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Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.

Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.

VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

Aero-engine components endure combined high and low cycle fatigue (CCF) loading during service, which has attracted more research attention in recent years. This study aims to construct a new framework for the prediction of probabilistic fatigue life and reliability evaluation of an aero-engine turbine shaft under CCF loading if considering the material uncertainty.

To study the CCF failure of the aero-engine turbine shaft, a CCF test is carried out. An improved damage accumulation model is first introduced to predict the CCF life and present high prediction accuracy in the CCF loading situation based on the test. Then, the probabilistic fatigue life of the turbine shaft is predicted based on the finite element analysis and Monte Carlo analysis, where the material uncertainty is taken into account. At last, the reliability evaluation of the turbine shaft is conducted by stress-strength interference models based on an improved damage accumulation model.

The results indicate that predictions agree well with the tested data. The improved damage accumulation model can accurately predict the CCF life because of interaction damage between low cycle fatigue loading and high cycle fatigue loading. As a result, a framework is available for accurate probabilistic fatigue life prediction and reliability evaluation.

The proposed framework and the presented testing in this study show high efficiency on probabilistic CCF fatigue life prediction and can provide technical support for fatigue optimization of the turbine shaft.

The novelty of this work is that CCF loading and material uncertainty are considered in probabilistic fatigue life prediction.

Mechatronics is a very important area of research in industrial applications. The purpose of this study is to find some of the most important components of the literature on this subject.

The analysis is based on the use of the database Compendex; it was searched in the broadest way for documents related to mechatronics. In addition, subject guides from libraries of universities with mechatronics programs were studied to find resources available in those areas.

The literature of mechatronics is extensive and multidisciplinary. Based on the results from Compendex, the following data were found: most productive authors, list of leading journals and conference proceedings, publishers and grant organizations, authors’ affiliations and other minor details. Based on the analysis of subject guides, the following types of resources were found: research databases, reference books and ebook collections.

Part of the analysis is based on a search performed in one technical database, Compendex; it was the database that generated the largest number of citations as compared to Inspec and the Web of Science. The results have a strong English language focus. It is possible that by using the results from multiple data bases, some additional sources could be obtained.

Mechatronics is a relatively new technological field comprising a number of scientific and engineering areas. The results obtained summarized a significant amount of bibliographic information.

The work is original; to the best of the authors’ knowledge, no other study has analyzed the literature on this subject.