Bardzokas D.I., Kydryavtsev B.A., Senik N.A. Wave Propagation in Electromagnetoelastic Media

Contents

Introduction

Discovered 100 years ago by French scientists Pierre and Jacques Curie the piezoelectric effect is widely applied in different fields of science and technology, but mainly in radio engineering, acoustics, non-destructive testing, metrology, computer engineering and acoustoptics. The basis of this phenomenon is the capability of some materials to deform under the influence of external electric fields. The reversibility of this phenomenon is well-known, which is manifested in the excitation of an electric field during the deformation of a piezoelectric by external mechanic loads. The first practice application of this phenomenon is connected with the name of Paul Langevin, who constructed a sonar, where a sensing element made from quartz was used as a radiator and receiver. From the middle of fifties of XX century after creating artificial materials possessing a piezoeffect, the field of application of piezoelectrics was broadened substantially and at present a large quantity of different devices has been developed based on the phenomenon of piezoelectric. Approximately that time started the investigation of the problem of interaction of deformed media with electromagnetic fields and up to now a series of models were developed, taking into account either aspects of the interaction. In particular, models of piezoelectric and piezomagnetic media were constructed, a piezoconductive medium, an electromagnetic conductive medium and a series of other models. A more full representation of various models of interaction, fields of their application and methods of calculations of various devices may be found in reviews [56], [79], [76], [75], [93], [80], and also in special monographs [32], [3], [8], [27], [125], [128]–[65], [36], [82], [84], [89], [97], [102], [106], [39], [64], and in references in them.

The increased requirements in calculations precision of numerous acoustoelectronics devices on the surface of acoustic waves, and also the necessity of estimation of the influence of external electromagnetic fields on their parameters stimulated intensive investigation in this field, which is stated in numerous publications. Substantial part of this investigation was fulfilled by using various approximation approaches. In connection with this the mathematical investigation of wave processes in electromagnetic media on the basis of a strict solution to the corresponding problems of electroelasticity is quite actual. Recently much attention is paid to this problem in the works of prominent scientists working in this field. Up to now different types of investigations and concrete results in the sphere of static and dynamic problems of electroelasticity appeared in [4], [5], [22]–[26], [55], [77], [70], [88], [99], [100], [107], [110], [47]–[60], [112], [1]–[126].

From the multiple effects appearing as a result of interaction between an elastic media and an electromagnetic field in the suggested monograph, the statement of main results obtained in the field of investigation of harmonic waves in piezoelectric magnitoelectric media is given. This choice may be explained by the scientific interests of the authors on the one hand, and by large practical application of harmonic waves in piezoelectric and magnitoelectric media on the other hand.

The given monograph consists of 6 chapters, introduction and references and arbitrarily may be divided into two parts. In the first part (the Introduction and Chapter 1) a brief review of basic problems is included, appearing in the process of calculation of volumic and surface waves in magnetoelastic and electroelastic media and of the methods of calculation of devices on surface acoustic waves in piezoelectrics.

In the first chapter, which is of subsidiary character, the basic relations of electrodynamics and the description of piezoelectric and magnetoelastic effects, the statement of corresponding problems of excitation and propagation of waves in various media, are given as well as, the main energetic characteristics of wave fields. One of our purposes was to give a brief but rather full statement of basic problems of electromagnetoelasticity, so that it would be possible to understand the material stated in the following chapters without reading the initial sources.

In the second chapter the results of investigation of harmonic waves in unbounded electromagnetoelastic media are given, and unlike other monographs on the subject, the investigation of volumic waves in piezoelectrics and the investigation of volumic waves in piezoelectrics and magnetoelastic media is built with due regard for electrodynamic effects and conductivity of materials. Taking into account the mentioned effects the real properties of materials are reflected more accurately and the stated results allows us to analyze the influence of these quantities on the basic parameters of the waves, and due to it to use more simple media models in a certain wave band.

In the third, fourth and fifth chapters the problems connected with excitation of surface Rayleigh waves, shear surface waves and Lamb waves are considered. Despite the large number of works connected with the investigation of excitation of harmonic surface waves in piezoelectrics with the help of surface electrodes, only in few of them the solutions of boundary problems are built by using the equations of electroelasticity without any additional simplification. The proposed method of investigation is based on the reduction of the solution of the problems to a system of singular integral equations which is solved by the Bubnov–Galerkin method and allows us to build efficient algorithms of solution of the problems on computers and with the help of them to investigate the cinematic and energetic characteristics of the excited waves. A rather detailed investigation of the behaviour of electroelastic waves in the vicinity of the electrode edges is given as well as; formulas of electrode capacities and displacement current, which are important for application, and at last the parametric investigation of intensity factor of the charge density is represented, which allows to consider differently the solution of the important problem of electromechanic breakdown of piezoelectrics with systems of electrodes. The sixth chapter of the book is devoted to the solution of this problem.

