Characterizing the Dynamic Response of a Thermally Loaded, Acoustically Excited Plate

Abstract In this work the dynamic response is considered of a homogeneous, fully clamped rectangular plate subject to spatially uniform thermal loads and narrow-band acoustic excitation. In both the pre-and post-buckled regimes, the small amplitude, linear response is confirmed. However, the primary focus is on the large amplitude, non-linear, snap-through response, because of the obvious implications for fatigue in aircraft components. A theoretical model is developed which uses nine spatial modes and incorporates initial imperfections and non-ideal boundary conditions. Because of the higher order nature of this model, it is inherently more complicated than a one-mode buckled beam equation (Duffing's equation). An experimental system was developed to complement the theoretical results, and also to measure certain system parameters for the model which are not available theoretically. Several analysis techniques are used to characterize the response. These include time series, power spectra and autocorrelation functions. In addition, the fractal dimension and Lyapunov exponents for the response are computed to address the issue of spatial dimension and temporal complexity (chaos), respectively. Comparisons between theory and experiment are made and show considerable agreement. However, these comparisons also serve to point out difficulties in computing the fractal dimension and Lyapunov exponents from experimental data.

[1]  E. F. Daniels,et al.  Capabilities of the thermal acoustic fatigue apparatus , 1992 .

[2]  Theiler,et al.  Efficient algorithm for estimating the correlation dimension from a set of discrete points. , 1987, Physical review. A, General physics.

[3]  William H. Press,et al.  Numerical recipes , 1990 .

[4]  E. Dowell.  Nonlinear oscillations of a fluttering plate. II. , 1966 .

[5]  Richard Vynne Southwell,et al.  On the analysis of experimental observations in problems of elastic stability , 1932 .

[6]  Phillip L. Gould.  Dynamics of structures: (theory and applications to earthquake engineering): Anil K. Chopra Prentice-Hall, Englewood Cliffs, NJ, 1995, 729pp , 1995 .

[7]  Sherman A. Clevenson,et al.  High-Intensity Acoustic Tests of a Thermally Stressed Plate , 1991 .

[8]  John Dugundji,et al.  Nonlinear Vibrations of a Buckled Beam Under Harmonic Excitation , 1971 .

[9]  Francis C. Moon,et al.  Chaotic and fractal dynamics , 1992 .

[10]  Leonard Meirovitch,et al.  Elements Of Vibration Analysis , 1986 .

[11]  C. Ng,et al.  Nonlinear and snap-through responses of curved panels to intense acoustic excitation , 1989 .

[12]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[13]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[14]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[15]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[16]  D. Ruelle,et al.  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems , 1992 .

[17]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[18]  Lawrence E. Kinsler,et al.  Fundamentals of acoustics , 1950 .

[19]  Biman Das,et al.  Calculating the dimension of attractors from small data sets , 1986 .

[20]  D. J. Mead.  Elements of Vibration Analysis, Second Edition, Leonard Meirovitch. McGraw-Hill Book Company, New York (1986) , 1987 .

[21]  Earl H. Dowell,et al.  Comparison of theory and experiment for nonlinear flutter of loaded plates , 1970 .

[22]  C. Chia.  Nonlinear analysis of plates , 1980 .

[23]  J. Yorke,et al.  Dimension of chaotic attractors , 1982 .

[24]  K. Zaman,et al.  Nonlinear oscillations of a fluttering plate. , 1966 .

[25]  Earl H. Dowell,et al.  Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system , 1982 .

[26]  B. B. Bauer,et al.  Fundamentals of acoustics , 1963 .

[27]  D. Newland.  An introduction to random vibrations and spectral analysis , 1975 .