Non-stationary vibration of electroelastic shallow spherical shell
Keywords:
electroelasticity, shallow spherical shell, non-stationary vibration, integral Laplace transformAbstract
The numerical-analytical method of solving of the problem of non-stationary axisymmetric vibration of shallow spherical shell, composed of thin elastic and electroelastic layers, under impulse electromechanical load is presented. Statement of the problem is executed within the limits of the theory of thin electroelastic shells. Integral Laplace transform on time coordinate, expansion of unknown functions into a series and methods of the theory of integral equations were used for problem solving. By the developed approach the problem is reduced to a system of Volterra’s integral equations of the 2nd kind which is solved numerically. Results of calculations and their analysis for various variants of fastening of shell’s edge are presented for step mechanical and electric load. The obtained expressions allow to investigate vibration of nonstationary loaded electroelastic element in the form of a shallow spherical shell or a round plate (at rather great value of radius of curvature of the surface of connection of layers) and at other variants of boundary conditions as mechanical, as electric groups. The stated approach can be generalized on a case of the partitioned current-carrying covering of an electroelastic layer. Advantages of the stated method are simplicity of computing realization and an opportunity to control an accuracy of results.
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