## Abstract

The vertical, horizontal and rocking vibrations of a body on the surface of an otherwise unloaded half plane are studied. The problems are formulated so that one stress vanishes over the entire surface, and an oscillating displacement is prescribed in the haded region. The problems are mixed with respect to the prescribed displacement and the remaining stress. Each case leads to a mixed boundary value problem represented by dual integral equations which are reduced to a single Frcdholm integral equation. Although numerical methods arc used to solve the integral equation, the contact stresses are found to be presentable in closed form to good accuracy. An estimate of the stiffnesses for coupled horizontal and rocking vibration is also suggested and it is found that the coupling effect is significant.

Original language | English (US) |
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Pages (from-to) | 697-705 |

Number of pages | 9 |

Journal | Journal of Applied Mechanics, Transactions ASME |

Volume | 35 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1964 |

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering