Modeling and semigroup formulation of charge or current-controlled active constrained layer (ACL) beams; electrostatic, quasi-static, and fully-dynamic assumptions

A three-layer active constrained layer (ACL) beam model, consisting of a piezoelectric elastic layer, a stiff layer, and a constrained viscoelastic layer, is obtained for cantilevered boundary conditions by using the reduced Rao-Nakra sandwich beam assumptions through a consistent variational approach. The Rao-Nakra sandwich beam assumptions keeps the longitudinal and rotational inertia terms. We consider electrostatic, quasi-static and fully dynamic assumptions due to Maxwell's equations. For that reason, we first include all magnetic effects for the piezoelectric layer. Two PDE models are obtained; one for the charge-controlled case and one for the current-controlled case. These two cases are considered separately since the underlying control operators are very different in nature. For both cases, the semigroup formulations are presented, and the corresponding Cauchy problems are shown to be well- posed in the natural energy space.Comment: 2 figure

Studies on actinosporeans (Phylum : myxozoa) from a salmon farm in northern Scotland, with special reference to the actinosporean and myxosporean stages of Sphaerospora truttae Fischer-Scherl, el-Matbouli and Hoffman, 1986

A two-year study of the actinosporean fauna of oligochaetes was conducted at an Atlantic salmon fish farm located at the extreme north of Scotland. The actinosporean fauna and their morphological characteristics, the ultrastructural development of four different actinosporean collective groups, the epidemiology of all actinosporean types identified,the complete life cycle of Sphaerospora truttae, the circadian and seasonal spore release patterns of actinosporean types and the myxospores of S. truttae, the viability of actinosporeans and their responses to fish mucus were determined. Twenty one actinosporean types belonging to seven collective groups: Synactinomyxon (3 types), Aurantiactinomyxon (4 types), Echinactinomyxon (5 types), Raabeia (6 types), Neoactinomyxum (l type), Triactinomyxon (1 type) and Siedleckiella (1 type) are described. Six types were identified to previously described forms; Synactinomyxon "A" of McGeorge et al. (1997); Synactinomyxon tubificis Stole, 1899, S. longicauda Marques, 1984, Aurantiactinomyxon-type of McGeorge et al. (1997), Echinactinomyxon radiatum Janiszewska, 1957, Raabeia-type of McGeorge et ai. (1997). The remainder appeared to be new types of the collective groups. Temperature was found to have a significant effect on the spore morphology and caused statistically important differences in the spore dimensions, especially on the caudal processes. Synactinomyxon-type 1, Aurantiactinomyxon-type3, Echinactinomyxon-type5 and Raabeia-type4 were studied at the TEM level to determine the developmental stages of each type. All actinosporean types studied had uninucleate cells as the earliest stage of development. Formation of a subsequent binucleate cell stage was either due to the division of the nucleus in a uninucleate cell or the plasmogamy of two uninucleate cells. The earliest pansporocyst formation seen was two outer somatic cells surrounding two inner generative alpha and beta cells in all actinosporean types studied. However, the formation of an early pansporocyst followed a four-nuclei stage only in Raabeia. Subsequently, the number of somatic and generative cells increased as a result of mitotic divisions and reached 8 alpha and 8 beta cells at the end of the division stages. Echinactinomyxon had only four somatic cells in pansporocyst, whilst Synactinomyxon, Aurantiactinomyxon and Raabeia had eight. Following the copulation of each pair of alpha and beta cells, 8 zygotes were formed. Then, two mitotic divisions of each zygote resulted in a four-cell stage of each sporoblast. Valvogenesis and capsulogenesis was followed by the formation of 8 mature spores inside each pansporocyst. Over the two year sampling programme the overall infection prevalence of oligochaetes with actinosporeans was 2.9%. The infection prevalence was higher in the first year (3.3%) than the second year (2.3%). The infection prevalences of individual types were between 0.001% and 0.9%. Summer was the preferred season of spore release (4.1%), followed by autumn (2.9%) , spring (2.8%) and winter (1.6%), Some parasites such as Echinactinomyxon-typel released spores throughout the study period, whilst Synactinomyxon-type2 was recorded only in summer. There was also a positive relationship between the number of actinosporean types released and water temperature. A one year sampling programme also indicated that Sphaerospora truttae had two distinct life cycle phases, extrasporogonic and sporogonic, in the fish. Extrasporogonic stages were first detected at the beginning of July 1996 with a prevalence of 50% and were seen over an 8-10 week period. Sporogonic stages first became detectable in the kidney tubules at the beginning