In this paper,a nonlinear wave equation with variable coefficients is studied,interestingly,this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities.With the aid of Lou’s direct method1,the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained.The corresponding numerical examples of exact solutions are presented by using different coefficients.Particularly,while the variable coefficients are taken as some special constants,the nonlinear wave equation with variable coefficients reduces to the one with constant coefficients,which can be used to describe the propagation of the travelling waves in general cylindrical rods composed of generally hyperelastic materials.Using the same method to solve the nonlinear wave equation,the validity and rationality of this method are verified.
利用MTS New 810电液伺服材料试验机,对不同强度的建筑钢筋在地震作用应变率范围(2.5×10-4/s～0.1/s)内的动态特性进行了试验研究。采用单调拉伸、常幅值循环和变幅值循环三种加载方式,加载过程由应变控制并保持应变率恒定。试验结果表明,钢筋的力学和变形性能在不同加载方式下均有应变率敏感性,应变率敏感性的大小与准静态屈服强度密切相关,相同应变率下循环加载的骨架曲线与单调加载的拉伸曲线基本重合。对试验数据进行回归分析,得到了钢筋的力学性能特征值和变形性能特征值随应变率变化的规律,进而结合Hoehler模型提出了一种钢筋动态循环本构模型,与试验结果对比表明该模型能很好地描述钢筋的动态行为,建议的钢筋动态本构模型可以应用在钢筋混凝土结构抗震分析中。
