[Paper Review] Calculations of Frequency Response Functions (FRF) Using Computer Smart Office Software and Nyquist Plot under Gyroscopic Effect Rotation

Hisham A. H. Al-Khazali, Mohamad R. Askari|arXiv (Cornell University)|Aug 16, 2012

Structural Health Monitoring Techniques4 references3 citations

TL;DR

This paper proposes a novel method for calculating Frequency Response Functions (FRF) and analyzing their behavior under gyroscopic effects in rotating structures using common smart office software (e.g., Excel) and Nyquist plot visualization. The approach enables accurate FRF curve regeneration and synthesis without specialized simulation tools, demonstrating that standard office software can effectively model dynamic systems with gyroscopic coupling, offering a low-cost, accessible alternative for modal analysis in mechanical systems.

ABSTRACT

Regenerated (FRF curves), synthesis of (FRF) curves there are two main requirement in the form of response model, The first being that of regenerating "Theoretical" curve for the frequency response function actually measured and analysis and the second being that of synthesising the other functions which were not measured,(FRF) that isolates the inherent dynamic properties of a mechanical structure. Experimental modal parameters (frequency, damping, and mode shape) are also obtained from a set of (FRF) measurements. The (FRF) describes the input-output relationship between two points on a structure as a function of frequency. Therefore, an (FRF) is actually defined between a single input DOF (point & direction), and a single output (DOF), although the FRF was previously defined as a ratio of the Fourier transforms of an output and input signal. In this paper we detection FRF curve using Nyquist plot under gyroscopic effect in revolving structure using computer smart office software. Keywords - FRF curve; modal test; Nyquist plot; software engineering; gyroscopic effect; smart office.

Motivation & Objective

• To develop a low-cost, accessible method for calculating FRF curves in rotating mechanical systems using standard office software.
• To investigate the influence of gyroscopic effects on FRF behavior in rotating structures through Nyquist plot visualization.
• To enable regeneration and synthesis of FRF data from limited experimental measurements using computational tools available in smart office software.
• To provide a practical alternative to specialized simulation software for modal analysis in mechanical engineering applications.
• To demonstrate that common office software can accurately model complex dynamic systems with gyroscopic coupling.

Proposed method

• The authors use standard smart office software (e.g., Microsoft Excel) to perform numerical computations for FRF calculations.
• FRF data is generated based on theoretical models of mechanical structures under gyroscopic effects.
• Nyquist plots are constructed from the computed FRF data to visualize dynamic system behavior and stability.
• The method leverages Fourier transform relationships to define FRF as the ratio of output to input in the frequency domain.
• The approach allows for both regeneration of measured FRF curves and synthesis of unmeasured FRF components from limited data.
• The gyroscopic effect is modeled by incorporating rotational dynamics into the system's stiffness and damping matrices.

Experimental results

Research questions

• RQ1 Can standard smart office software accurately compute and visualize FRF curves under gyroscopic effects in rotating structures?
• RQ2 How does the inclusion of gyroscopic effects alter the shape and characteristics of Nyquist plots in FRF analysis?
• RQ3 To what extent can FRF regeneration and synthesis be achieved using only office software tools?
• RQ4 What is the feasibility of replacing specialized simulation software with accessible office tools for modal analysis?
• RQ5 Can the proposed method reliably extract modal parameters (frequency, damping, mode shape) from FRF data using office software?

Key findings

• The study successfully demonstrates that smart office software can generate accurate FRF curves for rotating structures under gyroscopic effects.
• Nyquist plots created from office-software-generated FRF data clearly reflect the influence of gyroscopic coupling on system dynamics.
• The method enables effective regeneration of theoretical FRF curves from measured data, validating its accuracy.
• Synthesis of unmeasured FRF components is achievable using the proposed computational framework in office software.
• The approach provides a cost-effective and accessible alternative to high-end simulation tools for modal analysis in mechanical systems.
• The results confirm that standard office software can handle complex dynamic system modeling tasks traditionally requiring specialized engineering software.