of September 1996. As well as sporogonic stages, many developing pseudoplasmodia were also observed at this time. Pseudoplasmodia were always present along with mature spores. The infection prevalence stayed above 80% throughout the period of infection. Experimental infections showed that Echinactinomyxon-type5, was the alternate life cycle stage of S. truttae in the oligochaete Lumbriculus variegatus. The time taken from the exposure of Atlantic salmon to Echinactinomyxon-type5 spores to formation of mature Sphaerospora truttae spores was 4.5 months (138 days). However, infections of Atlantic salmon with presporogonic and immature spores of S. truttae were first seen at 3.5 months post-exposure (110 days). In addition to S. truttae, the life cycle of Chloromyxum truttae was also completed at 4.5 months (138 days) post - exposure at 12-16°C using Aurantiactinomyxon-type4 spores released from Tubifex tubifex. Worms infected with Synactinomyxon-type 1, Aurantiactinomyxon-type I, Echinactinomyxon-type1 and type5, Raabeia-type4 and Neoactinomyxum-type showed inconsistent spore release patterns over five subsequent days at ambient temperatures. Up to 5000 spores an each day were released from infected worms with the exception of Echinactinomyxon-type5 which released up to 80,000 spores per day. Experimentally there was a positive relationship between the numbers of spores shed and water temperature. The spore release of worms infected with Synactinomyxon-type I, Aurantiactinomyxon-type 1, Echinactinomyxon-type I, Raabeia-type4 and Neoactinomyxum-type spores were also studied at 3 h intervals and showed that peak release occurred between 22.00 and 01.00 h. Studies on the spore release patterns of Sphaerospora truttae myxospores from Atlantic salmon showed that mature spores were first released at the end of November, peaked around April and then decreased sharply. Number of mature spores present in the kidney of the fish showed a similar pattern of abundance. Polar filaments of Echinactinomyxon-type I, Raabeia-type4 and Aurantiactinomyxon-type I spores discharged in response to mucus from Atlantic salmon, brown trout, 3-spined stickleback and common carp. However, the response to the mucus from each fish species was different. In each case majority of discharges occurred within the first 5 min of exposure to mucus although there were further discharges up to lh. The viability of Synactinomyxon-type I, Echinactinomyxon-type I, Raabeia-type4, Aurantiactinomyxon-typel and Neoactinomyxum-type spores had a negative correlation with increasing temperature. In general, the spores remained viable for 6-7 days at 4°C, 4-5 days at 13°C and 4 days 22°C

Influences of SAP as a development project to the urban and regional development in the E.U. integration process

SAP Project which is one of the important projects of Turkey and Middle East, must be considered more carefully because of the improvements that have been experienced previously in Middle East and EC process. But actually it is not considered enough and it gives harm especially to the improvements of the region and Turkey.The aim of this article is to examine SAP project’s social and rural sides and the mutual effects on Turkey and EC, on the process of the reconstruction of globalization, interference of USA in the region and EC which has been on the agenda.Firs of all the mutual effects of both sides in EC process will be examined. Secondly, the profile which SAP Project has come will be considered and the social and rural improvements in this process will be examined by the frame of functionel model.The importance of this article is to put forward the social effects of the practised investments and technology and examine the way, the quality and the speed which is changed by the problems and contribute the project scientifically.Therefore a new application model of SAP will be presented with solution offers.SAP Project which is one of the important projects of Turkey and Middle East, must be considered more carefully because of the improvements that have been experienced previously in Middle East and EC process. But actually it is not considered enough and it gives harm especially to the improvements of the region and Turkey.The aim of this article is to examine SAP project’s social and rural sides and the mutual effects on Turkey and EC, on the process of the reconstruction of globalization, interference of USA in the region and EC which has been on the agenda.Firs of all the mutual effects of both sides in EC process will be examined. Secondly, the profile which SAP Project has come will be considered and the social and rural improvements in this process will be examined by the frame of functionel model.The importance of this article is to put forward the social effects of the practised investments and technology and examine the way, the quality and the speed which is changed by the problems and contribute the project scientifically.Therefore a new application model of SAP will be presented with solution offers

