In this work we propose and analyze an abstract parameter dependent model written as a mixed variational formulation based on Volterra integrals of second kind. For the analysis, we consider a suitable adaptation to the classic mixed theory in the Volterra equations setting, and prove the well posedness of the resulting mixed viscoelastic formulation. Error estimates are derived, using the available results for Volterra equations, where all the estimates are independent of the perturbation parameter. We consider an application of the developed theory in a viscoelastic Timoshenko beam, and report numerical experiments in order to assess the independence of the perturbation parameter.

翻译：在这项工作中,我们提出和分析一个抽象参数依赖模型,该模型是根据Volterra II类集成体编写的混合变异配方。在分析中,我们考虑对Volterra 方程式设置中的经典混合理论进行适当调整,并证明由此产生的混合粘弹性配方的精度。我们利用Volterra 公式的现有结果得出了误差估计,因为所有估计都独立于扰动参数。我们考虑将开发的理论应用到一个粘合弹性的Timoshenko baam中,并报告数字实验,以评估扰动参数的独立性。