Unsteady Electro-Magneto-Elastic Axisymmetric Oscillations of a Continuous Cylinder of Infinite Length
In the present work is considered an axisymmetric time-dependent waves of an infinite cylindrical body. The body material is taken to be isotropic and electro magneto elastic. Piezoelectric effects are not taken into account. The deformation process is described by a system of equation with respect to radial and angular components of deformation of the body points in cylindrical coordinate system. In additional, it takes into account the effect of current density, surface charges, electric and magnetic fields. All parameters and ratios are reduced to dimensionless form. To solve the problem, are used the Fourier transformation of angles and the Laplace transformation of time. Then, the resulting expressions expansion in series in terms of a small parameter. The small parameter characterizes the relationship between mechanic and electro-magnetic fields. To move into the space of the originals using the inverse Laplace transformation via residue theorem.
KeywordsElectromagnetoelasticity Axisymmetric waves Residue theorem Coupled problems Time-dependent axisymmetric problems Green’s functions
- 2.Vestyak V.A., Lemeshev V.A. Rasprostranenie nestatsionarnykh radialnykh vozmushcheniy ot tsilindricheskoy polosti v elektromagnitouprugoy srede.// Mater. XIV Intern. Symp. “Dynamic and technolo-ronmental problems of mechanics of structures and continua”, vol. 1. pp. 59–60. named A.G. Gorshkov. Moscow. (2008)Google Scholar
- 3.Gorshkov, A.G., Medvedsky, A.L., Rabinsky, L.N., Tarlakovsky, D.V.: Waves in continuous mediums. Textbook for Higher Education Institutions, p. 472. Fizmatlit, Moscow (2004)Google Scholar