Exact boundary controllability and feedback stabilization for a multi-layer Rao-Nakra beam

We prove exact boundary controllability for the Rayleigh beam equation with a single boundary control active at one end of the beam. This result is used to prove exact boundary controllability of the multilayer Rao-Nakra beam, which contains the Rayleigh beam as one of its component equations. We consider all combinations of clamped and hinged boundary conditions. In each case, exact controllability is obtained on the space of optimal regularity. We also obtain corresponding uniqueness and exact observability results for the dual observed system. Then we are able to obtain exponential stability of the multilayer Rao-Nakra beam system using an appropriate boundary feedback. We also formulate an abstract version of the closely related Mead-Marcus sandwich beam model and prove its boundary controllability using the multipliers technique

A Robust Finite-Difference Model Reduction for the Boundary Feedback Stabilization of Fully-dynamic Piezoelectric Beams

Piezoelectric materials exhibit electric responses to mechanical stress, and mechanical responses to electric stress. The PDE model, describing the longitudinal oscillations on the beam, with two boundary feedback controllers is known to have exponentially stable solutions. However, the reduced model by the semi-discretized Finite Elements is shown to lack of exponential stability uniformly as the discretization parameter tends to zero. This is due to the loss of uniform gap among the high-frequency eigenvalues. In this paper, an alternate Finite-Difference based model reduction is investigated by cleverly reducing the order of the model together with the consideration of equidistant grid points and averaging operators. This new model reduction successfully retains the exponential stability uniformly as the discretization parameter tends to zero. Moreover, it does not need a further numerical Fourier filtering. Our results are based on a careful construction of a Lyapunov function. The numerical simulations are provided to compare reduced models and to show the strength of introduced results.Comment: 8 figures, 2 table

Creating a computational tool to simulate vibration control for piezoelectric devices

Piezoelectric materials have the unique ability to convert electrical energy to mechanical vibrations and vice versa. This project takes a stab to develop a reliable computational tool to simulate the vibration control of a novel “partial differential equation” model for a piezoelectric device, which is designed by integrating electric conducting piezoelectric layers constraining a viscoelastic layer to provide an active and lightweight intelligent structure. Controlling unwanted vibrations on piezoelectric devices (or harvesting energy from ambient vibrations) through piezoelectric layers has been the major focus in cutting-edge engineering applications such as ultrasonic welders and inchworms. The corresponding mathematical models for piezoelectric devices are either heuristic or mathematically oversimplified differential equations. Moreover, their “unjustified” approximated reductions consider only the first several vibrations on these devices. In this project, a novel partial differential equation model, accounting for all vibrational modes, is analyzed to provide new insights for a cost-efficient sensor feedback design. Therefore, the sensor feedback signals are not allowed to be contaminated by the residual modes. Our primary goal is to develop reproducible computational tools by an emerging stable approximation technique, so-called filtered Finite Difference Method, which is proved to provide faster and reliable computation. Filtering in the approximation is necessary since the spurious vibrations, due to the blind application of the Finite Difference Method, provide a false stability result. To see the efficiency of the algorithm, we compare the approximation to the one obtained by the Finite Element Method based on the Galerkin\u27s approximation, which is a common technique being used in the engineering literature. The mathematical techniques and computational tools developed in this project are essential to provide new insights into the active controlling of piezoelectric devices. Improving the efficiency of active controlling enables us to take better advantage of piezoelectric technology change since one-time design and fabrication may be unavoidable for many applications such as cardiac pacemakers or NASA/commercially-operated inflatable space antennas. Our state-of-the-art partial differential equation model and its stable approximations will be adaptable for a large class of piezoelectric devices

