On the Dynamics of Large Systems With Localized Nonlinearities

1988 ◽  
Vol 55 (4) ◽  
pp. 946-951 ◽  
Author(s):  
P. Hagedorn ◽  
W. Schramm
Keyword(s):  
Integral Equation ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Dynamic System ◽  
Frequency Response ◽  
Time Domain ◽  
Numerical Procedure ◽  
Linear Subsystem ◽  
Large Systems ◽  
The Time Domain

In this paper, a certain class of dynamical systems is discussed, which can be decomposed into a large linear subsystem and one or more nonlinear subsystems. For this class of nonlinear systems the dynamic behavior is represented in the time domain by means of an integral equation. A simple numerical procedure for the solution of this integral equation is given. It is also shown how the decomposition of the system can be used in measuring the frequency response of the large linear subsystem, without actually separating it from the nonlinear subsystems. An elastostatic analogy is used to illustrate the ideas and a numerical example is given for a dynamic system.

Development of High Frequency Virtual Thermocouples

2017 ◽  
Author(s):  
James Braun ◽  
Shengqi Lu ◽  
Guillermo Paniagua
Keyword(s):  
Frequency Response ◽  
Time Domain ◽  
High Frequency ◽  
Conjugate Heat Transfer ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Digital Compensation ◽  
Fine Wire ◽  
The Time Domain ◽  
Thermocouple Probe

This paper presents a numerical procedure to enhance the frequency response of temperature probes equipped with two thermocouple junctions of different diameter. The output of the two thermocouples exposed to the same flow transient can be used to predict the output of a virtual smaller thermocouple, which cannot be physically realized. The approach is demonstrated numerically, with the aid of conjugate heat transfer simulations performed with 3D Unsteady Reynolds Averaged Navier-Stokes. The dual junction thermocouple with wire diameters of 50 μm, 25 μm were exposed to several inlet temperatures and pressures to analyze the overall recovery factor. Then multiple unsteady tests were performed. The analysis of those transient tests was used to determine the transfer function in the time domain between the two wires and to perform a digital compensation to predict the performance of a much thinner wire thermocouple. This method was assessed by recovering the theoretical response of the 12.5 μm thermocouple with our dual-junction thermocouple probe for several pressures and wall temperatures. Finally, the procedure was applied to a virtual fine wire thermocouple of 6 μm and a frequency response around 700 Hz.

scholarly journals Lightning Channel-Base Current Identification as Solution of a Volterralike Integral Equation

2008 ◽  
Vol 2 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Federico Delfino ◽  
Renato Procopio ◽  
Mansueto Rossi
Keyword(s):  
Integral Equation ◽  
Numerical Simulations ◽  
Time Domain ◽  
Measurement Noise ◽  
Induction Field ◽  
Base Current ◽  
Lightning Channel ◽  
Regularization Techniques ◽  
Ill Conditioning ◽  
The Time Domain

In this paper, a novel procedure to reconstruct the lightning channel-base current starting from the measurement of the induction field generated by it is presented. The procedure is based on a suitable mathematical manipulation of the equation expressing the induction field in the time domain, in order to transform it into a Volterra-like integral equation. Such kind of equations can be easily numerically solved without resorting to any sort of regularization techniques as they are not affected by the typical ill-conditioning of the inverse problems. The developed algorithm has been validated by means of several numerical simulations, which have shown its effectiveness also in presence of measurement noise on the induction field values.

scholarly journals Time-Domain Substructure Transient Vibration Transfer Path Analysis Based on Time-Varying Frequency Response Functions under Operational Excitations

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Rong He ◽  
Hong Zhou
Keyword(s):  
Path Analysis ◽  
Frequency Response ◽  
Time Domain ◽  
Time Varying ◽  
Response Functions ◽  
Transient Vibration ◽  
Transfer Path ◽  
Time Varying Systems ◽  
Transfer Path Analysis ◽  
The Time Domain

The time-domain substructure inverse matrix method has become a popular method to detect and diagnose problems regarding vehicle noise, vibration, and harshness, especially for those impulse excitations caused by roads. However, owning to its reliance on frequency response functions (FRFs), the approach is effective only for time-invariable linear or weak nonlinear systems. This limitation prevents this method from being applied to a typical vehicle suspension substructure, which shows different nonlinear characteristics under different wheel transient loads. In this study, operational excitation was considered as a key factor and applied to calculate dynamic time-varying FRFs to perform accurate time-domain transient vibration transfer path analysis (TPA). The core idea of this novel method is to divide whole coupled substructural relationships into two parts: one involved time-invariable components; normal FRFs could be obtained through tests directly. The other involved numerical computations of the time-domain operational loads matrix and FRFs matrix in static conditions. This method focused on determining dynamic FRFs affected by operational loads, especially the severe transient ones; these loads are difficult to be considered in other classical TPA approaches, such as operational path analysis with exogenous inputs (OPAX) and operational transfer path analysis (OTPA). Experimental results showed that this new approach could overcome the limitations of the traditional time-domain substructure TPA in terms of its strict requirements within time-invariable systems. This is because in the new method, time-varying FRFs were calculated and used, which could make the FRFs at the system level directly adapt to time-varying systems from time to time. In summary, the modified method extends TPA objects studied in time-invariable systems to time-varying systems and, thus, makes a methodology and application innovation compared to traditional the time-domain substructure TPA.

scholarly journals An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation

2019 ◽  
Vol 146 (3) ◽  
pp. 2068-2079 ◽  
Author(s):  
Rui Chen ◽  
Sadeed Bin Sayed ◽  
Noha Alharthi ◽  
David Keyes ◽  
Hakan Bagci
Keyword(s):  
Integral Equation ◽  
Time Domain ◽  
The Time Domain ◽  
Kirchhoff Integral
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