# US 2022/0034848 A1 · Young's modulus and poisson's ratio determination in objects of arbitrary geometry systems and methods

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 2022/0034848 A1
- Document ID: US20220034848A1
- Status: Published application
- Kind: A1
- Application number: 17/388,515
- Filed: 2021-07-29
- Published: 2022-02-03
- Earliest claimed: 2020-07-29
- Assignees: MetroLaser, Inc.
- Applicants: Metrolaser, Inc.
- Inventors: Andrei K. Dioumaev
- Web page: https://patentgrep.com/patent/US20220034848A1

## CPC

- G01N 29/045: {by imparting shocks to the workpiece and detecting the vibrations or the acoustic waves caused by the shocks (measuring resonant frequency G01H13/00; measuring strength properties by application of mechanical stress G01N3/00)}
- G01N 29/2437: {Piezoelectric probes}
- G01N 29/4418: {with a model, e.g. best-fit, regression analysis}
- G01N 29/4472: {Mathematical theories or simulation}
- G01N 29/46: by spectral analysis, e.g. Fourier analysis {or wavelet analysis (spectral signal processing per se G06F17/14)}
- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- G01N 2291/02827: Elastic parameters, strength or force
- G06F 2119/14: Force analysis or force optimisation, e.g. static or dynamic forces
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

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.

## Claims

### Claim 1

A method comprising:
collecting a measured vibrational response spectrum of an object under defined experimental conditions;
generating a simulated vibrational response spectrum of the object; and
identifying a Young's modulus and a Poisson's ratio that minimize a mismatch between the simulated vibrational response spectrum and the measured vibrational response spectrum.

### Claim 2 (depends on 1)

The method of claim 1, further comprising comparing two spectra that differ in the number of peaks and are available on two inconsistent frequency scales.

### Claim 3 (depends on 2)

The method of claim 2, further comprising creating an objective function for optimization based on a correlation coefficient.

### Claim 4 (depends on 1)

The method of claim 1, further comprising minimizing a mismatch between the measured vibrational response spectrum and the simulated vibrational response spectrum by optimizing both the Young's modulus and the Poisson's ratio.

### Claim 5 (depends on 4)

The method of claim 4, wherein the minimizing comprises using a stochastic search engine to solve a nonlinear least squares optimization in the space of multiple local minima.

### Claim 6 (depends on 1)

The method of claim 1, further comprising discriminating between measured peaks that do and do not originate from the object.

### Claim 7 (depends on 6)

The method of claim 6, wherein the discriminating comprises:
defining a threshold in the overlap level that subdivides the peaks into a first set of peaks originating from the object and a second set of peaks originating from suspected artifacts; and
performing a linear regression on the first set of peaks.

### Claim 8

A method of determining Young's modulus and Poisson's ratio of an object, the method comprising:
collecting a measured vibrational response spectrum of the object;
comparing the measured vibrational response spectrum with a simulated vibrational response spectrum; and
identifying a Young's modulus and a Poisson's ratio that minimize a mismatch between the simulated vibrational response spectrum and the measured vibrational response spectrum.

### Claim 9 (depends on 8)

The method of claim 8, further comprising generating the simulated vibrational response spectrum of the object, wherein the generating comprises predicting a vibrational response using a finite element method.

### Claim 10 (depends on 8)

The method of claim 8, wherein the comparing comprises creating an objective function for optimization based on a correlation coefficient.

### Claim 11 (depends on 10)

The method of claim 10, wherein the identifying comprises evaluating by nonlinear optimization the values of the Young's modulus and the Poisson's ratio that yield the global minimum of the objective function.

### Claim 12 (depends on 8)

The method of claim 8, further comprising minimizing a mismatch between the measured vibrational response spectrum and the simulated vibrational response spectrum by optimizing both the Young's modulus and the Poisson's ratio.

### Claim 13

A system comprising:
a non-transitory memory storing instructions; and
one or more hardware processors configured to execute the instructions that causes the system to perform operations comprising:
collecting a measured vibrational response spectrum of an object;
generating a simulated vibrational response spectrum of that object; and
minimizing a mismatch between the simulated vibrational response spectrum and the measured vibrational response spectrum by simultaneously optimizing both a Young's modulus and a Poisson's ratio using a nonlinear global optimization.

### Claim 14 (depends on 13)

The system of claim 13, wherein the operations further comprise comparing the measured vibrational response spectrum with the simulated vibrational response spectrum.

### Claim 15 (depends on 14)

The system of claim 14, wherein the comparing comprises:
transforming the measured vibrational response spectrum into a table of measured peaks;
using a table of simulated peaks from the simulated vibrational response spectrum; and
creating a spectrum with peaks of equal height and width from both the table of simulated peaks and the table of measured peaks.

### Claim 16 (depends on 14)

The system of claim 14, wherein the comparing is performed directly on the full spectra of the measured vibrational response spectrum and the simulated vibrational response spectrum.

### Claim 17 (depends on 14)

The system of claim 14, wherein the comparing comprises creating an objective function for optimization based on a correlation coefficient.

### Claim 18 (depends on 17)

The system of claim 17, wherein the operations further comprise identifying best-fitting values of the Young's modulus and the Poisson's ratio at a global minimum obtained by nonlinear optimization of the objective function.

### Claim 19 (depends on 13)

The system of claim 13, further comprising a laser doppler vibrometer configured to measure vibration of the object at one or more points on the object.

### Claim 20 (depends on 13)

The system of claim 13, further comprising:
a piezo-electric vibrator that provides excitation of the object over a wide frequency range; or an acoustic source that provides excitation of the object in a noncontact manner.