Forced vibration of three-layered spherical and ellipsoidal shells under axisymmetric loads

• Published in: Mechanics of composite materials Vol. 39; no. 5; pp. 439 - 446
• Main Authors: SHUL'GA, N. A, MEISH, V. F
• Format: Journal Article
• Language: English
• Published: New York, NY Consultants Bureau 01.09.2003
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Difference scheme; Stratified material; Axisymmetric shell; Forced vibration; Free vibration; Initial value problem; Sandwich structure; Axisymmetric load; Numerical method; Ellipsoidal shell; Axial symmetry; Strain wave; Kinematics; Variational calculus; Non linear effect; Ellipsoid; Reissner membrane; Finite difference method
• ISSN: 0191-5665; 1573-8922
• DOI: 10.1023/B:MOCM.0000003294.75072.58

A variant of vibration theory for three-layered shells of revolution under axisymmetric loads is elaborated by applying independent kinematic and static hypotheses to each layer, with account of transverse normal and shear strains in the core. Based on the Reissner variational principle for dynamic processes, equations of nonlinear vibrations and natural boundary conditions are obtained. The numerical method proposed for solving initial boundary-value problems is based on the use of integrodifferential approach for constructing finite-difference schemes with respect to spatial and time coordinates. Numerical solutions are obtained for dynamic deformations of open three-layered spherical and ellipsoidal shells, over a wide range of geometric and physical parameters of the core, for different types of boundary conditions. A comparative analysis is given for the results of investigating the dynamic behavior of three-layered shells of revolution by the equations proposed and the shell equations of Timoshenko and Kirchhoff-Love type, with the use of unified hypotheses across the heterogeneous structure of shells.