Nonlinear dynamic analysis of symmetric and antisymmetric cross-ply laminated orthotropic thin shells. (English) Zbl 1367.74035
Summary: In this paper, the governing equations for nonlinear free vibration of truncated, thin, laminated, orthotropic conical shells using the theory of large deformations with the Karman-Donnell-type of kinematic nonlinearity are derived. Applying superposition principle and Galerkin’s method, these equations are reduced to a time-dependent nonlinear differential equation. The frequency-amplitude relationship for the laminated orthotropic thin truncated conical shell is obtained using the method of weighted residuals. In the particular case, we can obtain the similar relationships for the single-layer and laminated orthotropic cylindrical shells, also. The influence played by geometrical parameters of the conical shell and physical parameters of the laminate (i.e. material properties, staking sequences and number of layers) on the non-linear vibration behavior of the conical shell is examined. It is noticed that the nonlinear vibration of shells is highly dependent on laminate characteristics and, from these observations, it is concluded that specific configurations of laminates should be designed for each kind of application. Present results are compared with available data for special cases.
MSC:
| 74K25 | Shells |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74E10 | Anisotropy in solid mechanics |
Keywords:
frequency-amplitude relation; superposition principle; Galerkin’s method; method of weighted residualsReferences:
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