Free Response and Absolute Vibration Suppression of Second-Order Flexible Structures—The Traveling Wave Approach

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Lea Sirota ◽  
Yoram Halevi
Keyword(s):  
Traveling Wave ◽  
Tracking Control ◽  
Vibration Suppression ◽  
Initial Conditions ◽  
Flexible Structures ◽  
Linear Boundary ◽  
Free Response ◽  
Flexible System ◽  
Propagating Waves ◽  
General Linear Boundary Conditions

The paper considers the problem of suppressing the free vibration, induced by nonzero initial conditions, in a flexible system governed by the wave equation. First an exact response of the system, with general linear boundary conditions, is derived in terms of propagating waves that are reflected from the boundaries. The solution is explicit and with clear physical interpretation. The general expressions for the response are then used to investigate the behavior of the system under control with the absolute vibration suppression controller, which was originally designed for tracking control. It is shown that the vibration suppression properties of this controller apply also to nonzero initial conditions. In cases where the load end is free or contains only damping, the vibration stops completely in finite time and if it contains only inertia and damping it decays exponentially without vibration.

Vibration Suppression of Flexible Structures Using the Infinite Dimensional Laplace Domain Approach

2008 ◽  
Author(s):  
Lea Sirota ◽  
Irit Peled ◽  
Yoram Halevi
Keyword(s):  
Vibration Suppression ◽  
Flexible Structures ◽  
Laplace Domain ◽  
Infinite Dimensional ◽  
Flexible System ◽  
Dimensional Modeling ◽  
Propagating Waves ◽  
The Absolute ◽  
General Conditions

The problem of obtaining an explicit, exact response of a flexible system to initial distributed input in infinite dimensional modeling is considered. The paper proposes a method to present the response in terms of propagating waves that are reflected from boundaries with general conditions. The result is then examined under control with the absolute vibration suppression (AVS) controller, which was originally designed for a concentrated input. It is shown that the vibration suppression properties of this controller are extended to systems with distributed input.

Modal Representation of Second Order Flexible Structures With Damped Boundaries

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Lea Sirota ◽  
Yoram Halevi
Keyword(s):  
Initial Conditions ◽  
Separation Of Variables ◽  
Complete Solution ◽  
Flexible Structures ◽  
Second Order ◽  
Free Response ◽  
Laplace Domain ◽  
Boundary Case ◽  
Sum Of Products ◽  
Infinite Sum

The problem of obtaining a modal (i.e., infinite series) solution of second order flexible structures with viscous damping boundary conditions is considered. In conservative boundary systems, separation of variables is well established and there exist closed form modal solutions. However, no counterpart results exist for the damped boundary case and previous publications fall short of providing a complete solution for the series, in particular, its coefficients. The paper presents the free response of damped boundary structures to general initial conditions in the form of an infinite sum of products of spatial and time functions. The problem is attended via Laplace domain approach, and explicit expressions for the series components and coefficients are derived. The modal approach is useful in finite dimension modeling, since it provides a convenient framework for truncation. It is shown via examples that often few modes suffice for approximation with good accuracy.

Vibration Reduction of Flexible Structures Using Extended Input Shaper and Smart Materials

2001 ◽  
Author(s):  
G. Song ◽  
B. Kotejoshyer ◽  
J. Fei
Keyword(s):  
Smart Materials ◽  
Vibration Suppression ◽  
Flexible Structures ◽  
Flexible Beam ◽  
Smart Sensor ◽  
New Approach ◽  
Active Vibration Suppression ◽  
Command Input ◽  
Active Vibration ◽  
Smart Actuator

Abstract This paper presents a new approach of integrating the method of command input shaping and the technique of active vibration suppression for vibration reduction of flexible structures during slew operations. The control object is a flexible composite beam driven by a high torque DC motor with the presence of nonlinearities such as backlash and stick-slip type of friction. Two piezoelectric patches are bonded on the surface of the flexible beam near its cantilevered end and are used as the smart actuator and the smart sensor respectively. In this new approach, the method of command input shaping is used to modify the existing command so that less vibration will be caused by the command itself. To overcome the nonlinearities associated with the DC motor, an extended shaper is designed. The technique of active vibration suppression using smart materials is used to actively control the vibration during and after the slew. With this pair of smart actuator and smart sensor, a strain rate feedback (SRF) controller is designed for active vibration suppression. With the extended Zero Vibration Derivative (ZVD) shaper and the SRF controller, the proposed new approach can effectively reduce the vibration of the flexible beam during slew operations.

