An approach to investigate the instability of the multiple-degree-of-freedom parametric dynamic systems

✍ Scribed by K. Takahashi

• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 543 KB
• Volume: 78
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(81)80122-8

✦ Synopsis

A new analytical approach to the investigation of the regions of instability of multiple-degree-of-freedom parametric dynamic systems is presented. Upon assuming a solution as a product of a characteristic component and a vector which has a periodic component, expanding this vector into a Fourier series and substituting it into the governing equations of motion, a system of homogeneous algebraic equations can be obtained by the harmonic balance method. Then the problem of the stability of the non-trivial solutions results in an eigenvalue problem of a non-symmetric matrix. Numerical results are presented for an undamped and damped Mathieu equation whose stability has been investigated by various methods of solution. The method has been applied to multiple-degree-of-freedom systems such as lateral bending-torsional vibration of a thin beam under parametric excitation and the parametric instability of a column under periodically varying axial loads.