Hybrid Probabilitic and Convex Modeling of Excitation and Response of Periodic Structures

Mathematical Problems in Engineering

Volumn 2, Issue 2, 1996, Pages 143-163

  Zhu, L P ^a   Elishakoff, I ^a  

^a Florida Atlantic Univ   (United States)

Author keywords

convex modeling; multi span structures; Probabilistic analysis

Indexed keywords

ACOUSTIC EXCITATION; ACOUSTIC LOADING; ACOUSTIC PRESSURE FIELD; ACOUSTIC PRESSURES; BOUNDED PARAMETERS; CLOSED FORM SOLUTIONS; CONVEX MODELING; CONVEX SET; CROSS-SPECTRAL DENSITIES; GAIN INSIGHT; MEAN SQUARE RESPONSE; MULTI-SPANS; PROBABILISTIC ANALYSIS; SPAN BEAMS; TRANSVERSE DISPLACEMENTS; UNCERTAINTY PARAMETERS;

ACOUSTIC WAVE TRANSMISSION; BENDING (DEFORMATION); BENDING MOMENTS; OFFSHORE PIPELINES; SET THEORY; SPECTRAL DENSITY;

PERIODIC STRUCTURES;

EID: 0009450523     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/S1024123X96000282     Document Type: Article

References (17)

1. H. Abramovich and I. Elishakoff, Application of the Krein’s Method for Determination of Natural Frequencies of Periodically Supported Beam Based on Simplified Bresse-Timoshenko Equations, Acta Mechanica 66 (1987), 39–59.
2. M. G. Krein, Vibration Theory of Multi-Span Beams, Vestnik Inzhenerov i Tekhnikov 4 (1933), 142–145 (in Russian).
3. Y. K. Lin, Free Vibration of a Continuous Beam on Elastic Supports, International Journal of Mechanical Sciences 4 (1962), 409–423.
4. J. W. Miles, Vibration of Beams on Many Supports, Journal of Engineering Mechanics 82 (1956), 1–9.
5. G. Sen Gupta, Natural Flexural Wave and the Normal Modes of Periodically-Supported Beams and Plates, Journal of Sound and Vibration 13 (1970), 89–101.
6. Y. K. Lin and T. J. McDaniel, Dynamics of Beam Type Periodic Structures, Journal of Engineering for Industry 93 (1969), 1133–1141.
7. Y. K. Lin, S. Maekawa, H. Nijim, and L. Maestrello, Response of Periodic Beam to Supersonic Boundary-Layer Pressure Fluctuations, in Stochastic Problems in Dynamics B. L. Clarkson, (Ed.), Pitman, 1977, pp. 468–485.
8. D. J. Mead, Free Wave Propagation in Periodically-Supported Infinite Beams, Journal of Sound and Vibration 11 (1970), 181–197.
9. D. J. Mead, Space-Harmonic Analysis of Periodically Supported Beams: Response to Convected Random Loading, Journal of Sound and Vibration 14 (1971), 525–541.
10. D. Li and H. Benaroya, Dynamics of Periodic and Near-Periodic Struvtures, Applied Mechanics Reviews 45 (1992), 447–460.
11. S. T. Ariaratnam and W. C. Xie, On the Localization Phenomenon in Randomly Disordered Engineering Structures, in Nonlinear Stochastic Mechanics N. Bellomo and F. Casciati, (Eds.), Springer New York, 1992, pp. 13–24.
12. C. H. Hodges and J. Woodhouse, Vibration Isolation from Irregularity in a Nearly Periodic Structure: Theory and Measurements, Journal of Acoustical Society of America 74 (1983), 894–905.
13. C. Pierre and E. H. Dowell, Localization of Vibrations due to Structural Irregularity, Journal of Sound and Vibration 114 (1987), 549–564.
14. I. Elishakoff, Y. W. Li, and J. H. Starnes, Jr., Buckling Mode Localization in Elastic Plates Due to Misplacements in the Stiffener Location, An Interdisciplinary Journal of Nonlinear Science: Chaos, Solitons and Fractals 5 (1995), to appear.
15. L. P. Zhu, I. Elishakoff, and Y. K. Lin, Free and Forced Vibrations of Periodic Multi-Span Beams, Journal of Shock and Vibration 1 (1994), 217–232.
16. I. Elishakoff and P. Colombi, Combination of Probability and Convex Models of Uncertainty When Scarce Knowledge Is Present on Acoustic Excitation Parameters, Computer Methods in Applied Mechanics and Engineering 104 (1993), 187–209.
17. I. Elishakoff, Y. K. Lin and L. P. Zhu, Probabilistic and Convex Modeling of Acoustically Excited Structures, Elsevier, Amsterdam, 1994.