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Transient response of general one-dimensional distributed systems through eigenfunction expansion with an implicit filter scheme

机译：一维分布式系统通过特征函数扩展和隐式滤波器的瞬态响应

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The current work is concerned with eigenfunction expansion of the transient response of general one-dimensional non-self-adjoint distributed dynamic systems. The main goal of the current work is to propose an alternative eigenfunction expansion approach for transient analysis of general one-dimensional non-self-adjoint systems which avoids complex-valued eigenvalue problems. With the implicit filter scheme proposed here one splits the solution into two additive components, namely, a filtered solution for which all boundary conditions are homogeneous and a carefully selected filter. Moreover, the eigenvalue problem associated with the differential equation for the filtered solution is self-adjoint and, therefore, all eigenvalues are real-valued and the eigenfunctions satisfy the classical orthogonality relations. The unknown time-dependent coefficients of the filter are then solved simultaneously with the modal co-ordinates of the filtered solution in order to satisfy the original boundary conditions. The proposed approach is demonstrated on a distributed system composed of a cantilever beam with end mass, viscous damper and linear spring.
机译：当前的工作涉及一般一维非自伴分布动力系统瞬态响应的本征函数扩展。当前工作的主要目的是为通用一维非自伴系统的瞬态分析提出一种替代的本征函数展开方法，该方法可以避免复杂值特征值问题。通过此处提出的隐式过滤器方案，可以将解决方案分为两个加法分量，即所有边界条件均是均值的过滤后解决方案和精心选择的过滤器。此外，与滤波解的微分方程有关的特征值问题是自伴的，因此，所有特征值都是实值，特征函数满足经典的正交关系。然后，将滤波器的未知时间相关系数与滤波后解的模态坐标同时求解，以满足原始边界条件。在由末端质量的悬臂梁，粘性阻尼器和线性弹簧组成的分布式系统上演示了该方法。

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