Journal of Zhejiang University-SCIENCE A

, Volume 19, Issue 5, pp 331–345

# Rocking of a rigid block freestanding on a flat pedestal

• Antonio Gesualdo
• Antonino Iannuzzo
• Michela Monaco
• Francesco Penta
Article

## Abstract

The seismic protection of objects contained within museums is a topic of great interest, especially with reference to how they are displayed or stored. This problem is the same as that of a large class of non-structural components, such as mechanical and electrical hospital and laboratory equipment that could lose their functionality because of earthquakes. Statues and ceramics simply supported on the floor represent a significant set of case. In some cases, like the Bronzes of Riace, isolation systems have been developed. However, in general museum exhibits are not equipped with devices capable of mitigating the oscillations induced by possible earthquakes. The case study of a marble statue placed on a freestanding squat rigid pedestal is examined. The system of algebraic differential equations governing the problem has been derived and included in an ad-hoc numerical procedure. It is shown that the insertion of a squat rigid body with low frictional resistance at the lower interface with the floor, and high frictional resistance at the upper interface with the artifact significantly reduces the amplitude of the rocking response. As a result the artifact rocks without sliding on the rigid base that slides without rocking with respect to the floor. The numerical analysis performed can be a tool to help in the choice of the optimal friction values in the surfaces of the flat block, designed as a simple isolation system.

## Key words

Rigid body Isolation Statues Friction Rocking dynamics

# 水平支座上独立式刚性块的摆动模型

## 摘要

### 创新点

1. 研究对象为两个叠合在一起的刚性块,较以往同类问题中的单一刚性块,更具现实意义;2. 同时研究了刚性块的摆动和滑动两类运动模式。

### 方法

1. 基于达朗贝尔原理构建摆动控制方程,分析单刚体情形下的摆动并利用数值手段描述其滑动状态;2. 在分析单刚体的基础上构建双刚体控制方程组并对其进行数值求解。

### 结论

1. 通过研究大理石雕塑置于蹲式刚性基底上且基底独立放置在移动地面上的情形发现,相比于滑动,雕塑自身的摆动是造成其损坏的主要原因;2. 在某些情况下,刚体表面延迟的存在可以避免细长刚性块的翻转,尤其是对于那些细长的摇摆块体以及上部块体质量增加的情形;3. 本文提出的数值分析可以成为优化简易隔振系统的一个有效工具。

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