Keywords: harmonic coupled finite strip method, numerical analysis, accuracy of numerical evaluation, meta-programming, multithreading, parallelization, basic functions, roots of characteristic equations.

This paper presents the hybrid software solution for solving the characteristic equations of the basic functions, used in harmonic coupled finite strip method (HCFSM). Functions are defined by the equation for the normal modes of a uniform beam under transverse free vibration. Some variants of beam’s boundary conditions involve hyperbolic sine and cosine functions, whose usage leads to exponential growth of rootfinding errors as mode increases. Also, there isn’t a single root-finding solver suitable for all boundary conditions. We found solution in arbitrary-precision floating point arithmetic, in framework for selecting best solver for any given boundary condition and in extensive parallelisation.

The obtained roots of characteristic equations are then used for solving the problem of free vibration, which requires calculating definite integrals over basic functions, as defined by HCFSM. The lengths (upper limit) of these definite integrals can be normalised due to their integrand formulation, so it is practical to create a table of pre-calculated normalised integrals. Generating this table is computationally and time expensive, and parallelisation is used on this stage too.

Every aspect of the software implementation is covered by tests, over 4400 in total, which help us assure the correctness of the hybrid method and its reference implementation.

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