scholarly journals A Transfer-Matrix-Perturbation Approach to the Dynamics of Chains of Nonlinear Sliding Beams

2005 ◽  
Vol 128 (2) ◽  
pp. 190-196 ◽  
Author(s):  
Angelo Luongo ◽  
Francesco Romeo
Keyword(s):  
Transfer Matrix ◽  
Harmonic Balance Method ◽  
The State ◽  
Single Element ◽  
Perturbation Approach ◽  
Matrix Perturbation ◽  
State Variables ◽  
Field Equations ◽  
Axial Forces ◽  
Nonlinear Shear

Chains of nonlinear shear indeformable beams with distributed mass, resting on movable supports, are considered. To determine the dynamic response of the system, the transfer-matrix approach is merged with the harmonic balance method and a perturbation method, thereby transforming the original space-temporal continuous problem into a discrete one-dimensional map xk+1=F(xk) expressed in terms of the state variables xk at the interface between adjacent beams. Such transformation does not imply any discretization, because it is obtained by integrating the single-element field equations. The state variables consist of both first-order variables, namely, transversal displacement and couples, and second-order variables, which are longitudinal displacement and axial forces. Therefore, while the linear problem is monocoupled, the nonlinear one becomes multicoupled. The procedure is applied to determine frequency-response relationship under free and forced vibrations.

scholarly journals Measurement of Transfer Matrices and Source Terms of Premixed Flames

1999 ◽  
Author(s):  
Christian Oliver Paschereit ◽  
Bruno Schuermans ◽  
Wolfgang Polifke ◽  
Oscar Mattson
Keyword(s):  
Gas Turbine ◽  
Transfer Matrix ◽  
Acoustic Waves ◽  
Combustion Process ◽  
The State ◽  
Acoustic Properties ◽  
Analytical Models ◽  
State Variables ◽  
Thermoacoustic Properties ◽  
Gas Turbine Burner

An experimental method to determine the thermoacoustic properties of a gas turbine combustor using a lean-premixed low emission swirl stabilized burner is presented. To model thermoacoustic oscillations, a combustion system can be described as a network of acoustic elements, representing for example fuel and air supply, burner and flame, combustor, cooling channels, suitable terminations, etc. For most of these elements, simple analytical models provide an adequate description of their thermoacoustic properties. However, the complex response of burner and flame (involving a three-dimensional flow field, recirculation zones, flow instabilities and heat release) to acoustic perturbations has — at least in a first step — to be determined by experiment. In our approach, we describe the burner as an active acoustical two-port, where the state variables pressure and velocity at the inlet and the outlet of the two port are coupled via a four element transfer matrix. This approach is similar to the “black box” theory in communication engineering. To determine all four transfer matrix coefficients, two test states, which are independent in the state vectors, have to be created. This is achieved by using acoustic excitation by loudspeakers upstream and downstream of the burner, respectively. In addition, the burner might act as an acoustic source, emitting acoustic waves due to an unsteady combustion process. The source characteristics were determined by using a third test state, which again must be independent from the two other state vectors. In application to a full size gas turbine burner, the method’s accuracy was tested in a first step without combustion and the results were compared to an analytical model for the burner’s acoustic properties. Then the method was used to determine the burner transfer matrix with combustion. An experimental swirl stabilized premixed gas-turbine burner was used for this purpose. The treatment of burners as acoustic two-ports with feedback including a source term and the experimental determination of the burner transfer matrix is novel.

scholarly journals Measurement of Transfer Matrices and Source Terms of Premixed Flames

2002 ◽  
Vol 124 (2) ◽  
pp. 239-247 ◽  
Author(s):  
C. O. Paschereit ◽  
B. Schuermans ◽  
W. Polifke ◽  
O. Mattson
Keyword(s):  
Gas Turbine ◽  
Transfer Matrix ◽  
Acoustic Waves ◽  
Combustion Process ◽  
The State ◽  
Acoustic Properties ◽  
Analytical Models ◽  
State Variables ◽  
Thermoacoustic Properties ◽  
Gas Turbine Burner

