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The purpose is to explore the free vibration behaviour of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The goal of this study is to gain a better knowledge of the dynamic response of nanoscale structures made of functionally graded materials and porous features. The Rayleigh-Ritz approach is used in this study to generate realistic mathematical models that take elastic foundation support into account. This research can contribute to the design and optimization of advanced nanomaterials with potential applications in engineering and technology by providing insights into the influence of material composition, porosity and foundation support on the vibrational properties of nanoplates.

A systematic methodology is proposed to evaluate the free vibration characteristics of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The study began by developing the mathematical model, adding material properties and establishing governing equations using the Rayleigh-Ritz approach. Numerical approaches to solve the problem are used, using finite element methods. The results are compared to current solutions or experimental data to validate the process. The results are also analysed, keeping the influence of factors on vibration characteristics in mind. The findings are summarized and avenues for future research are suggested, ensuring a robust investigation within the constraints.

The Rayleigh-Ritz technique is used to investigate the free vibration properties of elastic foundation-supported porous functionally graded nanoplates. The findings show that differences in material composition, porosity and foundation support have a significant impact on the vibrational behaviour of nanoplates. The Rayleigh-Ritz approach is good at modelling and predicting these properties. Furthermore, the study emphasizes the possibility of customizing nanoplate qualities to optimize certain vibrational responses, providing useful insights for engineering applications. These findings expand understanding of dynamic behaviours in nanoscale structures, making it easier to build innovative materials with specific features for a wide range of industrial applications.

The novel aspect of this research is the incorporation of elastic foundation support, porous structures and functionally graded materials into the setting of nanoplate free vibrations, utilizing the Rayleigh-Ritz technique. Few research have looked into this complex combo. By tackling complicated interactions, the research pushes boundaries, providing a unique insight into the dynamic behaviour of nanoscale objects. This novel approach allows for a better understanding of the interconnected effects of material composition, porosity and foundation support on free vibrations, paving the way for the development of tailored nanomaterials with specific vibrational properties for advanced engineering and technology applications.

Reverse logistics services are designed to move goods from their point of consumption to an endpoint to capture value or properly dispose of products and materials. Artificial intelligence (AI)-based reverse logistics will help Micro, Small, and medium Enterprises (MSMEs) adequately recycle and reuse the materials in the firms. This research aims to measure the adoption of AI-based reverse logistics to improve circular economy (CE) performance.

In this study, we proposed ten hypotheses using the theory of natural resource-based view and technology, organizational and environmental framework. Data are collected from 363 Indian MSMEs as they are the backbone of the Indian economy, and there is a need for digital transformation in MSMEs. A structural equation modeling approach is applied to analyze and test the hypothesis.

Nine of the ten proposed hypotheses were accepted, and one was rejected. The results revealed that the relative advantage (RA), trust (TR), top management support (TMS), environmental regulations, industry dynamism (ID), compatibility, technology readiness and government support (GS) positively relate to AI-based reverse logistics adoption. AI-based reverse logistics indicated a positive relationship with CE performance. For mediation analysis, the results revealed that RA, TR, TMS and technological readiness are complementary mediation. Still, GS, ID, organizational flexibility, environmental uncertainty and technical capability have no mediation.

The study contributed to the CE performance and AI-based reverse logistics literature. The study will help managers understand the importance of AI-based reverse logistics for improving the performance of the CE in MSMEs. This study will help firms reduce their carbon footprint and achieve sustainable development goals.

Few studies focused on CE performance, but none measured the adoption of AI-based reverse logistics to enhance MSMEs’ CE performance.