Summary

Paper-based smart systems are new and presented with their advantages along with their parametric studies. These systems are still in their early stages of development. The introdctory review of smart materials especially paper-based piezoelectric energy harvetsers is completely covered in the first chapeter. They possess exclusive merits in comparison to the conventional piezoelectric smart systems made entirely of PVDF or PZT. Unlike the conventioal piezoelectric materials they are lightweight, cost-effective, biodegradable, biocompatible, foldable, environmentally friendly, disposable, inexpensive to fabricate, portable and flexible. Additionally, compared to other flexible materials cellulose has a much lower coefficient of thermal expansion leading to the high thermal stability of final devices [17]. The only deficiency which needs to be surmounted is the lower performance. Based on the experimental research presented in the literature, the amount of extracted power from these smart materials are much lower than the regular piezoelectric energy harvesters. Hence, there is a need to study these structures to find out ways to improve the performance and efficiency enhancement. To satisfy the need, there are different venues which can be pursued including the enhancement of piezoelectric properties through functionalizing paper, geometry modification, and sizing. In this research, these solutions are separately considered and investigated. As there is no experimental work on paper based cantilever type piezoelectric energy harvesters, the validation of the proposed models made from PZT are available in the open literature. A first step in this investigation is the validation of the models and the concepts presented in the above work. This step has been completed and further investigations on paper based piezo cantilever like energy harvesters are now feasible.

In order to study the effects of different parameters, it is first necessary to formulate a theoretical model which can accurately predict the behavior of the system. Moreover, to solve the governing equations an efficient and accurate solution method is essential. Hence, the second chapter of this study is devoted to address these issues. In the second chapter, the structure of cantilever piezoelectric energy harvester is first modelled based on Euler-Bernoulli and Timoshenko beam theories. After that, finite element method with the application of a superconvergent element is applied to discretize the governing equations. The validation of the results using SCE shows a very good rate of convergence and excellent agreement between the

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theoretical and experimental results reported in literature. The material presented in the chapter was published in the Journal of Intelligent Material Systems and Structures.

As the second step, in order to study the influence of the geometry modification, the behavior of cantilever piezoelectric energy harvesters under bending motion is modelled and investigated in the third chapter. Polynomial function with different degrees of non-uniformity introduced by changing their highest degree term from one to five is the kind of structure considered. The results indicate that improvement of the electrical output is feasible using polynomial function with higher degrees of non-uniformity. Efficiency is another important factor scrutinized in this chapter showing that its enhancement is achievable using the application of non-uniform geometries. The material presented in the chapter was published in the Journal of Intelligent Material Systems and Structures.

Sizing is one of the most important factors which needs to be considered for the performnce enhancement and weight reduction simultaneously. By sizing, it is possible to improve the desired output power without the application of extra piezoelectric material. This important issue is addressed in the third chapter. Here, a new system consisting of an array of tapered beams (diverging beams) was presented. In the new system although the same amount of piezoelectric material was used the harvested electrical power output and the weight of substrate layer increased and reduced, respectively. It is worth mentioning that the operation frequency was kept constant for the design of the new system. The material presented in this chapter was submitted to publication to the International Journal of Smart and Nano Materials

To complete the study, the effect of functionalizing is studied in the 5th _{chapter. In this chapter,}

the performance analysis of non-uniform bimorph functionally graded piezoelectric energy harvesters are analyzed. Study indicates that the degree of non-uniformity and the ratio of volume fraction play important roles in the 1st _{resonance frequency and subsequently the amount of}

scavenged energy. The material presented in this chapter was submitted to publication to the Journal of Intelligent Material Systems and Structures.

6.2 Conclusions

As it has been mentioned in the abstract, one of the main objective of this study is the performance enhancement piezoelectric energy harvesters which is met using the geometry modification, sizing

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analysis and functionalizing the structure. Based on the investigations carried out in each chapter devoted to every recommended solution, the main conclusions could be briefly listed below:

● SCE is an element with a great range of convergence which only requires very few elements to capture the output resulting in the reduction of time and the cost of computation.

● It is more suitable to model the beam using the Timoshenko assumptions only for smaller values of slenderness ratio (less than 5).

● The degree of polynomial function has an increasing effect on the output voltage so that changing the degree from one to five results in enhancement of electrical voltage by 306%. ● Changing the geometry from a converging beam (𝛼 = −0.6) to a diverging beam (𝛼 = 0.6) leads to increasing the maximum output voltage by 2867.3%.

● Application of the diverging beams can both increase the electrical output and decrease the fundamental resonance frequency, respectively. This is an advantageous feature for scavenge energy from sources with low fundamental frequencies.

● The maximum output voltage is produced by the bimorph structure in parallel connection.

● By converging the beam and raising the power “n” from 1 to 5 the efficiency can be improved by 22%.

● The results indicate that the maximum efficiency is located between the open-circuit and short-circuit frequencies.

● By the application of a series of beams with optimized sizing the harvested electrical power output increased significantly by 140% although the same amount of piezoelectric material was used. Additionally, the weight of substrate layer is reduced by 15.64% by the application of thinner substrate layer.

● The fundamental frequency decreases uniformly as the material volume fraction rises while the output power rises such that the maximum values belong to the pure piezoelectric constituent.

● Increasing the volume fraction parameter widens the frequency gap difference between the short-circuit and open-circuit frequencies. In other words, the maximum amount of frequency difference occurred for the pure piezoelectric condition (𝑛 → ∞).

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● Rising the volume fraction parameter pushes the peak values of output power towards the lower external load resistances.

● For each excitation frequency there is always an optimal volume fraction parameter and tapering geometry leading to the maximal output power.

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