We think that, investigation of the phenomenon of electromechanic breakdown of piezoelectrics, when the site of breakdown or puncture is the edge of electrodes, has theoretical and practical interest. The necessity of electromechanic breakdown prediction of various devices on surface waves, excited by electrodes, stimulated the work of the authors in that direction, and its results are stated in the sixth chapter. The proposed new approach to the solution of this problem, based on the generalized methods of breakdown mechanics in case of piezoelectric media with systems of electrodes. The suggested in this chapter criteria of puncture of dielectrics and electromechanic breakdown of piezoelectric are based on the laws of conservation of energy and generalize the ideas and methods of linear mechanics of breakdown. It should be noted that in case of vacuum puncture the suggested criteria give results which agree with the experiment. The obtained in this chapter results indicate the efficiency of the proposed criteria of electromechanic breakdown of piezoelectrics and dielectrics, and due to it approach of the solution of the problem of electromechanic breakdown of piezoelectrics is feasible. We expect that the material of this chapter will attract the attention of researchers and developers of devices with surface electrodes to the problem of electromechanic breakdown of piezoelectrics.

About the authors

Kudryavtsev Boris Alexandrovich – was born in 1937 near Ribinsk of Yaroslavl region. After school he entered Moscow aviation institute, which he finished in 1959, and he was accepted at Central Research Institute of Machine Building, where he worked for 10 years, studying the problems of providing the strength of products of rocket and space technology and concentrating his attention on the problems of development of the methods of calculation of thinwalled shells and plates, including the problems of studying of the features of stress-deformed state in the vicinity of heterogeneous inclusions, cavities and cracks, and also the practical problems including a series of problems of breakdown mechanics. In the beginning of 70s B.A.Kudryavtsev was invited to the Department of Higher Mathematics of Moscow Institute of Chemical Engineering Industry, where he worked for 20 years starting from a lecturer and becoming a chief of the Department. During these years he organized an All-Union Seminar on mechanics of hard deformed body, where the problems connected with the investigation of interaction of a hard deformed body with electromagnetic fields were considered. In 1983–1984 B.A.Kudryavtsev wrote and defended a thesis for Doctorate degree in Leningrad State University, which connected the problems of interaction of an elastic medium with an electromagnetic field including the questions of interaction of bodies with cracks with magnetic and electric fields. During the work in the Seminar he supervised about 20 PhD's and 3 theses for Doctorate degrees in Science. The Seminar was very popular in the USSR and cooperated with related Seminars, which where led by such scientists as I.I.Vorovich (Rostov-on-Don), A.N.Guz (Institute of Mechanics, Kiev), A.F.Ulitko (Kiev University), A.A.Iliushin (Moscow University), A.S.Kosmodamiansky (Donetsk University), S.A.Ambartsumyan (Institute of Mechanics, Erevan).

B.A.Kudryavtsev is the author of 130 scientific articles and the books "Electromagnetoelasticity of piezoelectric and electroconductive bodies" (with V.Z.Parton as a co-author). He was also the supervisor of many scientific and research works which where done in the Department by orders of commercial institutes.

The book suggested to the reader was planned to be written in the beginning of 90s by B.A.Kudryavtsev, and the initial variant was almost ready during the life of our teacher. However, in 1994 B.A.Kudryavtsev died suddenly. We, his pupils, hope that publishing of this book, the ideologist of which he was, and in which the new works which appeared during the last decade are also considered, will be deserving the memory of B.A.Kudryavtsev – a great scientist and teacher.

Bardzokas Demosthenis Ioannis – is a professor at National Technological University of Athens (NTUA). He was born in Tashkent in 1952 in a family of Greek political refugees. After finishing secondary school in 1970 he entered Tashkent State University, mechanicomathematical faculty and graduated it in 1975.

After the fall of the dictratorship in Greece all his family returns back home. In 1976 he became a research worker of National Technological University of Athens, department of mechanics, the head of which was well-known scientist, academician P.S.Teocaris. Under his supervision he defended the thesis "Investigation of plane problems of strengthening bodies with cracks and plane contact problems of elastic bodies by the method of the theory of functions of complex variables". From 1987 to 1990 he worked on probation in Moscow Institute of Chemical Engineering under the supervision of V.Z.Parton and B.A.Kudryavtsev.

At present he is a professor of the department of mechanics, faculty of applied mathematics and physical sciences of National Technological University of Athens. He has published more than 100 works concerning various fields of the mechanics of continuous media (mechanics of destruction, elasticity, heat conductivity, electroelasticity, mechanics of composite materials, theory of waves, etc.).

Senik Nikolai Alexandrovich – was born near Zaporozie (Ukraine) in 1955. He graduated the mechanicomathematical faculty of Moscow State University in 1978. In 1981 he started his postgraduate studies in the Department of higher mathematics of Moscow Institute of Chemical Engineering Industry, where B.A.Kudryavtsev was lecturing at that time. In 1984 he defended a thesis connected with the theory of thinwalled piezoelectric shells for his Phd of physical and mathematical sciences. From 1985 he works as a senior research worker at Scientific and Research Institute of Electromechanics. Simultaneously he took active part in the Seminar of the mechanics of hard deformed body in Department of higher mathematics of Moscow Institute of Chemical Engineering Industry. In 1992 he defended a thesis for a doctorate degree of physical and mathematical sciences at Moscow State University. In 1994 he became a chief of Scientific and research laboratory of developing of perspective cosmic apparatus and also of providing strength parameters and heat regimes of space apparatus of series "Meteor" in the same institute. In 2001 he became a deputy chief constructor of space apparatus "Vulkan". At present he is a chief of Department of perspective space developments at Scientific and Research Institute of Electromechanics.