High frequency vibrations and wave propagation in elastic shells: Variational-asymptotic approach

• Published in: International journal of solids and structures Vol. 34; no. 30; pp. 3923 - 3939
• Main Author: Le Khanh, Chau
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-10-1997; Elsevier Science
• 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; Cut off frequency; Vibration; Variational calculus; Two dimensional model; Numerical method; Asymptotic approximation; Elastic waves; Cylindrical shell; High frequency; Wave dispersion
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/S0020-7683(97)00011-5

Two-dimensional equations are derived for high-frequency vibrations of linear elastic shells. The derivation is based on the variational asymptotic analysis of the three-dimensional action functional. This guarantees the exactness of the derived equations for the classical and thickness branches of vibrations in the long-wave range. A best short-wave extrapolation is chosen so as to reach the qualitative agreement with the threedimensional theory in the short-wave range. Comparisons are made with the similar results of the three-dimensional theory.