### Abstract

Original language | English |
---|---|

Pages (from-to) | 949-961 |

Number of pages | 13 |

Journal | Journal of Theoretical and Applied Mechanics |

Volume | 55 |

Issue number | 3 |

Publication status | Published - 27 Jul 2017 |

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### Keywords

- Kirchhoff plate theory
- infinite plate
- ring load
- circular load
- Hankel transform
- particular solution

### Cite this

**Solutions of vibration problems for thin infinite plates subjected to harmonic loads.** / Klanner, Michael; Ellermann, Katrin.

Research output: Contribution to journal › Article › Research › peer-review

*Journal of Theoretical and Applied Mechanics*, vol. 55, no. 3, pp. 949-961.

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TY - JOUR

T1 - Solutions of vibration problems for thin infinite plates subjected to harmonic loads

AU - Klanner, Michael

AU - Ellermann, Katrin

PY - 2017/7/27

Y1 - 2017/7/27

N2 - New closed form solutions for harmonic vibrations of infinite Kirchhoff plates subjected to a constant harmonic ring load, a constant harmonic circular load and an alternating harmonic circular load are derived. Two different approaches are used to define the closed form solutions. The first approach uses the integration of the harmonic point force and the addition theorem for Bessel functions, while the second approach applies the Hankel transform to solve the inhomogeneous partial differential equation of the Kirchhoff plate theory. The new closed form particular solutions can especially be used in Trefftz like methods and extend their field of application.

AB - New closed form solutions for harmonic vibrations of infinite Kirchhoff plates subjected to a constant harmonic ring load, a constant harmonic circular load and an alternating harmonic circular load are derived. Two different approaches are used to define the closed form solutions. The first approach uses the integration of the harmonic point force and the addition theorem for Bessel functions, while the second approach applies the Hankel transform to solve the inhomogeneous partial differential equation of the Kirchhoff plate theory. The new closed form particular solutions can especially be used in Trefftz like methods and extend their field of application.

KW - Kirchhoff plate theory

KW - infinite plate

KW - ring load

KW - circular load

KW - Hankel transform

KW - particular solution

M3 - Article

VL - 55

SP - 949

EP - 961

JO - Journal of Theoretical and Applied Mechanics

JF - Journal of Theoretical and Applied Mechanics

SN - 1429-2955

IS - 3

ER -