An experimental method to determine the thermoacoustic properties of a gas turbine combustor using a lean-premixed low emission swirl stabilized burner is presented. To model thermoacoustic oscillations, a combustion system can be described as a network of acoustic elements, representing for example fuel and air supply, burner and flame, combustor, cooling channels, suitable terminations, etc. For most of these elements, simple analytical models provide an adequate description of their thermoacoustic properties. However, the complex response of burner and flame (involving a three-dimensional flow field, recirculation zones, flow instabilities, and heat release) to acoustic perturbations has—at least in a first step—to be determined by experiment. In our approach, we describe the burner as an active acoustical two-port, where the state variables pressure and velocity at the inlet and the outlet of the two port are coupled via a four element transfer matrix. This approach is similar to the “black box” theory in communication engineering. To determine all four transfer matrix coefficients, two test states, which are independent in the state vectors, have to be created. This is achieved by using acoustic excitation by loudspeakers upstream and downstream of the burner, respectively. In addition, the burner might act as an acoustic source, emitting acoustic waves due to an unsteady combustion process. The source characteristics were determined by using a third test state, which again must be independent from the two other state vectors. In application to a full size gas turbine burner, the method’s accuracy was tested in a first step without combustion and the results were compared to an analytical model for the burner’s acoustic properties. Then the method was used to determine the burner transfer matrix with combustion. An experimental swirl stabilized premixed gas turbine burner was used for this purpose. The treatment of burners as acoustic two-ports with feedback including a source term and the experimental determination of the burner transfer matrix is novel.

Damaged Structural Vibration Analysis Using the Hamiltonian Matrix Perturbation Theory

2008 ◽  
Vol 44-46 ◽  
pp. 91-96
Author(s):  
Long Liu ◽  
Fu Zhen Xuan
Keyword(s):  
Numerical Simulation ◽  
Perturbation Theory ◽  
Vibration Analysis ◽  
Structural Vibration ◽  
Hamiltonian Matrix ◽  
Perturbation Approach ◽  
Matrix Perturbation ◽  
State Variables ◽  
Matrix Perturbation Theory ◽  
Orthogonal Relation

This paper proposes a Hamiltonian perturbation approach for analyzing the dynamic characteristics of the damaged structure. Firstly, structural vibration governing equation is transformed to the general expression of state variables composed of displacement and momentum. On the basis of the conjugate symplectic orthogonal relation, the first-, and second- order perturbation expression of the damaged structural eigensolution are obtained. Finally, the numerical simulation and cantilever experiment prove the effectiveness of this approach.

Non Linear State and Parameters Estimation in Chemical Processes: Analysis and Improvement of Three Estimation Structures Applied to a CSTR

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Héctor Botero ◽  
Hernán Álvarez
Keyword(s):  
Parameter Estimation ◽  
Chemical Process ◽  
Chemical Processes ◽  
The State ◽  
Convergence Speed ◽  
Parameters Estimation ◽  
State Variables ◽  
Input Output ◽  
On Line ◽  
Linear State

This paper proposes a new composite observer capable of estimating the states and unknown (or changing) parameters of a chemical process, using some input-output measurements, the phenomenological based model and other available knowledge about the process. The proposed composite observer contains a classic observer (CO) to estimate the state variables, an observer-based estimator (OBE) to obtain the actual values of the unknown or changing parameters needed to tune the CO, and an asymptotic observer (AO) to estimate the states needed as input to the OBE. The proposed structure was applied to a CSTR model with three state variables. With the proposed structure, the concentration of reactants and other CSTR parameters can be estimated on-line if the reactor and jacket temperatures are known. The procedure for the design of the proposed structure is simple and guarantees observer convergence. In addition, the convergence speed of state and parameter estimation can be adjusted independently.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

scholarly journals Exploring the Limits of Floating-Point Resolution for Hardware-In-the-Loop Implemented with FPGAs

