NON-LINEAR VIBRATION OF CABLE–DAMPER SYSTEMS PART I: FORMULATION

✍ Scribed by Z. YU; Y.L. XU

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 156 KB
• Volume: 225
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2203

✦ Synopsis

This paper presents a formulation for determining the non-linear dynamic response of sag cables equipped with discrete oil dampers and subject to harmonic loading. The state-space method is "rst employed to convert the second order non-linear partial di!erential equations of motion of the system to "rst order non-linear partial di!erential equations. Then, in terms of the complex modes of vibration and their orthogonality properties achieved by a hybrid method, the generalized modal superposition method is used to reduce the "rst order non-linear partial di!erential equations to "rst order non-linear ordinary di!erential equations with respect to time functions only. Finally, the harmonic balance method is applied to obtain the non-linear algebraic equations, from which the real solutions for the time functions and non-linear dynamic responses of the cable}damper system are found. The application and veri"cation of the suggested approach are presented in Part II of this paper.

where x, y and z are the Cartesian co-ordinates in the horizontal, vertical and lateral directions respectively (see Figure 1); u, w and v are the cable dynamic displacement components in the x, y and z directions respectively, measured from 448 Z. YU AND Y. L. XU

where E is the cable elastic modulus and A the cable cross-sectional area.