Systems and methods to determine elastic properties of materials

• US 7,107,159 B2
• Filed: 03/29/2005
• Issued: 09/12/2006
• Est. Priority Date: 03/29/2004
• Status: Expired due to Fees

• Current Assignee: Peter Thomas German
• Original Assignee: Peter Thomas German
• Inventors: German, Peter Thomas
• Primary Examiner(s): Barlow, John
• Assistant Examiner(s): KUNDU, SUJOY K
• Application Number:
  US11/093,482
• Publication Number:
  US 20050267695A1
• Time in Patent Office: 532 Days
• Field of Search: None
• US Class Current: 702/41
• CPC Class Codes: G01N 2203/0051 Piezoelectric means
• CPC Class Codes: G01N 2203/0075 Strain-stress relations or elastic constants
• CPC Class Codes: G01N 2203/0218 Calculations based on experimental data
• CPC Class Codes: G01N 2291/02827 Elastic parameters, strength or force
• CPC Class Codes: G01N 3/30 by applying a single impulsive force, e.g. by falling weight
• CPC Class Codes: G01N 3/48 by performing impressions under impulsive load by indentors, e.g. falling ball G01N3/54 takes precedence
• CPC Class Codes: H03H 17/025 Notch filters

Abstract

The present invention provides systems and methods to used a measured driving-point response of a nonlinear material to determined one or more elastic properties of the material. The present invention takes advantage of the full information represented by the transient component, the steady-state component, the anharmonic components, and the nonlinear response components of a measured driving-point response of a real nonlinear material, without limitation in the use of large-amplitude forces. The elastic properties are determined by forming and solving a time-domain system of linear equations representing a differential equation model of the driving-point motions of the material. Based on a single, short duration, large-amplitude driving point measurement, both linear and nonlinear properties can be determined; both large-amplitude and near-zero amplitude properties can be determined; and elastic-wave speed and elastic moduli and their variation with depth can be determined.

Claims

1. A system for determining one or more elastic properties of a material, the system comprising:

a first input means for receiving a first input signal representative of a driving force exerted on the material by an actuator at a driving-point;

a second input means for receiving a second input signal representative of a driving-point velocity corresponding to the driving force;

a third input means for receiving a third input signal representative of a driving-point displacement corresponding to the driving force;

a signal generator means for generating a basis function signal for each one of a set of basis functions, the set of basis functions corresponding to the terms of a differential equation model of the motion of the driving-point, and each basis function comprising a function of any one or more of the input signals; and

a processor means for analyzing the set of basis function signals in relation to the first input signal to determine coefficients of a linear combination of the basis function signals which best fits the first input signal, one or more of the coefficients then being representative of a value of one or more elastic properties of the material.

2. The system of claim 1 wherein the material further comprises an in situ material or an isolated sample of material.

3. The system of claim 1 wherein the material further comprises cohesive material, cohesionless material, porous material, drained porous material, undrained porous material, or combinations thereof.

4. The system of claim 1 wherein the material further comprises one or more of the following earth materials:

soil, subsoil, rock, weathered rock, sand, gravel, silt, clay, fill, geologic formations, foundation soil, or combinations thereof.

5. The system of claim 1 wherein the actuator comprises any one of the following types:

a reciprocating actuator, a servo-hydraulic actuator, an electro-dynamic actuator, a seismic vibrator, a rotating mass actuator, or an impulse actuator.

6. The system of claim 1 wherein the differential equation model further comprises a force balance differential equation model of a spring-damper system.

7. The system of claim 6 wherein the differential equation model further comprises a linear spring-damper system, and the coefficient corresponding to the displacement term is then representative of a stiffness property of the material, and the coefficient corresponding to the velocity term is then representative of a viscosity property of the material.

8. The system of claim 6 wherein the differential equation model further comprises a nonlinear spring-damper system represented by polynomial function of driving-point displacement and a polynomial function of driving-point velocity;

and each coefficient corresponding to a displacement term is then representative of a stiffness property of the material, and each coefficient corresponding to a velocity term is then representative of a viscosity property of the material.

9. The system of claim 6 wherein the differential equation model further comprises a force balance differential equation model of a mass-spring-damper system.