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 219 ◽  
Author(s):  
Alberto Sanchez ◽  
Elías Todorovich ◽  
Angel de Castro
Keyword(s):  
The State ◽  
Floating Point ◽  
Hardware In The Loop ◽  
State Variables ◽  
Numerical Resolution ◽  
Digital Devices ◽  
State Variable ◽  
Simulation Step ◽  
Field Programmable ◽  
The Difference

As the performance of digital devices is improving, Hardware-In-the-Loop (HIL) techniques are being increasingly used. HIL systems are frequently implemented using FPGAs (Field Programmable Gate Array) as they allow faster calculations and therefore smaller simulation steps. As the simulation step is reduced, the incremental values for the state variables are reduced proportionally, increasing the difference between the current value of the state variable and its increments. This difference can lead to numerical resolution issues when both magnitudes cannot be stored simultaneously in the state variable. FPGA-based HIL systems generally use 32-bit floating-point due to hardware and timing restrictions but they may suffer from these resolution problems. This paper explores the limits of 32-bit floating-point arithmetics in the context of hardware-in-the-loop systems, and how a larger format can be used to avoid resolution problems. The consequences in terms of hardware resources and running frequency are also explored. Although the conclusions reached in this work can be applied to any digital device, they can be directly used in the field of FPGAs, where the designer can easily use custom floating-point arithmetics.

Observability and Estimation Error Analysis of the Initial Fine Alignment Filter for Nonleveling Strapdown Inertial Navigation System

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Seong Yun Cho ◽  
Hyung Keun Lee ◽  
Hung Kyu Lee
Keyword(s):  
Navigation System ◽  
Inertial Navigation System ◽  
Inertial Navigation ◽  
Strapdown Inertial Navigation System ◽  
The State ◽  
State Model ◽  
Low Grade ◽  
State Variables ◽  
Estimation Errors ◽  
Strapdown Inertial Navigation

In this paper, performance of the initial fine alignment for the stationary nonleveling strapdown inertial navigation system (SDINS) containing low-grade gyros is analyzed. First, the observability is analyzed by conducting a rank test of an observability matrix and by investigating the normalized error covariance of the extended Kalman filter based on the ten-state model. The results show that the accelerometer biases on horizontal axes are unobservable. Second, the steady-state estimation errors of the state variables are derived using the observability equation. It is verified that the estimates of the state variables have errors due to the unobservable state variables and nonleveling attitude angles of a vehicle containing the SDINS. Especially, this paper shows that the larger the attitude angles of the vehicle are, the greater the estimation errors are. Finally, it is shown that the performance of the eight-state model excluding the two unobservable state variables is better than that of the ten-state model in the fine alignment by a Monte Carlo simulation.

A Modified Transfer Matrix Method for Asymmetric Rotor-Bearing Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 309-317 ◽  
Author(s):  
Yuan Kang ◽  
An-Chen Lee ◽  
Yuan-Pin Shih
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Harmonic Balance Method ◽  
Continuous System ◽  
Euler Beam ◽  
Rotating Shaft ◽  
Rotor Bearing ◽  
Asymmetric Rotor ◽  
Steady State Responses

A modified transfer matrix method (MTMM) is developed to analyze rotor-bearing systems with an asymmetric shaft and asymmetric disks. The rotating shaft is modeled by a Rayleigh-Euler beam considering the effects of the rotary inertia and gyroscopic moments. Specifically, a transfer matrix of the asymmetric shaft segments is derived in a continuous-system sense to give accurate solutions. The harmonic balance method is incorporated in the transfer matrix equations, so that steady-state responses of synchronous and superharmonic whirls can be determined. A numerical example is presented to demonstrate the effectiveness of this approach.

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