Zhibao Cheng

Seismic isolation of two dimensional periodic foundations

Phononic crystal is now used to control acoustic waves. When the crystal goes to a larger scale, it is called periodic structure. The band gaps of the periodic structure can be reduced to range from 0.5 Hz to 50 Hz. Therefore, the periodic structure has potential applications in seismic wave reflection. In civil engineering, the periodic structure can be served as the foundation of upper structure. This type of foundation consisting of periodic structure is called periodic foundation. When the frequency of seismic waves falls into the band gaps of the periodic foundation, the seismic wave can be blocked. Field experiments of a scaled two dimensional (2D) periodic foundation with an upper structure were conducted to verify the band gap effects. Test results showed the 2D periodic foundation can effectively reduce the response of the upper structure for excitations with frequencies within the frequency band gaps. When the experimental and the finite element analysis results are compared, they agree well with each other, indicating that 2D periodic foundation is a feasible way of reducing seismic vibrations.

Locally resonant periodic structures with low-frequency band gaps

Presented in this paper are study results of dispersion relationships of periodic structures composited of concrete and rubber, from which the frequency band gap can be found. Two models with fixed or free boundary conditions are proposed to approximate the bound frequencies of the first band gap. Studies are conducted to investigate the low-frequency and directional frequency band gaps for their application to engineering. The study finds that civil engineering structures can be designed to block harmful waves, such as earthquake disturbance.

Three dimensional periodic foundations for base seismic isolation

Based on the concept of phononic crystals, periodic foundations made of periodic materials are investigated in this paper. The periodic foundations can provide low frequency band gaps, which cover the main frequency ranges of seismic waves. Therefore, the periodic foundations are able to protect the upper structures during earthquake events. In this paper, the basic theory of three dimensional periodic foundations is studied and the finite element method was used to conduct the sensitivity study. A simplified three-dimensional periodic foundation with a superstructure was tested in the field and the feasibility of three dimensional periodic foundations was proved. The test results showed that the response of the upper structure with the three dimensional periodic foundation was reduced under excitation waves with the main frequency falling in the attenuation zones. The finite element analysis results are consistent with the experimental data, indicating that three dimensional periodic foundations are a feasible way of reducing seismic vibrations.

Dispersion Differences and Consistency of Artificial Periodic Structures

Dispersion differences and consistency of artificial periodic structures, including phononic crystals, elastic metamaterials, as well as periodic structures composited of phononic crystals and elastic metamaterials, are investigated in this paper. By developing a

Multi-mass-spring model and energy transmission of one-dimensional periodic structures

K(\omega )

A new perspective for analyzing complex band structures of phononic crystals

method, complex dispersion relations and group/phase velocity curves of both the single-mechanism periodic structures and the mixing-mechanism periodic structures are calculated at first, from which dispersion differences of artificial periodic structures are discussed. Then, based on a unified formulation, dispersion consistency of artificial periodic structures is investigated. Through a comprehensive comparison study, the correctness for the unified formulation is verified. Mathematical derivations of the unified formulation for different artificial periodic structures are presented. Furthermore, physical meanings of the unified formulation are discussed in the energy-state space.

Periodic Materials-Based 3D Seismic Base Isolators for Nuclear Power Plants

This paper deals with a classical problem on a linear elastic lattice. A multi-mass-spring model is proposed to build the unit cell. Based on this multi-mass-spring model, a detailed investigation on the band of frequency gaps of one-dimensional periodic structures is conducted. A unified formulation to study the band structures of one-dimensional periodic structures is obtained. To determine the bound frequencies of the bands of frequency gaps, a very simple method without investigating the dispersion curves is proposed based on the modal analytical method. The method presented in this paper is applicable to general cases and is much more convenient than that proposed by other related investigations. In addition, the dynamic property of a finite periodic structure is investigated from the view of energy input, energy distribution, and interactions between the external excitation and the finite periodic structure, from which the energy flow pattern is illustrated clearly.

Novel composite periodic structures with attenuation zones

Rewriting the formulation of the Bloch waves, this paper presents a new perspective for analyzing the complex band structures of the in-plane waves in 2D phononic crystals. Using the proposed formulation, a new finite element based method is developed for analyzing 2D periodic systems. The results of the validation example prove that the proposed method can provide exact solutions for both the real and complex band structures of 2D periodic systems. Furthermore, using the proposed method, the complex band structures of a 2D periodic structure are calculated. The physical meanings of the obtained complex band structures are discussed by performing the wave mode analysis.

Seismic isolation foundations with effective attenuation zones

The concept of periodic materials, based on solid state physics theory, is applied to earthquake engineering. The periodic material is a material which possesses distinct characteristics that do not allow waves with certain frequencies to be transmitted through; therefore, this material can be used in structural foundations to block unwanted seismic waves with certain frequencies. The frequency band of periodic material that can filter out waves is called the band gap, and the structural foundation made of periodic material is referred to as the periodic foundation. In designing a periodic foundation, the first step is to match band gaps of the periodic foundation with the natural frequencies of the superstructure. This is an iterative process. Starting with a design of the periodic foundation, the band gaps are identified by performing finite element analyses using ABAQUS. This design process is repeated until the band gaps match natural frequencies of the superstructure, and the field tests of a scaled specimen are conducted to validate the design. This is an on-going research project. Presented in this paper are the preliminary results, which show that the three dimensional periodic foundation is a promising and effective way to mitigate structural damage caused by earthquake excitations.Copyright