Young’s Modulus and Poisson’s Ratio via Arbitrary-Geometry Spectrum Matching
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Solution Overview
Problem
Existing methods for determining Young's modulus and Poisson's ratio are limited by the need for specific geometries and assumptions, and struggle with comparing vibrational spectra with different peak counts and frequency scales.
Innovation Solution
A method and system that utilize a global nonlinear optimization to minimize the mismatch between measured and simulated vibrational response spectra, allowing for the determination of Young's modulus and Poisson's ratio in objects of arbitrary geometry without prior assumptions, by adjusting material parameters through a comparison of experimental and theoretical spectra.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional vibrational resonance methods are used to determine Young's modulus and Poisson's ratio, then measurement can be performed, but the method requires assumptions about known material parameters and is limited to specific geometries
Solution Approach 1:
The patent changes the approach from assuming known material parameters to treating them as unknown variables to be optimized. By formulating the problem as an optimization task where Young's modulus and Poisson's ratio are adjusted to minimize the mismatch between measured and simulated spectra, the method eliminates the need for prior assumptions about material properties while maintaining measurement accuracy.
Solution Approach 2:
The patent creates a virtual copy or simulation of the object's vibrational behavior using finite element analysis. By generating a simulated vibrational response spectrum based on geometric data and comparing it with the measured spectrum, the method enables determination of material parameters for objects of any geometry without requiring physical test specimens of specific shapes.
2Adaptability or versatility
If spectral comparison methods are used with different peak counts and frequency scales, then various objects can be analyzed, but the comparison becomes complex and difficult
Solution Approach 1:
The patent replaces the manual or complex algorithmic process of matching individual spectral peaks with an optimization-based approach. Instead of attempting to identify and match corresponding peaks between spectra with different numbers and positions, the method uses global optimization to directly adjust material parameters until the overall spectral mismatch is minimized, automatically handling the complexity of peak correspondence.
Solution Approach 2:
The patent introduces an optimization algorithm as an intermediary between the measured and simulated spectra. This intermediary process automatically handles the complex task of comparing spectra with different characteristics by iteratively adjusting material parameters to minimize the overall mismatch, eliminating the need for direct peak-by-peak comparison.
3Measurement precision
If traditional measurement methods are used, then material parameters can be determined, but specific test sample geometries are required
Solution Approach 1:
The patent creates a universal measurement method that can determine material parameters for objects of any geometry. By using finite element simulation combined with optimization, the method eliminates the need for geometry-specific test specimens. The same procedure can be applied to any object shape, making the measurement technique universally applicable while maintaining accuracy.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Accurately determines Young's modulus and Poisson's ratio with an accuracy of better than 1% for objects of any geometry, applicable to Additive Manufacturing and other varied material parameters, without requiring specific test objects or assumptions beyond linearity.
Implementation Method 1
Methods employed for measurements of Young's modulus and Poisson's ratio often use vibrational resonance-response spectra
Data Source
AI summary
Described herein are systems and methods for Young's modulus and Poisson's ratio determination of an object of arbitrary geometry. A measured vibrational response spectrum of the object is collected, and a simulated vibrational response spectrum of the object is generated. The measured vibrational response spectrum is compared with the simulated vibrational response spectrum. The comparison is treated as a global nonlinear optimization problem. An objective function is proposed to enable comparison of two spectra, which are available on two incompatible frequency scales, and have different number of peaks. The actual values of the Young's modulus and the Poisson's ratio are identified as the best-fitting values that minimize a mismatch between the simulated vibrational response spectrum and the measured vibrational response spectrum. Suitable systems for performing the methods are also provided.