Distributed Transfer Function Synthesis of Complex Flexible Systems

1993 ◽  
Author(s):  
Bingen Yang
Keyword(s):  
Closed Form ◽  
Transfer Functions ◽  
Force Balance ◽  
Flexible Systems ◽  
Adjoint Systems ◽  
Lumped Parameter ◽  
Space Technique ◽  
Vibration Problems ◽  
Distributed Transfer Function ◽  
Dynamics And Vibration

Abstract This paper presents a new analytical and numerical method for modeling and synthesis of complex flexible systems (CFS) that are multiple continua combined with lumped parameter systems. In the analysis, the CFS 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 CFS 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.

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.

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

Jerk Limited Input Shapers

2004 ◽  
Vol 126 (1) ◽  
pp. 215-219 ◽  
Author(s):  
Tarunraj Singh
Keyword(s):  
Time Delay ◽  
Closed Form ◽  
Transfer Functions ◽  
Filter Design ◽  
Limited Time ◽  
Design Technique ◽  
Closed Form Solutions ◽  
First Order ◽  
Damped Systems

The focus of this paper is on the design of jerk limited input shapers (time-delay filters). Closed form solutions for the jerk limited time-delay filter for undamped systems is derived followed by the formulation of the problem for damped systems. Since the jerk limited filter involves concatenating an integrator to a time-delay filter, a general filter design technique is proposed where smoothing of the shaped input can be achieved by concatenating transfer functions of first order, harmonic systems, etc.

Synchronous Rotor Vibration Driven by Fluid Forces From a Geometrically Imperfect Labyrinth Seal

1995 ◽  
Author(s):  
Knox T. Millsaps ◽  
William C. Williston
Keyword(s):  
Labyrinth Seal ◽  
Radial Force ◽  
Lumped Parameter Model ◽  
Solution Technique ◽  
Labyrinth Seals ◽  
Fluid Forces ◽  
Lumped Parameter ◽  
Manufacturing Tolerances ◽  
Vibration Problems ◽  
Wear Damage

The radial force acting on a rotor, due to an asymmetric pressure distribution inside the seal gland, generated from a slightly non-circular single gland labyrinth seal rotating inside a circular outer casing is investigated theoretically. A fluid mechanical lumped parameter model for the flow in and out of the seal as well as the flow around the gland in the seal is developed. The model includes first and second knife imperfections as well as rotating gland depth variations. Knife non-circularity on the rotor may be due to manufacturing tolerances or defects from in service wear damage. An appropriate solution technique for the coupled one-dimensional equations is presented. Results from this model are presented that indicate these fluid induced forces are comparable in magnitude to those generated by a rotating unbalance under some conditions. Considerations for design are given for avoiding synchronous vibration problems due to non-circular labyrinth seals.

scholarly journals Generalized Schur–Nevanlinna functions and their realizations

2020 ◽  
Vol 92 (5) ◽  
Author(s):  
Lassi Lilleberg
Keyword(s):  
Transfer Functions ◽  
Schur Functions ◽  
Inner Function ◽  
Pontryagin Space ◽  
State Spaces ◽  
Limit Values ◽  
Adjoint Systems ◽  
Generalized Schur Functions ◽  
Nevanlinna Functions ◽  
Weak Similarity

Abstract Pontryagin space operator valued generalized Schur functions and generalized Nevanlinna functions are investigated by using discrete-time systems, or operator colligations, and state space realizations. It is shown that generalized Schur functions have strong radial limit values almost everywhere on the unit circle. These limit values are contractive with respect to the indefinite inner product, which allows one to generalize the notion of an inner function to Pontryagin space operator valued setting. Transfer functions of self-adjoint systems such that their state spaces are Pontryagin spaces, are generalized Nevanlinna functions, and symmetric generalized Schur functions can be realized as transfer functions of self-adjoint systems with Kreĭn spaces as state spaces. A criterion when a symmetric generalized Schur function is also a generalized Nevanlinna function is given. The criterion involves the negative index of the weak similarity mapping between an optimal minimal realization and its dual. In the special case corresponding to the generalization of an inner function, a concrete model for the weak similarity mapping can be obtained by using the canonical realizations.

