Computer-Aided Nonlinear Frequency Response Method for Investigating the Dynamics of Chemical Engineering Systems

The Nonlinear Frequency Response (NFR) method is a useful Process Systems Engineering tool for developing experimental techniques and periodic processes that exploit the system nonlinearity. The basic and most time-consuming step of the NFR method is the derivation of frequency response functions (FRFs). The computer-aided Nonlinear Frequency Response (cNFR) method, presented in this work, uses a software application for automatic derivation of the FRFs, thus making the NFR analysis much simpler, even for systems with complex dynamics. The cNFR application uses an Excel user-friendly interface for defining the model equations and variables, and MATLAB code which performs analytical derivations. As a result, the cNFR application generates MATLAB files containing the derived FRFs in a symbolic and algebraic vector form. In this paper, the software is explained in detail and illustrated through: (1) analysis of periodic operation of an isothermal continuous stirred-tank reactor with a simple reaction mechanism, and (2) experimental identification of electrochemical oxygen reduction reaction.

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Rapid Multi-Objective Optimization of Periodically Operated Processes Based on the Computer-Aided Nonlinear Frequency Response Method

Processes ◽

10.3390/pr8111357 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1357

Author(s):

Luka A. Živković ◽

Viktor Milić ◽

Tanja Vidaković-Koch ◽

Menka Petkovska

Keyword(s):

Steady State ◽

Frequency Response ◽

Dynamic Optimization ◽

Nonlinear Frequency ◽

Multi Objective Optimization ◽

Periodic Operation ◽

Multi Objective ◽

Computer Aided ◽

State Point ◽

Nonlinear Frequency Response

The dynamic optimization of promising forced periodic processes has always been limited by time-consuming and expensive numerical calculations. The Nonlinear Frequency Response (NFR) method removes these limitations by providing excellent estimates of any process performance criteria of interest. Recently, the NFR method evolved to the computer-aided NFR method (cNFR) through a user-friendly software application for the automatic derivation of the functions necessary to estimate process improvement. By combining the cNFR method with standard multi-objective optimization (MOO) techniques, we developed a unique cNFR–MOO methodology for the optimization of periodic operations in the frequency domain. Since the objective functions are defined with entirely algebraic expressions, the dynamic optimization of forced periodic operations is extraordinarily fast. All optimization parameters, i.e., the steady-state point and the forcing parameters (frequency, amplitudes, and phase difference), are determined rapidly in one step. This gives the ability to find an optimal periodic operation around a sub-optimal steady-state point. The cNFR–MOO methodology was applied to two examples and is shown as an efficient and powerful tool for finding the best forced periodic operation. In both examples, the cNFR–MOO methodology gave conditions that could greatly enhance a process that is normally operated in a steady state.

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Evaluation of Electrochemical Process Improvement Using the Computer-Aided Nonlinear Frequency Response Method: Oxygen Reduction Reaction in Alkaline Media

Frontiers in Chemistry ◽

10.3389/fchem.2020.579869 ◽

2020 ◽

Vol 8 ◽

Author(s):

Luka A. Živković ◽

Saikrishnan Kandaswamy ◽

Menka Petkovska ◽

Tanja Vidaković-Koch

Keyword(s):

Oxygen Reduction Reaction ◽

Process Improvement ◽

Reduction Reaction ◽

Electrochemical Process ◽

Alkaline Media ◽

Nonlinear Frequency ◽

Computer Aided ◽

Nonlinear Frequency Response ◽

Frequency Response Method ◽

Response Method

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Study of plate vibrating in fluids having part-through crack at random angles and locations

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/09544062211012717 ◽

2021 ◽

pp. 095440622110127

Author(s):

Ruqia Ikram ◽

Asif Israr

Keyword(s):

Frequency Response ◽

Multiple Scales ◽

Peak Amplitude ◽

Nonlinear Frequency ◽

Response Curves ◽

Crack Location ◽

Cracked Plate ◽

Nonlinear Frequency Response ◽

Angle Crack ◽

Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

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