The Analysis of Stress Waves at a Junction of Beam and String

Mu Chen,Zhuojie Zhang,Ronghui Wang,Niujing Ma

doi:10.1155/2018/4863503

Abstract

In the bridge engineering, there are some problems about the dynamics that traditional theory cannot solve. So, the theory about stress waves is introduced to solve the related problems. This is a new attempt that the mechanic theory is applied to practical engineering. The stress wave at a junction of the structure composed of beams and strings is investigated in this paper. The structure is studied because the existence of a soft rope makes the transmission of the force in the bridge structure different from the traditional theory, and it is the basis for further research. The equilibrium equations of the displacement and the internal force are built based on the hypothesis. The fast Fourier transform (FFT) numerical algorithm is used to express an incident pulse of arbitrary shape. The analytical solutions are substantiated by comparing with the finite element programs. The conclusion that if the cross section of the string is relatively small, then the energy density of the structure is relatively large, which is disadvantageous to the structure, can be obtained from this paper.

Highlights

Complex structures, such as arch bridge, suspension bridge, and cable-stayed bridge, are used increasingly in the world
Different from the traditional theory, the vehicle load is regarded as the vibration load in the bridge structure. e theory about stress waves is introduced to study the influence of the vibration load. e propagation speed of longitudinal waves and transverse waves in the concrete and steel is in the range of 1000 m/s to 5000 m/s, and in those large structures, the time scale of vehicle load and stress wave in balance are in the same order of magnitude
Lee and Kolsky [1] investigate the generation of stress pulses at the junction of two noncollinear rods. ey used the simple one-dimensional theory to describe the propagation of longitudinal waves and used the Timoshenko equation for flexural propagation. e analytic relations between the incident pulse and the four generated pulses are derived both for an incident longitudinal pulse and an incident flexural pulse

Summary

Introduction

Complex structures, such as arch bridge, suspension bridge, and cable-stayed bridge, are used increasingly in the world. E propagation speed of longitudinal waves and transverse waves in the concrete and steel is in the range of 1000 m/s to 5000 m/s, and in those large structures, the time scale of vehicle load and stress wave in balance are in the same order of magnitude. Doyle and Kamle [5, 6] had taken an experimental study of the reflection and transmission of flexural waves at an arbitrary T-joint. Li et al [12] developed a fractal damage joint model based on the fractal damage theory to investigate the transmission and reflection of stress waves across joints. According to the need of practical engineering, the distribution of the stress wave that was produced by transverse impact in the junction of the beam and string is the focus of the study in this paper

Theoretical Analysis

Numerical Validation of the Cosine Wave