Vibration suppression for large-scale flexible structures based on cable-driven parallel robots

2020 ◽  
pp. 107754632096194
Author(s):  
Haining Sun ◽  
Xiaoqiang Tang ◽  
Senhao Hou ◽  
Xiaoyu Wang
Keyword(s):  
Large Scale ◽  
Vibration Suppression ◽  
Control Method ◽  
External Disturbance ◽  
Flexible Structures ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Lyapunov Theory ◽  
Normal Operation ◽  
Control Methods

Specific satellites with ultralong wings play a crucial role in many fields. However, external disturbance and self-rotation could result in undesired vibrations of the flexible wings, which affect the normal operation of the satellites. In severe cases, the satellites would be damaged. Therefore, it is imperative to conduct vibration suppression for these flexible structures. Utilizing fuzzy-proportional integral derivative control and deep reinforcement learning (DRL), two active control methods are proposed in this article to rapidly suppress the vibration of flexible structures with quite small controllable force based on a cable-driven parallel robot. Inspired by the output law of DRL, a new control method named Tang and Sun control is innovatively presented based on the Lyapunov theory. To verify the effectiveness of these three control methods, three groups of simulations with different initial disturbances are implemented for each method. Besides, to enhance the contrast, a passive pretightening scheme is also tested. First, the dynamic model of the cable-driven parallel robot which comprises four cables and a flexible structure is established using the finite element method. Then, the dynamic behavior of the model under the controllable cable force is analyzed by the Newmark-ß method. Finally, these control methods are implemented by numerical simulations to evaluate their performance, and the results are satisfactory, which validates the controllers’ ability to suppress vibrations.

Watershed initial conditions for propagating waves in a system with bistability: A weight-function approach

2019 ◽  
Vol 91 ◽  
pp. 106-112
Author(s):  
S.D. Watt ◽  
H.S. Sidhu ◽  
Z. Jovanoski ◽  
I.N. Towers ◽  
Z. Huang
Keyword(s):  
Weight Function ◽  
Initial Conditions ◽  
Function Approach ◽  
Propagating Waves

Optimal Vibration Control of Membrane Structures with In-Plane Polyvinylidene Fluoride Actuators

2020 ◽  
Vol 20 (08) ◽  
pp. 2050095
Author(s):  
Yifan Lu ◽  
Qi Shao ◽  
Fei Yang ◽  
Honghao Yue ◽  
Rongqiang Liu
Keyword(s):  
Vibration Control ◽  
Polyvinylidene Fluoride ◽  
Vibration Suppression ◽  
Flexible Structures ◽  
Control Force ◽  
Membrane Structures ◽  
Optimization Criteria ◽  
High Flexibility ◽  
And Control ◽  
Actuator Placement

Different kinds of membrane structures have been proposed for future space exploration and earth observation. However, due to the low stiffness, high flexibility, and low damping properties, membrane structures are likely to generate large-amplitude (compared to the thickness) vibrations, which may lead to the degradation of their working performance. In this work, the governing equations are established at first, taking into account the modal control force induced by the polyvinylidene fluoride (PVDF) actuator. The optimal vibration control of the membrane structure is explored subsequently. A square PVDF actuator is attached on the membrane to achieve the vibration suppression. The influence of actuator position and control gains on the vibration control performance are studied. The optimal criteria for actuator placement and energy allocation are developed. Several case studies are numerically simulated to demonstrate the validity of the proposed optimization criteria. The analytical results in this study can serve as guidelines for optimal vibration control of membrane structures. Additionally, the proposed optimization criteria can be applied to active control of different flexible structures.

scholarly journals The Dynamic Response of Tuned Impact Absorbers for Rotating Flexible Structures

2005 ◽  
Vol 1 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Dynamic Response ◽  
Flexible Structures ◽  
Experimental Studies ◽  
Analytical Investigation ◽  
Design Parameters ◽  
System Response ◽  
Rotor Speed ◽  
Flexible System ◽  
Restoring Forces ◽  
And Performance

This paper describes an analytical investigation of the dynamic response and performance of impact vibration absorbers fitted to flexible structures that are attached to a rotating hub. This work was motivated by experimental studies at NASA, which demonstrated the effectiveness of these types of absorbers for reducing resonant transverse vibrations in periodically excited rotating plates. Here we show how an idealized model can be used to describe the essential dynamics of these systems, and used to predict absorber performance. The absorbers use centrifugally induced restoring forces so that their nonimpacting dynamics are tuned to a given order of rotation, whereas their large amplitude dynamics involve impacts with the primary flexible system. The linearized, nonimpacting dynamics are first explored in detail, and it is shown that the response of the system has some rather unique features as the hub rotor speed is varied. A class of symmetric impacting motions is also analyzed and used to predict the effectiveness of the absorber when operating in its impacting mode. It is observed that two different types of grazing bifurcations take place as the rotor speed is varied through resonance, and their influence on absorber performance is described. The analytical results for the symmetric impacting motions are also used to generate curves that show how important absorber design parameters—including mass, coefficient of restitution, and tuning—affect the system response. These results provide a method for quickly evaluating and comparing proposed absorber designs.

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