具有Zener粘弹性地基和分布力的Euler-Bernoulli模型的广义解
Generalized solutions for the Euler-Bernoulli model with Zener viscoelastic foundations and distributional forces
摘要：
本文研究粘弹性地基上具有不连续弯曲刚度的Euler-Bernoulli梁模型的初边值问题，该梁模型同时受Dirac型轴向力和外载荷作用.相应的模型方程为四阶偏微分方程，其系数不连续且为分布函数，且存在分布右端。此外，粘弹性基础是齐纳型和描述的分数阶微分方程关于时间。我们展示了如何将抽象变分问题的泛函分析方法与正则化技术相结合来证明广义解的存在性和唯一性。
英文摘要：
We study the initial-boundary value problem for an Euler-Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The corresponding model equation is fourth order partial differential equation and involves discontinuous and distributional coefficients as well as a distributional right-hand side. Moreover the viscoelastic foundation is of Zener type and described by a fractional differential equation with respect to time. We show how functional analytic methods for abstract variational problems can be applied in combination with regularization techniques to prove existence and uniqueness of generalized solutions.
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