Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

中文翻译：

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具有随机激励的分数齐纳模型中的波传播动力学

摘要 研究了描述粘弹性杆的 Zener 模型的运动方程，并获得了确保解的存在性、唯一性和规律性的条件。本构方程中系数的限制由耗散不等式的弱形式决定。与 Karhunen-Loéve 展开定理相关的各种随机过程被呈现为随机扰动的模型。结果表明位移扰动以无限速度传播。还提供了对非随机模型已发布结果的一些更正。