Using the Modal and Trigonometric Collocation Methods in Rotor Dynamic Systems

This article deals with the computational modeling of nonlinear rotor dynamic systems. The theoretical basis of the modal method, and combination with the method of dynamic compliances supplemented by the method of trigonometric collocation, is presented. The main analysis is focused on the solutions of transient and steady state responses. The algorithms for solving this range of problems are presented. The finite element method is the basis for both methods. The theoretical analysis is supplemented with a solution of an example model.

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Using the Modal Method in Rotor Dynamic Systems

International Journal of Rotating Machinery ◽

10.1155/s1023621x03000174 ◽

2003 ◽

Vol 9 (3) ◽

pp. 181-196

Author(s):

Eduard Malenovský

Keyword(s):

Finite Element Method ◽

Collocation Method ◽

Dynamic Systems ◽

Theoretical Basis ◽

The Finite Element Method ◽

Transient Responses ◽

Technical Application ◽

Trigonometric Collocation ◽

Rotor Dynamic ◽

Modal Method

This article deals with computational modeling of nonlinear rotor dynamic systems. The theoretical basis of the method of dynamic compliances and the modal method, supplemented by the method of trigonometric collocation, are presented. The main analysis is focused on the solutions of the eigenvalue problem and steady-state and transient responses. The algorithms for solving this range of problems are presented. The finite element method, the method of dynamic compliances, and the modal method are supplemented by the trigonometric collocation method. The theoretical analysis is supplemented by the solution of a model task, which is focused on the application of the trigonometric collocation method. The solution of a technical application, which is a pump, is presented in this article.

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Periodic Solutions in Rotor Dynamic Systems With Nonlinear Supports: A General Approach

Journal of Vibration and Acoustics ◽

10.1115/1.3269840 ◽

1989 ◽

Vol 111 (2) ◽

pp. 187-193 ◽

Cited By ~ 51

Author(s):

C. Nataraj ◽

H. D. Nelson

Keyword(s):

Dynamic Systems ◽

Original Problem ◽

Squeeze Film ◽

Algebraic Equations ◽

Trigonometric Collocation ◽

Nonlinear Algebraic Equations ◽

The Stability ◽

Future Work ◽

Rotor Dynamic ◽

Large Rotor

A new quantitative method of estimating steady state periodic behavior in nonlinear systems, based on the trigonometric collocation method, is outlined. A procedure is developed to analyze large rotor dynamic systems with nonlinear supports by the use of the above method in conjunction with Component Mode Synthesis. The algorithm discussed is seen to reduce the original problem to solving nonlinear algebraic equations in terms of only the coordinates associated with the nonlinear supports and is a big improvement over commonly used integration methods. The feasibility and advantages of the procedure so developed are illustrated with the help of an example of a typical rotor dynamic system with an uncentered squeeze film damper. Future work on the investigation of the stability of the periodic response so obtained is outlined.

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Trigonometric Collocation for Computation of Steady State Responses of Cracked Structures

Volume 12: Vibration, Acoustics and Wave Propagation ◽

10.1115/imece2012-86682 ◽

2012 ◽

Author(s):

Bakeer Bakeer ◽

Oleg Shiryayev ◽

Ammaar Tahir

Keyword(s):

Steady State ◽

Fatigue Cracks ◽

Equations Of Motion ◽

Dynamic Responses ◽

Vibration Period ◽

State Response ◽

Trigonometric Collocation ◽

Steady State Responses ◽

Cracked Structures ◽

State Responses

Development of vibration-based structural health monitoring techniques requires the use of various computational methods to predict dynamic responses of damaged structures. The method described in this work can be used for prediction of steady state harmonic responses for structures with fatigue cracks and may have several advantages over alternative techniques. The method appears to be relatively easy to implement and computationally inexpensive. The steady state response of the system at a given number of time points distributed over one vibration period is represented in terms of Fourier series containing higher frequency harmonics. Equations of motion are formulated in the form that allows for easy computation of Fourier coefficients for all terms in the series. Iterative procedure is used for determining the time of stiffness change in order to capture bilinear dynamic behavior. We present results of initial investigation by applying the method to a model of a cantilever beam with a crack.

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