10. The system of claim 1 wherein the differential equation model further comprises a displacement-dependent damping term, and the coefficient determined for the function signal corresponding to this term comprises a coefficient of displacement-dependent damping.

11. The system of claim 1 wherein the set of basis function signals further comprises an overdetermined system of linear equations.

12. The system of claim 1 wherein generating a basis function signal further comprises generating a basis function value at a set of distinct times, and wherein the linear combination further comprises a linear combination of the basis function signals which best fits the first input signal at the set of distinct times.

13. The system of claim 12 wherein the set of distinct times further comprises a set of distinct times in time-sequential order, not in time-sequential order, at uniform intervals of time, at non-uniform intervals of time, comprising gaps in time, or a set of times in any combinations thereof.

14. The system of claim 1 further comprising a signal buffer means for storing the set of basis function signals and the first input signal, and further comprising a signal sampling means for retrieving selected time windows of the stored signals and for repeatedly initiating successive analysis of a sequence of selected time windows, thereby determining a series of values of each coefficient, the series of values being representative of one or more elastic properties as a function of time.

15. The system of claim 1 further comprising an amplitude control means adapted for scaling one or more of the basis function signals with a distinct amplitude scale factor, such that two or more of the basis function signals are scaled to approximately the same amplitude level.

16. The system of claim 15 further comprising a descaling means for adjusting the value of each of the coefficients by substantially the same amplitude scale factor applied to the corresponding basis function signal by the amplitude control means.

17. The system of claim 1 wherein analyzing the set of basis function signals further comprises singular value decomposition of a design matrix representative of the function signals to thereby determine the coefficients of the best-fit linear combination.

18. The system of claim 1 further comprising a fourth input signal representative of a driving-point acceleration corresponding to the driving force.

20. The system of claim 1 further comprising:

a phase detector for generating a phase-sample timing signal representative of a sequence of times corresponding to substantially equal intervals of phase of a phase reference signal, wherein the equal intervals of phase comprise an integer number N of phase intervals per cycle of the phase reference signal;

a sampler for sampling an input signal at the sequence of times corresponding to the phase-sample timing signal, thereby generating a phase-sampled signal; and

a filter adapted for filtering the phase-sampled signal to generate a filtered signal, wherein, the filter is adapted to either attenuate or preserve each of one or more selected signal components.

21. The system of claim 20 further comprising a re-sampler adapted to resample the filtered signal at uniform intervals of time, to produce a re-sampled time series output signal.

22. The system of claim 20 wherein the selected signal components further comprise one or more harmonic multiples of the fundamental frequency of the phase reference signal, such that the filter response function comprises a magnitude response either substantially equal to zero or substantially equal to unity at each of the selected harmonic multiples.

23. The system of claim 20 wherein the phase reference signal further comprises a parametric representation of a function representative of the phase reference signal.

24. The system of claim 20 wherein the phase reference signal further comprises a driving force reference signal.

25. The system of claim 20 wherein the input signal further comprises any one of the following:

a driving-force signal, a driving-point acceleration signal, a driving-point velocity signal, a driving-point displacement signal, or a driving-point motion signal.

19. A system for determining one or more elastic properties of an in situ material, the system comprising:

a first input means for receiving a first input signal representative of a driving force exerted on the material by an dynamic actuator at a driving-point;

a second input means for receiving a second input signal representative of a driving-point velocity corresponding to the driving force;

a third input means for receiving a third input signal representative of a driving-point displacement corresponding to the driving force;

a signal generator means for generating a basis function signal for each one of a set of basis functions, the set of basis functions corresponding to the terms of a force balance differential equation model of the motion of the driving-point, the differential equation model comprising a nonlinear spring-damper system represented by polynomial function of the driving-point displacement and a polynomial function of the driving-point velocity, and each other basis function comprising a function of any one or more of the input signals; and

a processor means for analyzing the set of basis function signals in relation to the first input signal to determine coefficients of a linear combination of the function signals which best fits the first input signal, wherein each coefficient corresponding to a displacement term is then representative of a stiffness property of the material, and each coefficient corresponding to a velocity term is then representative of a viscosity property of the material.