Development and Application of Acoustic Metamaterials with Locally Resonant Microstructures

Transcription

1 Development and Application of Acoustic Metamaterials with Locally Resonant Microstructures AFOSR grant #FA Program manager: Dr. Les Lee PI: C.T. Sun Purdue University West Lafayette, Indiana AFOSR Annual Grantees Meeting Arlington, VA August 2, 2012

2 Report Documentation Page Form Approved OMB No Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 02 AUG REPORT TYPE 3. DATES COVERED to TITLE AND SUBTITLE Development and Application of Acoustic Metamaterials with Locally Resonant Microstructures 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Purdue University,,West Lafayette,IN, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 11. SPONSOR/MONITOR S REPORT NUMBER(S) 13. SUPPLEMENTARY NOTES Presented at the 2nd Multifunctional Materials for Defense Workshop in conjunction with the 2012 Annual Grantees /Contractors Meeting for AFOSR Program on Mechanics of Multifunctional Materials & Microsystems Held 30 July - 3 August 2012 in Arlington, VA. Sponsored by AFRL, AFOSR, ARO, NRL, ONR, and ARL. U.S. Government or Federal Rights License 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Same as Report (SAR) 18. NUMBER OF PAGES 32 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

3 Wave Propagation in Elastic Solids With Negative Mass Density or Modulus What would happen if mass or modulus becomes negative? Dispersion equation: q E i Wave attenuates: u Ae Ae i( qxt ) x e it Is attenuation factor Wave cannot propagate without attenuation in elastic solids with negative mass density or modulus

4 Metamaterials with Local Resonators Composite with Resonators 1D Lattice Model

5 Metamaterials with Negative Effective Mass u Be i( qxt ) Negative effective mass eff, Eeff Wave attenuation eff 0 k m 2 2

6 Acoustic Metamaterial with Negative Effective Young s Modulus A Mechanical Unit Model and Its Representative Elastic Solid

7 Frequency-dependent Modulus (stress-strain curves) (5) Extreme Modulus: Very stiff (4) Negative Modulus E eff (1) Static Modulus (1) Static Modulus 0 k2 / m2 Is local resonance frequency Strain (3) Extreme Modulus: Very soft

8 Wave Attenuation in Metamaterial with Negative Effective Modulus Wave amplitude decays when its frequency falls inside the band gap, especially if frequency is near the frequency

9 Metamaterial with Double Negativity (DN) Metamaterial with negative mass density (NMD) Metamaterial with negative modulus (NEM) Double Negativity (green area) Negative effective mass (Band Gap, red area) Negative effective modulus (Band Gap, red area) Metamaterial with Double Negativity (DN)

10 Wave Propagation in Metamaterial with Double Negativity NMD /

11 Double Positive Metamaterial T* = ON 0 ; -1 ~.... ~ D X D y PURDUE U N I V E R S I T Y..

12 Double Negative Metamaterial

13 Derivation for Reflection and Transmission Coefficients Material 1 Material 2 u i u u t r Assume x 0 u u u i r t uˆ e i uˆ e uˆ e t r i( tq x) 1 i( tq x) 2 1 i( tq x) uˆ r E q E q R u ˆ E q E q T i uˆ t 2Eq 1 1 uˆ E q E q i If E E,, then R 0, T If E E,, then R 0, T

14 Material 1 (Regular Material) Material 2 Material 2 (Metamaterial) Material 1 (Regular Material) 0MOD k m 2 2 E eff 2 L 1 k2 L k1 2 2 A 2 0MOD D ( )( )( ) 2 eff 1 m AL ( ) 2 0MASS 1m MASS 0MASS A 1 k m 3 3

15 Material 1 Material 1 (Ordinary Material) Material 2 (Metamaterial) Material 1 (Ordinary Material) E eff kl A m AL 4 4 eff where A 1

16 Frequncy 2500 Dispersion Curve for Metamaterial Dispersion Curve Negative Mass Region DN Region Non-dimensionalized wave number ql OP2 OP1 AC

