Active Mode Localization in Distributed Parameter Systems with Consideration of Limited Actuator Placement, Part 2: Simulations and Experiments

1995 ◽  
Vol 122 (2) ◽  
pp. 165-168 ◽  
Author(s):  
F. J. Shelley ◽  
W. W. Clark
Keyword(s):  
Vibration Isolation ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Limiting Factor ◽  
Parameter System ◽  
Sensors And Actuators ◽  
Mode Localization ◽  
Active Mode ◽  
Shaping Technique ◽  
Actuator Placement

The purpose of this two-part work is to apply active mode localization techniques to distributed parameter systems where control actuator and sensor placement is a limiting factor. In this paper, Part 2 of the study, the SVD eigenvector shaping technique examined in Part 1 is utilized to numerically and experimentally localize the response of a simply supported beam. This is done for two reasons. First, it demonstrates the application of this modified mode localization technique to a distributed parameter system. Second, it shows that it is possible to use this method to produce vibration isolation, reducing the absolute displacements in designated portions of the system while simultaneously curtailing the number of necessary control sensors and actuators. [S0739-3717(00)70302-3]

Active Mode Localization in Distributed Parameter Systems with Consideration of Limited Actuator Placement, Part 1: Theory

1995 ◽  
Vol 122 (2) ◽  
pp. 160-164 ◽  
Author(s):  
Franz J. Shelley ◽  
William W. Clark
Keyword(s):  
Distributed Parameter Systems ◽  
Theoretical Development ◽  
Distributed Parameter ◽  
Limiting Factor ◽  
Sensors And Actuators ◽  
Mode Localization ◽  
Active Mode ◽  
Value Decomposition ◽  
Actuator Placement ◽  
Do So

The purpose of this two-part work is to apply active mode localization to distributed parameter systems where the number of control sensors and actuators is a limiting factor. In this part, the theoretical development portion of the study, two approaches are presented that shape system eigenvectors using feedback control, generating localization to produce areas of isolation with relatively low vibration amplitudes compared to other parts of the structure. The first approach uniformly shapes all eigenvectors of a vibrating system, but can require many actuators to do so. The second more general approach uses singular value decomposition (SVD) to shape selected eigenvectors of a system, localizing the response of these modes to any disturbance, and requiring few actuators. [S0739-3717(00)70202-9]

Active Mode Localization in Distributed Parameter Systems With Consideration of Limited Actuator Placement

1995 ◽  
Author(s):  
Franz J. Shelley ◽  
William W. Clark
Keyword(s):  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Limiting Factor ◽  
Beam Model ◽  
Sensors And Actuators ◽  
Lower Mode ◽  
Mode Localization ◽  
Active Mode ◽  
Value Decomposition ◽  
Actuator Placement

Abstract The purpose of this work is to investigate the application of active mode localization to discretized models of distributed parameter systems where the number of control sensors and actuators is a limiting factor. A modified eigenvector scaling technique using singular value decomposition is developed which scales the lower-mode eigenvectors, producing localization over the range of these lower natural frequencies. An example using a simply supported beam model is provided, with mode localization achieved in at least the lower 3 modes utilizing as few as two control sensor/actuator pairs.

Transfer Function Formulation of Constrained Distributed Parameter Systems, Part II: Applications

1993 ◽  
Vol 60 (4) ◽  
pp. 1012-1019 ◽  
Author(s):  
C. H. Chung ◽  
C. A. Tan
Keyword(s):  
Transfer Function ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Displacement Method ◽  
Mode Localization ◽  
Function Formulation ◽  
Free Beam ◽  
Symmetric Systems

In this paper, the application of the transfer function formulation and the generalized displacement method (GDM) to the analysis of constrained distributed parameter systems is illustrated. Two kinds of classical examples are considered. In the constrained free-free beam example, it is shown how the GDM gives the eigensolutions without requiring knowledge of the normal modes of the unconstrained beam. In the string on a partial elastic foundation example, mode localization and eigenvalue loci veering phenomena are examined. It is shown that mode localizaation can occur in spatially symmetric systems and for modes whose frequency loci do not veer.

Distributed Transfer Function Analysis of Complex Distributed Parameter Systems

1994 ◽  
Vol 61 (1) ◽  
pp. 84-92 ◽  
Author(s):  
B. Yang
Keyword(s):  
Closed Form ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Force Balance ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Lumped Parameter ◽  
Space Technique ◽  
Transfer Function Analysis

This paper presents a new analytical and numerical method for modeling and synthesis of complex distributed parameter systems that are multiple continua combined with lumped parameter systems. In the analysis, the complex distributed parameter system is first divided into a number of subsystems; the distributed transfer functions of each subsystem are determined in exact and closed form by a state space technique. The complex distributed parameter system is then assembled by imposing displacement compatibility and force balance at the nodes where the subsystems are interconnected. With the distributed transfer functions and the transfer functions of the constraints and lumped parameter systems, exact, closed-form formulation is obtained for various dynamics and vibration problems. The method does not require a knowledge of system eigensolutions, and is valid for non-self-adjoint systems with inhomogeneous boundary conditions. In addition, the proposed method is convenient in computer coding and suitable for computerized symbolic manipulation.

scholarly journals Reliability index of distributed parameter system

2000 ◽  
Vol 22 (4) ◽  
pp. 248-256
Author(s):  
Nguyen Van Pho
Keyword(s):  
Reliability Index ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Dependent Probability

In this paper, a method to determine the reliability index of distributed parameter systems by using a method of approximation the multi-condition dependent probability by a one-condition dependent probability is proposed. Therefore, the problem of the reliability index of distributed parameter system is transformed into the defined case. To illustrate for the method, the reliability index of air tube is considered.

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