite shaft with simply supported boundary condition are presented; the effects of thickness of constraining layer and viscoelastic damping layers, lamination angle, and rotating speed on the natural frequencies and modal dampings are discussed.

On the Vibration Suppression and Energy Harvesting of Building Structures Using an Electromagnetic-Inerter-Absorber

2018 ◽  
Author(s):  
Eshagh F. Joubaneh ◽  
Oumar R. Barry ◽  
Lei Zuo
Keyword(s):  
Energy Harvesting ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Optimization Technique ◽  
Building Structures ◽  
Earthquake Excitation ◽  
Mechanical Coupling ◽  
Rlc Circuit ◽  
Tuning Ratio

This paper studies the performance of an electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI) in terms of simultaneously suppressing unwanted vibration and harvesting energy in a vibrating building. The ERS-TMDI is attached to a building, which is subjected to an earthquake excitation. An inerter is connected between the TMD and the ground. The electromagnetic transducer and associated circuit, which replaces the viscous damping in the classical tuned mas-damper (TMD), is assumed to be an ideal transducer shunted with a resistor, an inductor, and a capacitor (RLC) circuit. Two RLC circuit configurations are investigated: one in series and another in parallel. The governing equations of motion are presented and H2 optimization technique is employed to derive explicit expressions for the optimal mechanical tuning ratio, electrical damping ratio, electrical tuning ratio, and electromagnetic mechanical coupling coefficient. The validity of the obtained closed-form expressions is examined using Matlab optimization toolbox. Parametric studies are carried out to investigate the effect of the mass and inertance ratios on the obtained optimal parameters. Numerical examples are also conducted to demonstrate the role of key design variables on vibration mitigation and energy harvesting performances. Also, the performance of a parallel RLC circuit configuration is compared to that of a series configuration.

Nonlinear Modeling and Partial Linearizing Control of a Slewing Timoshenko-Beam

1996 ◽  
Vol 118 (1) ◽  
pp. 75-83 ◽  
Author(s):  
King Yuan ◽  
Chen-Meng Hu
Keyword(s):  
Timoshenko Beam ◽  
Slenderness Ratio ◽  
Nonlinear Modeling ◽  
Equations Of Motion ◽  
Nonlinear Controller ◽  
Elastic Mode ◽  
Modeling And Control ◽  
Centrifugal Stiffening ◽  
Orthogonality Conditions ◽  
And Control

The modeling and control of a horizontally slewing inextensible Timoshenko beam, taking into account the centrifugal stiffening effect and a tip payload, are considered. Partial differential equations of motion and orthogonality conditions for the constrained modes are derived. A finite dimensional dynamic model simplified by using the orthogonality conditions is obtained. To achieve the joint angle trajectory tracking with simultaneous suppression of elastic vibrations, a nonlinear controller is designed using input-output linearization and elastic-mode stabilization. A sufficient condition for asymptotic stability of the closed-loop system is established. Numerical examples with the role of slenderness ratio of the slewing beam highlighted are presented to demonstrate the effectiveness of the proposed control strategy.

Design of a slender turning cutting tool via a vibration absorber equipped with piezoelectric ceramic

2021 ◽  
pp. 107754632110144
Author(s):  
Yiqing Yang ◽  
Haoyang Gao ◽  
Qiang Liu
Keyword(s):  
Piezoelectric Ceramic ◽  
Cutting Tool ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Electrical Energy ◽  
Diameter Ratio ◽  
Vibration Absorber ◽  
Machined Surface ◽  
Structural Part ◽  
Machined Surface Roughness

Turning cutting tool with large length–diameter ratio has been essential when machining structural part with deep cavity and in-depth hole features. However, chatter vibration is apt to occur with the increase of tool overhang. A slender turning cutting tool with a length–diameter ratio of 7 is developed by using a vibration absorber equipped with piezoelectric ceramic. The vibration absorber has dual functions of vibration transfer to the absorber mass and vibration conversion to the electrical energy via the piezoelectric effect. Equations of motion are established considering the dual damping from the piezoelectric ceramic and rubber gasket. The equivalent damping of piezoelectric ceramic is derived, and the geometries are optimized to achieve optimal vibration suppression. The modal analysis demonstrates that the cutting tool with the vibration absorber can reach 80.1% magnitude reduction. Machining tests are carried out in the end. The machining acceleration and machined surface roughness validate the vibration suppression of the VA, and the output voltage by the piezoelectric ceramic demonstrates the ability of vibration sensing.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Sign in / Sign up

Export Citation Format

Share Document