The Numerical Assembly Technique for arbitrary planar systems based on an alternative homogeneous solution

TL;DR

This paper extends the Numerical Assembly Technique to arbitrary planar frames, enabling highly accurate natural frequency computations without spatial discretization, using a novel homogeneous solution approach for improved stability.

Contribution

It introduces a new homogeneous solution method within the Numerical Assembly Technique for better stability and accuracy in natural frequency analysis of planar structures.

Findings

Accurate natural frequency computation without spatial discretization.

Improved numerical stability with the novel homogeneous solution.

Validation on two frame structures showing high precision.

Abstract

The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial discretization. To this end, we systematically introduce a frame structure as a set of nodes, beams, bearings, springs, and external loads and formulate the corresponding boundary and interface conditions. As the underlying homogeneous solution of the governing equations, we use a novel approach recently presented in the literature. This greatly improves the numerical stability and allows the stable computation of very high natural frequencies accurately. We show this numerically at two frame structures by investigation of the condition number of the system matrix and also by the use of variable precision arithmetic.