A modal superposition method for non-linear structures

Date

1996-01-25

Author

Kuran, B
Özgüven, Hasan Nevzat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

147
views

0
downloads

The dynamic response of multi-degree of freedom (MDOF) non-linear structures is usually determined by the numerical integration of equations of motion. This is computationally very costly for steady state response analysis. In this study, a powerful and economical method is developed for the harmonic response analysis of non-linear structures. In this method, the equations of motion are first converted into a set of non-linear algebraic equations, and then the number of equations to be solved is reduced by employing linear modes of the system. The resulting coupled algebraic equations are solved iteratively. The concept of the pseudo-receptance matrix is introduced in calculating the steady state response. It is shown that the reduction in computational time can be considerable as very accurate results can be obtained by using only a limited number of modes. Several example problems are solved in order to illustrate the performance of the method. Effects of higher modes and higher harmonic components of the response are discussed in detail. In order to illustrate the accuracy and speed of the method suggested, the results obtained by applying the so called Iterative Modal Method are compared with those obtained by the Newmark method which is used as a classical time domain analysis technique. (C) 1996 Academic Press Limited

Subject Keywords

Mechanical Engineering, Acoustics and Ultrasonics, Mechanics of Materials, Condensed Matter Physics

URI

https://hdl.handle.net/11511/36099

Journal

JOURNAL OF SOUND AND VIBRATION

DOI

https://doi.org/10.1006/jsvi.1996.0022

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

A NEW METHOD FOR HARMONIC RESPONSE OF NONPROPORTIONALLY DAMPED STRUCTURES USING UNDAMPED MODAL DATA Özgüven, Hasan Nevzat (Elsevier BV, 1987-09-08) A method of calculating the receptances of a non-proportionally damped structure from the undamped modal data and the damping matrix of the system is presented. The method developed is an exact method. It gives exact results when exact undamped receptances are employed in the computation. Inaccuracies are due to the truncations made in the calculation of undamped receptances. Numerical examples, demonstrating the accuracy and speed of the method when truncated receptance series are used are also presented. ...
THE RESIDUAL VARIABLE METHOD APPLIED TO ACOUSTIC-WAVE PROPAGATION FROM A SPHERICAL SURFACE AKKAS, N; ERDOGAN, F (ASME International, 1993-01-01) The classical wave equation in spherical coordinates is expressed in terms of a residual potential applying the Residual Variable Method. This method essentially eliminates the second derivative of the potential with respect to the radial coordinate from the wave equation. Thus, the dynamic pressure distribution on the surface of a spherical cavity can be studied by considering the cavity surface only. Moreover, the Residual Variable Method, being amenable to ''marching'' solutions in a finite-difference im...
A NEW FAMILY OF MODE-SUPERPOSITION METHODS FOR RESPONSE CALCULATIONS AKGUN, MA (Elsevier BV, 1993-10-22) A new family of mode-superposition methods for the computation of the forced response of proportionally damped systems with and without rigid body modes is investigated. The method may be considered to be an extension of the mode-acceleration method. It allows response calculations to be done with a very small subset of the modes of the system. Numerical examples are given for systems of order 20 and 40. Execution times and number of modes required for convergence are recorded. The particular order of the m...
THE HARMONIC RESPONSE OF UNIFORM BEAMS ON MULTIPLE LINEAR SUPPORTS - A FLEXURAL WAVE ANALYSIS MEAD, DJ; Yaman, Yavuz (Elsevier BV, 1990-09-22) A wave approach is developed for the exact analysis of the harmonic response of uniform finite beams on multiple supports. The beam may be excited by single or multi-point harmonic forces or moments; its supports may have general linear characteristics which may include displacement-rotation coupling. Use is made of the harmonic response function for an infinite beam subjected to a single-point harmonic force or moment. The unknowns of the finite beam problem are the support reaction forces/moments and the ...
One-dimensional dynamic microslip friction model Ciğeroğlu, Ender; Menq, Ch (Elsevier BV, 2006-05-09) A one-dimensional dynamic microslip friction model, including the damper inertia, is presented in this paper. An analytical approach is developed to obtain the steady-state solution of the resulting nonlinear partial differential equations when subjected to harmonic excitation. In the proposed approach, according to the excitation frequency, a single mode of the system is considered in the steady-state solution for simplicity; consequently, phase difference among spatially distributed points is neglected. T...

Citation Formats

B. Kuran and H. N. Özgüven, “A modal superposition method for non-linear structures,” JOURNAL OF SOUND AND VIBRATION, pp. 315–339, 1996, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36099.