17 Material Design Case1: 1200 ( rad / s) Case 2: 650 ( rad / s) Frequency for double negativity Frequency for negative mass m m m m ( kg) ( kg) ( kg) ( kg) k ( N / mm) 1 k ( N / mm) 2 k ( N / mm) 3 k ( N / mm) 4

18 Displacement (mm) Case 1: Simulation Result in DN Region 1200 rad / s Material 1 (Regular Material) Material 2 (Metamaterial) Material 1 (Regular Material) Distance in number of unit cells t Distance in number of unit cells 0.07 s t s t s Distance in number of unit cells

19 Displacement (mm) Case 2: Simulation Result in Negative Mass Region 650 rad / s Material 1 (Regular Material) Material 2 (Metamaterial) Material 1 (Regular Material) Distance in number of unit cells Distance in number of unit cells t s t s t s

20 Refraction of Metamaterials 2D Double-Negativity Metamaterial y x θ Negative refraction θ Positive refraction Metamaterial Normal medium

21 Boundary Condition: Plane wave Metamaterial Normal medium

22 Simulation Window (15x20 units) Interface Negative refraction Normal to interface Positive refraction

23 U, Magnitude e e e e e e e e e e e e 04 +O.OOOe +OO Step: Step l Frame : Total Time: DN ODB: WaveProp_Gen.odb

24 71e-03 98e-03 26e-03 S3e-03 81e-03 08e-03 3Se-03 28e-04 03e-04 77e-04 Sle-04 26e-04 OOe+OO DP y t ODB : WaveProp_Gen.odb

25 Simulation: Plane wave (DN region: 1) Interface Normal to interface

26 Simulation: Plane wave (DN region: 2) Interface Normal to interface

27 Simulation: Plane wave (DN region: 3) Interfac e Normal to interface

28 Simulation: Plane wave (DN region: 4) Interfac e Normal to interface

29 Simulation: Plane wave (DP region: 1) Interface Normal to interface

30 Simulation: Plane wave (DP region: 2) Interface Normal to interface

31 Simulation: Plane wave (DP region: 4) Interface Normal to interface

32 Plane Wave Comparison: DN vs. DP Double Negativity Double Positivity Interface Interface

33 List of Publications H. H. Huang and C. T. Sun, Locally Resonant Acoustic Metamaterials with 2D Anisotropic Effective Mass Density, Philosophical Magazine, Vol. 91, No.6, 2011, pp H. H. Huang and C. T. Sun, A study of Band-gap Phenomena of Two Locally Resonant Acoustic Metamaterials, J. Nanoengineering and Nanosystems, X. N. Liu, G. K. Hu, C.T. Sun, and G. L. Huang, Wave Propagation Characterization and Design of Two-Dimensional Elastic Chiral Metacomposite, J. of Sound and Vibration, 330, pp , 2011 X.N. Liu, G. K. Hu, G. L. Huang, and C.T. Sun, An Elastic Metamaterial with Simultaneously Negative Mass Density and Bulk Modulus, Applied Physics Letters, 98, , H.H. Huang and C.T. Sun, Behavior of an Acoustic Metamaterial with Extreme Young s Modulus, J. Mechanics and Physics Solids, doi: /j.jmps , R. Zhu, G. L. Huang, H.H. Huang, and C. T. Sun, Experimental and Numerical Study of Guided Wave Propagation in a Thin Metamaterial Plate, Physics Letters A, 375,, 2011, pp H.H. Huang and C.T. Sun, Continuum Modeling of a Composite Material with Internal Resonators, Mechanics of Materials, 46, 2012, pp Hsin-Haou Huang and C. T. Sun, "Anomalous Wave Propagation in a One-dimensional Acoustic Metamaterial Having Simultaneously Negative Mass Density and Young's Modulus, to appear in the Journal of the Acoustical Society of America, 2012