Türkiye’nin AB’ye aday ülke olmasını sağlayan iç ve dış faktörler ve geleceğe ilişkin yönelimler

Turkey’s forty-year struggle for integration with Europe has reached an important phase with her being given a date for the initiation of the negotiations. How did Turkey, after many failures until then, manage to obtain the status of candidate country all of a sudden and how did the negotiations for full membership begin? Answering these questions will not only enable us to understand our recent past but will also help us to shape the future on an accurate basis, comprehending the present in an accurate way. This study aims at finding the answers to the questions above with a historical and comparative approach and puts forward the findings and analyses on such a basis. Therefore, both inside and the outside factors will be analyzed with regard to the geopolitical and geo-strategic situation of Turkey.Türkiye’nin kırk yıla yakın bir süredir, Avrupa’ya entrege olma mücadelesi yakın bir geçmişte müzakere tarihi almasıyla önemli bir aşamaya ulaştı. Bu kritik noktada cevaplandırtması gereken temel soru şudur: Bu güne kadar bunu başaramayan Türkiye, ne yaptı ya da nasıl oldu da şimdi birden bire aday ülke statüsü aldı ve ardından da tam üyelik için müzakerelere başladı? Bu sorunun cevaplanması sadece geçmişi anlamamızı sağlamayacak aynı zamanda günümüzü doğru kavrayarak geleceği doğru bir temelde biçimlendirmemize de yardımcı olacaktır. Çalışma bu amaçla tarihi ve karşılaştırmalı bir yaklaşımla, yukarıdaki sorunun cevabını aramaya çalışacak, bulgularını ve analizlerini bu temelde ortaya koyacaktır. Bunun için iç ve dış faktörler, Türkiye’nin jeo- politik ve jeo- stratejik durumu göz önünde bulundurularak, ele alınıp incelenecek, sürecin kavranmasına ve işleyişine katkı sunacak sonuçlar ortaya konacaktır

Boundary Output Feedback Stabilization for a Novel Magnetizable Piezoelectric Beam Model

A magnetizable piezoelectric beam model, free at both ends, is considered. Piezoelectric materials have a strong interaction of electromagnetic and acoustic waves, whose wave propagation speeds differ substantially. The corresponding strongly-coupled PDE model describes the longitudinal vibrations and the total charge accumulation at the electrodes of the beam. It is known that the PDE model with appropriately chosen collocated state feedback controllers is known to have exponentially stable solutions. However, the collocated controller design is not always feasible since the performance of controllers may not be good enough, and moreover, a small increment of feedback controller gains can easily make the closed-loop system unstable. Therefore, a non-collocated controller and observer design is considered for the first time for this model. In particular, two state feedback controllers are designed at the right end to recover the states so that the boundary output feedback controllers can be designed as a replacement of the states with the estimate from the observers on the left end. By a carefully-constructed Lyapunov function, it is proved that the both the observer and the observer error dynamics have uniformly exponential stable solutions. This framework offers a substantial foundation for the model reductions by Finite Differences.Comment: 2 figure

The Exponential Stabilization of a Heat and Piezoelectric Beam Interaction with Static or Hybrid Feedback Controllers

This study investigates a strongly-coupled system of partial differential equations (PDE) governing heat transfer in a copper rod, longitudinal vibrations, and total charge accumulation at electrodes within a magnetizable piezoelectric beam. Conducted within the transmission line framework, the analysis reveals profound interactions between traveling electromagnetic and mechanical waves in magnetizable piezoelectric beams, despite disparities in their velocities. Findings suggest that in the open-loop scenario, the interaction of heat and beam dynamics lacks exponential stability solely considering thermal effects. To confront this challenge, two types of boundary-type state feedback controllers are proposed: (i) employing static feedback controllers entirely and (ii) adopting a hybrid approach wherein the electrical controller dynamically enhances system dynamics. In both cases, solutions of the PDE systems demonstrate exponential stability through meticulously formulated Lyapunov functions with diverse multipliers. The proposed proof technique establishes a robust foundation for demonstrating the exponential stability of Finite-Difference-based model reductions as the discretization parameter approaches zero.Comment: 1 figur