Abstract
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Kármán and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin’s technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.
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Communicated by ZHENG Quan-shui
Biography: WANG Young-gang (1965 ≈), Associate Professor, Doctor
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Yong-gang, W., Shi-liang, D. Thermoelastically coupled axisymmetric nonlinear vibration of shallow spherical and conical shells. Appl Math Mech 25, 430–439 (2004). https://doi.org/10.1007/BF02437527
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DOI: https://doi.org/10.1007/BF02437527
Key words
- shallow spherical shell
- shallow conical shell
- thermoelastically coupled
- nonlinear vibration
- perturbation method