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**Static and dynamic analysis of clamped orthotropic plates using Lagrangian multiplier technique.**
*(English)*
Zbl 0615.73071

An analysis was developed to predict the static and dynamic response of clamped orthotropic laminates. The dynamic loading conditions included low-velocity impact by a hard object. Shear deformation effects in the clamped plate were accounted for using a higher-order plate theory. The natural frequencies and the corresponding mode shapes were computed by solving the eigenvalue problem using Lagrangian multiplier technique. The dynamic analysis incorporated the static response and the eigenvalue solutions into the mode acceleration technique. The static and dynamic analyses were validated by demonstrating a good correlation between the calculated results, available experimental data, and other analytical results. The validated analysis was used to predict the damage introduced in clamped orthotropic plates due to low-velocity impact by a hard object.

### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

49R50 | Variational methods for eigenvalues of operators (MSC2000) |

74K20 | Plates |

74E10 | Anisotropy in solid mechanics |

74E30 | Composite and mixture properties |