Formulation and program development of damping matrix of viscoelastic body

粘弹性体阻尼矩阵的编制和程序开发已进行了两年。在第一年的实验已经进行了研究的线性和非线性特性的粘弹性材料。从线性实验出发，阐明了粘弹性体的频率特性，建立了本构关系的分数阶微分模型。从非线性实验，频率和应变依赖性阐明，并获得频率和应变依赖性的阻尼特性。在第二年，通过有限元程序，建立了包含新开发的阻尼矩阵的非线性有限元运动方程。在这项研究的同时，提出了高性能的数值积分算法。基于所推导的非线性有限元程序和已建立的数值积分格式，发展了数值算法，推导的阻尼矩阵的性质有待进一步研究。

Formulation and program development of damping matrix of viscoelastic body have been carried out for two years. In the first year the experiments have been conducted for investigating linear and nonlinear characteristics of a viscoelastic material. From linear experiments, frequency characteristics of viscoelastic body were elucidated and fractional differentiation model for constitutive law was established. From nonlinear experiments, frequency and strain dependences were elucidated, and the damping characteristics for frequency and strain dependences were obtained. In the second year, nonlinear finite element equations of motion involving newly developed damping matrix were established by means of the finite element procedure. In parallel to this study, high performance numerical integration algorithms were proposed. Numerical algorithm based on the derived nonlinear finite procedure and established numerical integration schemes was developed.Properties of the derived damping matrix are needed to be investigated in the future.