Vibration Control of a Beam Using a Sliding Support

2001 ◽  
Author(s):  
Phillip H. Nguyen ◽  
Jerry H. Ginsberg
Keyword(s):  
Vibration Control ◽  
Phase Angle ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Reduction ◽  
Flexural Vibration ◽  
Basis Functions ◽  
Resonant Frequencies ◽  
Periodic Fluctuation

Abstract This paper discusses a concept for controlling flexural vibration of a beam in which a pin support oscillates harmonically parallel to the beam’s axis. This induces a periodic fluctuation of the effective inertia and stiffness, which represents a source of parametric excitation. A model of the response is developed by using a Ritz series modified to allow the basis functions to be time, as well as position, dependent. Solutions are obtained by numerically integrating the equations of motion. Vibration control requires identification of the support frequency, amplitude, and phase angle that reduce the overall motion relative to what would be obtained if the support were stationary. It is shown that resonances can be controlled in this manner. However, the concept is shown to be ineffective for broadband vibration reduction because the parametric excitation merely shifts the resonant frequencies, while it also induces new resonances.

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.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

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.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

scholarly journals Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
D. A. Maturi ◽  
A. J. M. Ferreira ◽  
A. M. Zenkour ◽  
D. S. Mashat
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Transverse Displacement ◽  
Laminated Shells ◽  
Radial Basis

The static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to Murakami’s zig-zag (ZZ) function (MZZF) theory . The MZZF theory accounts for through-the-thickness deformation, by considering a ZZ evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions.

Dynamic analysis of a microelectromechanical systems resonant gyroscope excited using combination parametric resonance

2006 ◽  
Vol 220 (9) ◽  
pp. 1463-1479 ◽  
Author(s):  
B J Gallacher ◽  
J S Burdess
Keyword(s):  
Perturbation Analysis ◽  
Parametric Excitation ◽  
Microelectromechanical Systems ◽  
Equations Of Motion ◽  
Multiple Time ◽  
Excitation Scheme ◽  
Electrostatically Actuated ◽  
Modes Of Vibration ◽  
The Stability ◽  
Electrostatic Coupling

This paper investigates the application of parametric excitation to a resonant microelectromechanical systems (MEMS) gyroscope. The modal equations of motion of an electrostatically actuated ring are derived and shown to be coupled via the electrostatic stiffness. Such electrostatic coupling between in-plane modes of vibration permits parametric instabilities that may be exploited in a novel excitation scheme. A multiple time scale perturbation method is used to analyse the response of the ring gyroscope to the combination parametric excitations with the principal objective of separating the drive and response frequencies of the ring gyroscope. As pairs of flexural modes of the perfect ring are degenerate, the combination excitation between distinct modes demand the ring to be analysed as a four degree of freedom system. Slight mis-tuning between the otherwise degenerate modes is incorporated in the perturbation analysis. The results of the perturbation analysis are subsequently used to determine the stability boundaries for a typical ring gyroscope when excited using a sum combination resonance between the flexural modes of order 2 and 5. In this case, the ratio of the drive and response frequencies is approximately 10:1. Drive and sense configurations that enable effective parametric excitation of a desired mode are investigated. Simulation of the oscillator scheme is achieved using MATLAB Simulink and this validates the perturbation analysis. Agreement between the models within 10 per cent is demonstrated.

Active Vibration Control of Smart Hull Structure Using Piezoelectric Composite Actuators

2008 ◽  
Vol 47-50 ◽  
pp. 137-140 ◽  
Author(s):  
Jung Woo Sohn ◽  
Seung Bok Choi
Keyword(s):  
Vibration Control ◽  
Fiber Composite ◽  
Equations Of Motion ◽  
Active Vibration Control ◽  
Piezoelectric Composite ◽  
Governing Equations ◽  
Linear Quadratic ◽  
Element Analysis ◽  
Hull Structure ◽  
Active Vibration

In this paper, active vibration control performance of the smart hull structure with Macro-Fiber Composite (MFC) is evaluated. The governing equations of motion of the hull structure with MFC actuators are derived based on the classical Donnell-Mushtari shell theory. Subsequently, modal characteristics are investigated and compared with the results obtained from finite element analysis and experiment. The governing equations of vibration control system are then established and expressed in the state space form. Linear Quadratic Gaussian (LQG) control algorithm is designed in order to effectively and actively control the imposed vibration. The controller is experimentally realized and control performances are evaluated.

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