Port-Based Modeling of Distributed-Lumped Parameter Systems

2010 ◽  
Vol 164 ◽  
pp. 183-188
Author(s):  
Cezary Orlikowski ◽  
Rafał Hein
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
Distributed System ◽  
Function Method ◽  
Input Data ◽  
Distributed Parameter ◽  
Transfer Function Method ◽  
Lumped Parameter ◽  
Concise Representation ◽  
Distributed Transfer Function

This paper presents a uniform, port-based approach for modeling of both lumped and distributed parameter systems. Port-based model of the distributed system has been defined by application of bond graph methodology and distributed transfer function method (DTFM). The proposed approach combines versatility of port-based modeling and accuracy of distributed transfer function method. A concise representation of lumped-distributed systems has been obtained. The proposed method of modeling enables to formulate input data for computer analysis by application of DTFM.

Development of an Experimental Method to Estimate the Operating Force of a Hand-Held Power Tool Utilizing Measured Transfer Functions

2013 ◽  
Author(s):  
Alvin Lim ◽  
Jay Kim ◽  
Edward Zechmann
Keyword(s):  
Experimental Method ◽  
Prolonged Exposure ◽  
Transfer Functions ◽  
Work Piece ◽  
Basic Information ◽  
Vibration Syndrome ◽  
Input Point ◽  
Circular Saw ◽  
Tool Force ◽  
Vibration Problems

Hand-arm vibration syndrome (HAVS) collectively refers to diseases caused by prolonged exposure to intensive hand-transmitted vibration, which has been affecting millions of workers who use hand-held power tools. The force interacting between a hand-held power tool and the work-piece is valuable basic information in studying hand-arm vibration problems, however cannot be measured directly. An experimental method is developed to estimate this tool force by utilizing the input point impedance of the hand and measured transfer functions of the tool. The developed method is applied to calculate the tool force of a hand-held grinder and a circular saw to demonstrate and validate the method. Possible applications of the method to study hand-arm vibration or tool design are explained.

Transfer Functions of One-Dimensional Distributed Parameter Systems

1992 ◽  
Vol 59 (4) ◽  
pp. 1009-1014 ◽  
Author(s):  
B. Yang ◽  
C. A. Tan
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Axially Moving Beam ◽  
System Response ◽  
Distributed Parameter ◽  
One Dimensional ◽  
Adjoint Systems ◽  
The Laplace Transform ◽  
Axially Moving

Distributed parameter systems describe many important physical processes. The transfer function of a distributed parameter system contains all information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. This paper presents a new method for evaluating transfer functions for a class of one-dimensional distributed parameter systems. The system equations are cast into a matrix form in the Laplace transform domain. Through determination of a fundamental matrix, the system transfer function is precisely evaluated in closed form. The method proposed is valid for both self-adjoint and non-self-adjoint systems, and is extremely convenient in computer coding. The method is applied to a damped, axially moving beam with different boundary conditions.

Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)

2003 ◽  
Vol 125 (3) ◽  
pp. 398-405 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Optimization Problem ◽  
Vibration Suppression ◽  
Transfer Functions ◽  
New Method ◽  
Algebraic Solution ◽  
Vibration Absorbers ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

H ∞ optimization of the dynamic vibration absorbers is a classical optimization problem, and has been already solved more than 50 years ago. It is a well-known solution, but we know this solution is only an approximate one. Recently, one of the authors has proposed a new method for attaining the H∞ optimization of the absorber in linear systems. The new method enables us to obtain the exact algebraic solution of the H∞ optimization problem of the absorber. In this paper, we first apply this method to the design optimization of a viscous damped (Voigt type) absorber and a hysteretic damped absorber attached to undamped primary systems. For each absorber, six different transfer functions are taken here as performance indices to vibration suppression or isolation. As a result, we found the closed-form exact solutions to all transfer functions. The solutions obtained here are then compared with those of the approximate ones. Finally, we present the closed-form exact solutions to the hysteretic damped absorber attached to damped primary systems.

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