Research Report RR-25-347, 3 Fabruary 2025
In many industries, for example aerospace or defense, waveform analysis
is commonly conducted to compute the resonance of physical objects,
with the Finite Element Method (FEM) being the standard approach. The
Finite Difference Method (FDM) is seldom used, and this preference is often
stated without formal justification in the literature. In this work, the accuracy,
feasibility and the time of simulation of FEM and FDM are compared
by simulating the vibration of a guitar string. Python simulations for both
methods are implemented, and their results are compared against analytical
solutions and experimental data. Additionally, FDM is applied to analyze
the sound of a cycling bell to assess its reliability compared to a real cycling
bell. Final results show that both FEM and FDM yield similar error margins
and accurately predict the system’s behavior. Moreover, the error from
FEM and FDM follow the same periodicity with a phase shift when varying
the assumed analytical tension and without a phase shift when changing the
time interval. However, FEM converges faster with increasing mesh complexity,
whereas FDM demonstrates quicker computational performance and
achieves stable solutions even with bigger time intervals. Despite this, FDM
is limited to simpler configurations and often demands extensive mathematical
formulation, which can become cumbersome for intricate shapes. For
example, modeling a hemispherical object using FDM results in significant
simulation times and big calculations. In conclusion, while FDM may offer
faster convergence and computation times in certain cases, FEM remains the
preferred method in industrial contexts due to its flexibility, scalability, and
ease of implementation for complex geometries.
Type:
Report
Date:
2025-02-03
Department:
Digital Security
Eurecom Ref:
8193
Copyright:
© EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in Research Report RR-25-347, 3 Fabruary 2025 and is available at :
