Page 495 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

482 Nonlinear Vibrations Chap. 14

[2] Brock, J. E. “An Iterative Numerical Method for Nonlinear Vibrations,” J. Appl.
Mech. (March 1951), pp. 1-11.
[3] Butenin, N. V. Elements of the Theory of Nonlinear Oscillations. New York: Blaisdell
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[5] Davis, H. T. Introduction to Nonlinear Dijferential and Integral Equations. Washing­
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[6] Duffing, G. Erwugene Schwingungen bei veränderlicher Eigenfrequenz. Braunschweig:
F. Vieweg u. Sohn, 1918.
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& Publishing Co., 1953.
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[9] Minorsky, N. Nonlinear Oscillations. Princeton: D. Van Nostrand Co., 1962.
[10] Rauscher, M. “Steady Oscillations of Systems with Nonlinear and Unsymmetrical
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[11] Stoker, J. J. Nonlinear Vibrations. New York: Interscience Publishers, 1950.

P R O B L E M S

14-1 Using the nonlinear equation
jc + 0
show that if JCj and X2 are solutions satisfying the differential equation, their
superposition (xj + X2) is not a solution.
14-2 A mass is attached to the midpoint of a string of length 2/, as shown in Fig. P14-2.
Determine the differential equation of motion for large deflection. Assume string
tension to be T.

Figure P14-2.

14-3 A buoy is composed of two cones of diameter 2r and height h, as shown in Fig.
PI4-3. A weight attached to the bottom allows it to float in the equilibrium position