Modern Analytical Methods Applied to Mechanical Engineering Systems

In the following lectures modern analytical methods are applied to several industrial systems. The first application is the use of singular perturbation analysis in the eigenvalue problem of a vibrating string with a small bending stiffness. This models the behavior of overhead transmission lines. A more complicated system is the eigenvalue problem of a cylinder vibrating in an cylindrical duct, which is filled with a viscous fluid.

[1]  Peter Hagedorn,et al.  Bonding stresses between piezoelectric actuators and elastic beams , 1997, Smart Structures.

[2]  B. Schäfer,et al.  Dynamical modelling of wind-induced vibrations of overhead lines☆ , 1984 .

[3]  H. F. Tiersten,et al.  Linear Piezoelectric Plate Vibrations , 1969 .

[4]  Fluid mechanics and singular perturbations , 1967 .

[5]  L. Segel,et al.  Introduction to Singular Perturbations. By R. E. O'MALLEY, JR. Academic Press, 1974. $ 16.50. , 1975, Journal of Fluid Mechanics.

[6]  T. J. Moran,et al.  Finite-Element Solution of Added Mass and Damping of Oscillation Rods in Viscous Fluids , 1979 .

[7]  Vimal Singh,et al.  Perturbation methods , 1991 .

[8]  J.D. Cole: Perturbation Methods in Applied Mathematics, Blaisdell-Hall, 1968, 260頁, 16×24cm, 5,080円. , 1969 .

[9]  Peter Hagedorn,et al.  On the energy dissipation in spacer dampers in bundled conductors of overhead transmission lines , 1995 .

[10]  J. Wallaschek.  Piezoelectric Ultrasonic Motors , 1995 .

[11]  Thomas Staubli.  Untersuchung der oszillierenden Kräfte am querangeströmten, schwingenden Kreiszylinder , 1983 .

[12]  J. A. Jendrzejczyk,et al.  Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids , 1976 .

[13]  Giorgio Diana,et al.  On the forces transmitted to a vibrating cylinder by a blowing fluid , 1971 .

[14]  W. Reichardt,et al.  L. Cremer, Vorlesungen über Technische Akustik. XIII + 334 S. m. 177 Abb. Berlin/Heidelberg/New York 1971. Springer-Verlag. Preis brosch. DM 29.40 , 1972 .

[15]  W. Eckhaus.  Matched Asymptotic Expansions and Singular Perturbations , 1973 .

[16]  Edmund Taylor Whittaker,et al.  A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS , 1988 .

[17]  L. Cremer,et al.  Vorlesungen über technische Akustik , 1971 .

[18]  W. Seemann,et al.  Stresses in a Thin Piezoelectric Element Bonded to a Half-Space , 1997 .

[19]  Peter Hagedorn.  Ein einfaches Rechenmodell zur Berechnung winderregter Schwingungen an Hochspannungsleitungen mit Dämpfern , 1980 .

[20]  Peter Hagedorn,et al.  On the computation of damped wind-excited vibrations of overhead transmission lines , 1982 .

[21]  J. Horáček,et al.  Acoustic-structural coupling ofvibrating cylindrical shells with flowing fluid , 1991 .

[22]  R. Ibrahim.  Book Reviews : Nonlinear Oscillations: A.H. Nayfeh and D.T. Mook John Wiley & Sons, New York, New York 1979, $38.50 , 1981 .

[23]  Peter Hagedorn,et al.  Stochastic field processes in the mathematical modelling of damped transmission line vibrations , 1987 .

[24]  P. Hagedorn,et al.  A simple variational approach to a converse of the Lagrange-Dirichlet theorem , 1992 .

[25]  Peter Hagedorn,et al.  TRAVELLING WAVE ULTRASONIC MOTORS, PART I: WORKING PRINCIPLE .AND MATHEMATICAL MODELLING OF THE STATOR , 1992 .

[26]  F. B. Farquharson,et al.  Wind Tunnel Investigation of Conductor Vibration with Use of Rigid Models [includes discussion] , 1956, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[27]  M. P. Païdoussis,et al.  A theoretical study of the stability of cantilevered coaxial cylindrical shells conveying fluid , 1991 .

[28]  P. Hagedorn.  Die umkehrung der stabilitätssätze von Lagrange-Dirichlet und Routh , 1971 .

[29]  W. Eckhaus.  Asymptotic Analysis of Singular Perturbations , 1979 .