An Efficiency Study of Transient Wave Generation in a Thermoelastic Layer with a Pulsed Laser
Tóm tắt
The efficiency of transient wave generation in a thermoelastic silicon layer excited by a pulsed laser is considered. First a principle-based transfer matrix formulation with relaxation effect, also referred to as the generalized dynamic theory of linear thermoelasticity, is used in obtaining transfer functions between the input heat field and the elements of the thermoelastic state vector. The second sound effect, through this relaxation time term, is included to eliminate the thermal wave travelling with infinite velocity as predicted by the diffusion heat transfer model. By employing the fast Fourier transform (FFT) algorithm, the transient response of a silicon thermoelastic layer under a thermal excitation (by a pulsed laser) is investigated to quantify the conversion efficiency from thermal to mechanical energy. The transient acceleration, stress, heat, temperature, and mechanical power flux responses are presented. The pulse duration of the laser excitation is submicrosecond level and, consequently, a large number of modes of motion are excited. Rigid body singularities are eliminated by considering the higher order time derivatives of the state variables. A layer made of bulk silicon under this laser excitation is considered and it is found that the amplitude ratio of the applied heat field to the propagating heat flux at the data points is in the order of 10°. The ratio of the applied power (heat flux) to the generated mechanical power flux is in the order of 10°. The resulting rigid body motion of the layer due to the laser excitation is excluded in calculating the mechanical power.
Tài liệu tham khảo
C. B. Scruby and L. E. Drain, Laser Ultrasonics: Techniques and Applications, Adam Hilger, (1990).
A. Mandelis (Ed.), Non-Destructive Evaluation (NDE), Prentice Hall, (1994).
C. Cetinkaya, Cunli Wu, and Chen Li, “Laser-Based Transient Surface Acceleration for Thermoelastic Layers,” J. Sound Vibration, vol. 231,no. 1, pp. 195-217, (2000).
C. Cetinkaya and Chen Li, “Propagation and Localization of Longitudinal Thermoelastic Waves in Layered Structures,” ASME J. Vibration Acoustics, vol. 122, pp. 263-271, (2000).
H. W. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids, vol. 15, pp. 299-309, (1967).
V. Peshkov, “Second Sound in He II” (in Russian), J. Physics, USSR, vol. 8, pp. 131, (1944).
D. D. Joseph and L. Preziosi, “Heat Waves,” Rev. Mod. Phys., vol. 61, pp. 41-73, (1989).
D. D. Joseph and L. Preziosi, “Addendum to the Paper ‘Heat Waves,”’ Rev. Mod. Phys., vol. 62, pp. 375-391, (1990).
L. R. F. Rose, “Point-Source Representative for Laser-Generated Ultrasound,” J. Acoust. Soc. Amer., vol. 75,no. 3, pp. 723-732, (1984).
B. A. Boley, “Survey of Recent Developments in the Fields of Heat Conduction in Solids and Thermoelasticity,” Nucl. Engineer. Design, vol. 18, pp. 377-399, (1972).
D. S. Chandrasekharaiah, “Thermoelasticity with Second Sound: A Review,” Appl. Mech. Rev., vol. 39, pp. 355-376, (1986).
D. S. Chandrasekharaiah, “Hyberbolic Thermoelasticity: A Review of Recent Literature,” Appl. Mech. Rev., Pt 1, vol. 51, pp. 705-729, (1998).
M. A. Hawwa and A. H. Nayfeh, “Thermoelastic Waves in a Laminated Composite with a Second Sound Effect,” J. Appl. Phys., vol. 80,no. 5, pp. 2733-2738, (1996).
C. Sve and J. Miklowitz, “Thermally Induced Stress Waves in an Elastic Layer,” J. Appl. Mech., March, pp. 161-167, (1973).
J. B. Spicer, “Laser Ultrasonics in Finite Structures: Comprehensive Modeling with Supporting Experiment”, Doctoral dissertation, Johns Hopkins University, (1991).
F. A. McDonald, “On the Precursor in Laser-Generated Ultrasound Waveforms in Metals,” Appl. Phys. Lett., vol. 56,no. 3, pp. 230-232, (1990).
C. Cetinkaya and A. F. Vakakis, “Transient Axisymmetric Stress Wave Propagation in Weakly Coupled Layered Structures,” J. Sound Vibration, vol. 194, pp. 389-416, (1996).
T. Kundu and A. K. Mal, “Elastic Waves in a Multilayered Solid due to a Dislocation Source,” Wave Motion, vol. 7, pp. 459-471, (1985).
A. K. Mal, “Wave Propagation in Layered Composite Laminates Under Periodic Surface Loads,” Wave Motion, vol. 10, pp. 257-266, (1988).
W. T. Thomson, “Transmission of Elastic Waves Through a Stratified Solid Medium,” J. Appl. Phys., vol. 21, pp. 89-93, (1950).
N. A. Haskell, “The Dispersion of Surface Waves on Multilayered Media,” Bull. Seismol. Soc. Amer., vol. 54, pp. 17-34, (1953).
A. A. Mohammed Fakir, “An Integration Transformation-Based Numerical Technique for Stress Wave Propagation in Layered Structures,” M. S. thesis, Mechanical Engineering, University of Illinois at Urbana-Champaign, (1995).
C. Cetinkaya, J. Brown, A. A. F. Mohammed, and A. F. Vakakis, “Near Field Transient Axisymmetric Stress Wave Propagation in Layered Structures,” Int. J. Numer. Meth. Engin., vol. 40, pp. 1639-1665, (1997).
James F. Shackelford (Ed.), CRC Materials Science and Engineering Handbook, (3rd ed.) William Alexander, p. 340, (2000).
Language Reference Manual, DIGITAL Fortran, Digital Corp., (1997).