Elastic Plate Material Property Estimation via Frequency Response
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Solution Overview
Problem
Current methods for estimating complex Young's and shear moduli of materials are inaccurate below 15 kHz and fail to provide reliable measurements in the 4 kHz to 8 kHz frequency range, particularly for elastic plates.
Innovation Solution
A laboratory test method that involves measuring the experimental frequency response transfer function of normal velocity to input force, converting it to normal displacement divided by force, and using a modeled frequency response transfer function to calculate material properties by minimizing error function values, allowing for simultaneous estimation of complex Young's and shear moduli in the 1 kHz to 10 kHz range.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If acoustic methods are used to estimate mechanical properties, then measurement can be performed, but accuracy deteriorates below 15 kHz due to acoustic diffraction
Solution Approach 1:
The patent changes the measurement parameters by using frequency response functions measured at multiple discrete frequencies (4-8 kHz range) and transforming them to the wave-vector domain, rather than using traditional acoustic methods that fail at these frequencies. This parameter transformation allows accurate estimation despite the frequency limitations of conventional acoustic techniques.
2Measurement precision
If resonant techniques are used to measure stiffness and loss properties, then eigenvalues can be measured, but the method requires well defined eigenvalues and eigenvectors which limits applicability
Solution Approach 1:
The patent replaces the traditional resonant technique approach (which relies on mechanical eigenvalue analysis) with a frequency response function approach in the wave-vector domain. This substitution eliminates the need for well-defined eigenvalues and eigenvectors while still enabling measurement of stiffness and loss properties through a more flexible mathematical framework.
3Measurement precision
If wave based methods are used on beams to estimate mechanical parameters, then damping and loss can be measured, but the method is limited to beam geometries and cannot be applied to plates
Solution Approach 1:
The patent creates a universal method that works for plate geometries by developing frequency response functions specifically for plate structures and transforming them to the wave-vector domain. This universal approach enables measurement of damping and loss in plates (not just beams) by using a standardized procedure that can be applied to any plate configuration.
4Measurement precision
If DMA is used to measure material properties, then displacement and force can be measured, but frequency range is limited to 0.01-200 Hz and transformation to higher frequencies is inaccurate
Solution Approach 1:
Instead of transforming low-frequency DMA data to high frequencies (which is inaccurate), the patent inverts the approach by directly measuring frequency response at the target high frequencies (4-8 kHz) and using wave-vector domain transformation to extract material properties. This inversion eliminates the need for inaccurate frequency transformation while expanding the measurable frequency range.
Data Source
AI summary
A method is provided for increasing accuracy in measuring complex Young's modulus and complex shear modulus of a material using a processing system. The material is tested to obtain an experimental frequency response transfer function of normal displacement to input force. A model panel is developed in the processing system as a modeled frequency response transfer function. The modeled transfer function is used at a range of fixed frequencies to calculate displacements of the model panel divided by the input force while varying material parameters. The modeled frequency response transfer function is compared with the experimental frequency response transfer function to compute error function values. These values indicate the most accurate material property values as those minimizing the computed error function values.