Low Frequency Property of a Fractal Vibration Model for a Concrete Beam

Abstract

A concrete beam is a basic element for many applications in architectural engineering, and its vibration property plays an important role in safety and life-span. Previous vibration models were based on continuum beam theories, which could not take into account the porous property of the concrete beam. This paper adopts a two-scale fractal vibration model, and its low frequency property is revealed. This new finding can explain the vibration attenuation and vibration absorption of the porous concrete, and the present theory sheds a new light on the concrete design.

Instability of the printing jet during the three-dimensional-printing process

“…We will discuss the problem in a forthcoming paper by establishing a fractal vibration model. 3,30,31 The instability of the printing jet will also affect the mechanical and electrical properties of graphene/sic composites. 2…”

A study of the fractal foam drainage model in a microgravity space

“…In this work, the variational principle 35–38 is successfully developed by using the fractal semi‐inverse method, 39–44 which helps to analyze the structure of the solution and establish the conservation law. Based on the variational formula, we propose a new analytical technique to solve the fractal model, which perfectly combines the advantages of both the variational theory and the fractal two‐scale transform method 45–49 . The fractal two‐scale transform method is an excellent transform, which converts the fractal space into continuous space.…”

Low-frequency vibro-acoustic response of an optimized fiber-reinforced graphite truss sandwich panel filled with wood-based material

“…1 Low-frequency property has recently become a widely research topic in various nonlinear vibration systems. For instance, because of the significant role of low-frequency vibration in concrete beam systems, He et al 6 theoretically revealed the vibration behavior of the porous concrete, including vibration attenuation and vibration absorption, to enhance the structural safety and life span of the beams. What is more, He et al 7 applied their exclusive methodology, called the fractal frequency formulation, to investigate the nonlinear vibration behavior of fractal oscillators, in which the low-frequency property was found to be of important significance for sound and vibration attenuation.…”