超材料混凝土单胞骨料的无阻尼自由振动特性研究

超材料概念的提出引起了功能混凝土的研究热潮,基于one-dimensional spring-mass system模型,以超材料混凝土单胞骨料为研究对象,在线弹性变形下,建立了单胞骨料的三维振动模型,模型中软涂层和砂浆均用弹簧等效代替,其等效长度和等效刚度被计算。对单胞骨料系统进行受力分析,由达朗贝尔原理导出了无阻尼自由振动的控制方程。设振动的复数解,代入方程,得到系统的固有频率。使用初始条件,获得振动解。用MATLAB软件编程进行算例分析,讨论初始条件、骨料内部尺寸及软涂层和砂浆的弹性模量等参数对固有频率和振动特性的影响。算例分析表明:固有频率随软涂层、砂浆弹性模量和振幅的增大而增大;软涂层弹性模量和振幅相同时,固有频率随软涂层厚度的增加而减小;初相位随软涂层、砂浆弹性模量增大而增大;骨料不同内部尺寸对振动有明显影响。这对超材料混凝土抵抗高频荷载和冲击荷载的研究有工程指导价值。

A study of undamped free vibration characteristics on a metaconcrete unit cell

The research boom of functional concrete is aroused by the concept of metamaterials.In the paper,based on an one-dimensional spring-mass system model,a three-dimensional vibration model of a unit cell that is taken as the study object was established under linearelastic deformation.The soft coating and mortar were assumed as spring that has equivalent stiffness and equivalent length in the model.Analyzed the force of the system,the equation of undamped free vibration was deduced using the D′Alembert law.Supposing the complex solution of the vibration,the natural frequency was acquired.Using the initial conditions,the vibration solution was obtained.The influences of the initial conditions,aggregate geometry data,the elastic modulus of the soft coating and the mortar on the natural frequency and the vibration characteristics were analyzed by using the MATLAB.The results show that:the natural frequency increases with the soft coating,mortar elastic modulus,and amplitude;when the soft coating elastic modulus and amplitude are the same,the natural frequency decreases with the soft coating thickness;the initial phase increases with the soft coating and mortar elastic modulus;the effect of different aggregate geometry data upon vibration characteristics is significant.The research of the metaconcrete structures resisted to high-frequency loads and impact loads has engineering guiding value.