02897oam 2200529 450 991048499480332120210420061555.03-030-60064-510.1007/978-3-030-60064-8(CKB)4100000011558770(DE-He213)978-3-030-60064-8(MiAaPQ)EBC6386042(PPN)252508351(EXLCZ)99410000001155877020210420d2020 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierRandom fields of piezoelectricity and piezomagnetism correlation structures /Anatoliy Malyarenko, Martin Ostoja-Starzewski, and Amirhossein Amiri-Hezaveh1st ed. 2020.Cham, Switzerland :Springer,[2020]©20201 online resource (XI, 97 p. 2 illus., 1 illus. in color.) SpringerBriefs in Applied Sciences and Technology, Mathematical methods3-030-60063-7 Preface -- 1. Continuum Theory of Piezoelectricity and Piezomagnetism -- 2. Mathematical preliminaries -- 3. The Choice of a Basis in the Space VG -- 4. Correlation Structures -- References -- Index.Random fields are a necessity when formulating stochastic continuum theories. In this book, a theory of random piezoelectric and piezomagnetic materials is developed. First, elements of the continuum mechanics of electromagnetic solids are presented. Then the relevant linear governing equations are introduced, written in terms of either a displacement approach or a stress approach, along with linear variational principles. On this basis, a statistical description of second-order (statistically) homogeneous and isotropic rank-3 tensor-valued random fields is given. With a group-theoretic foundation, correlation functions and their spectral counterparts are obtained in terms of stochastic integrals with respect to certain random measures for the fields that belong to orthotropic, tetragonal, and cubic crystal systems. The target audience will primarily comprise researchers and graduate students in theoretical mechanics, statistical physics, and probability.SpringerBriefs in applied sciences and technology, mathematical methods.Electromagnetic theoryRandom fieldsPiezoelectricityElectromagnetic theory.Random fields.Piezoelectricity.530.141Malyarenko Anatoliy938186Ostoja-Starzewski MartinAmiri-Hezaveh AmirhosseinMiAaPQMiAaPQUtOrBLWBOOK9910484994803321Random fields of piezoelectricity and piezomagnetism2113490UNINA