论文标题
广义分布级麦克斯韦模型
A generalised distributed-order Maxwell model
论文作者
论文摘要
在这项工作中，我们使用分布式衍生物提出了广义的粘弹性模型。该模型由串联连接的两个分布式元素（分布式的跳锅）组成，如Maxwell模型。新模型概括了[H. Schiessel，A。Blumen，分数弛豫方程的分层类似物，物理学杂志：数学和一般26（1993）（1993）5057-50]，当选择了衍生物阶顺序的适当加权功能时，可以对复杂流体进行更广泛和准确的描述。我们讨论了分布式顺序的经典，分数和粘弹性模型之间的联系，并突出显示支持这些本构方程的基本概念。我们还得出了放松模量，存储和损失模量以及特定加权功能的蠕变依从性。
In this work we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented in [H. Schiessel, A. Blumen, Hierarchical analogues to fractional relaxation equations, Journal of Physics A: Mathematical and General 26 (1993) 5057-50] and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. We discuss the connection between classical, fractional, and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. We also derive the relaxation modulus, the storage and loss modulus, and the creep compliance for specific weighting functions.
