Modal Superposition Method for Computationally Economical Nonlinear Structural Analysis

1979 ◽  
Vol 101 (2) ◽  
pp. 134-141 ◽  
Author(s):  
V. N. Shah ◽  
G. J. Bohm ◽  
A. N. Nahavandi
Keyword(s):  
Seismic Analysis ◽  
Equations Of Motion ◽  
Test Problems ◽  
Superposition Method ◽  
Structural Dynamic ◽  
Large Wave ◽  
Modal Superposition ◽  
Nonlinear Structural ◽  
Direct Integration Method ◽  
Modal Superposition Method

A modal superposition method for analyzing nonlinear structural dynamic problems involving impact between components is developed and evaluated. The finite-element method is used to express the equations of motion with nonlinearities represented by pseudo force vector. Three test problems are solved to verify this method. This has demonstrated the applicability of this method to seismic analysis of large, complex structural systems. It is concluded that the modal superposition method has a significant cost advantage over the direct integration method for problems with large wave fronts and the source of nonlinearities restricted to a limited portion of the structure.

Seismic Analysis of Structures With Coulomb Friction

1983 ◽  
Vol 105 (2) ◽  
pp. 171-178 ◽  
Author(s):  
V. N. Shah ◽  
C. B. Gilmore
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Seismic Event ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Relative Displacement ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Superposition Method ◽  
Modal Superposition Method

A modal superposition method for the dynamic analysis of a structure with Coulomb friction is presented. The finite element method is used to derive the equations of motion, and the nonlinearities due to friction are represented by pseudo-force vector. A structure standing freely on the ground may slide during a seismic event. The relative displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. Three single degree-of-freedom problems are solved to verify this method. In a fourth problem, the dynamic response of a platform standing freely on the ground is analyzed during a seismic event.

Efficient Mode Superposition Method for Seismic Analysis of Nonlinear Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S264-S272 ◽  
Author(s):  
Roberto Villaverde ◽  
Melad M. Hanna
Keyword(s):  
Nonlinear Systems ◽  
Comparative Study ◽  
Integration Method ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Superposition Method ◽  
Direct Integration ◽  
Mode Superposition ◽  
Mode Superposition Method ◽  
Direct Integration Method

A step-by-step integration method is proposed to compute within the framework of the conventional mode superposition technique the response of bilinear hysteretic structures subjected to earthquake ground motions. The method is computationally efficient because only a few modes need to be considered to obtain an accurate estimate of such a response, and because it does not require the use of excessively small time steps to avoid problems of accuracy or stability. It is developed on the basis that the nonlinear terms in the equations of motion for nonlinear systems may be considered as additional external forces, and on the fact that by doing so such equations of motion can be interpreted as the equations of motion of an equivalent linear system, excited by a modified ground motion. These linear equations are then subjected to a conventional modal decomposition and transformed, as with linear systems, into a set of independent differential equations, each representing the system’s response in one of its modes of vibration. To increase the efficiency of the method and properly account for the participation of higher modes, these independent equations are solved using Nigam-Jennings technique in conjunction with the so-called mode-acceleration method. In addition, an iterative scheme is introduced to avoid an inefficient recalculation of the system’s eigenvectors and eigenvalues every time there is a change in the stiffness of one of its elements. The accuracy and efficiency of the method is verified by means of a comparative study with solutions obtained with a conventional direct integration method. In this comparative study, with only a few modes considered, the proposed method accurately predicts the seismic response of three two-dimensional frame structures, but requiring only, on the average, about 43 per cent of the computer time spent when using the direct integration method.

Structural Shape Reconstruction of FBG Flexible Plate Using Modal Superposition Method

2017 ◽  
Author(s):  
Li Li ◽  
Ben S. Zhong ◽  
Zi Y. Geng ◽  
Wei Sun
Keyword(s):  
Mode Shape ◽  
Shape Reconstruction ◽  
Displacement Sensor ◽  
Superposition Method ◽  
Flexible Plate ◽  
Structural Shape ◽  
Modal Superposition ◽  
Displacement Mode ◽  
Modal Superposition Method ◽  
Strain Data

Structural shape reconstruction is a critical issue for real-time structural health monitoring in the fields of engineering application. This paper shows how to implement structural shape reconstruction using a small number of strain data measured by fiber Bragg grating (FBG) sensors. First, the basic theory of structural shape reconstruction is introduced using modal superposition method. A transformation is derived from the measured discrete strain data to global displacement field through modal coordinate, which is the same for strain mode shape superposition and displacement mode shape superposition. Then, optimization of the sensor layout is investigated to achieve the effective reconstruction effect. Finally, structural shape reconstruction algorithm using modal superposition method is applied in experiments. The experiment results show that the reconstructed displacements match well with those measured by a laser displacement sensor and the proposed approach is a promising method for structural shape reconstruction.

An Error Compensation Method for Structural Responses and Sensitivities

2011 ◽  
Vol 421 ◽  
pp. 743-749
Author(s):  
Xiao Ming Wu ◽  
Chun Liu
Keyword(s):  
Error Compensation ◽  
Truncation Error ◽  
Compensation Method ◽  
Superposition Method ◽  
Truncation Errors ◽  
Modal Superposition ◽  
Modal Superposition Method ◽  
Structural Responses ◽  
Epsilon Algorithm ◽  
Modal Method

Abstract. The computation of the responses and their design sensitivities play an essential role in structural analysis and optimization. Significant works have been done in this area. Modal method is one of the classical methods. In this study, a new error compensation method is constructed, in which the modal superposition method is hybrid with Epsilon algorithm for responses and their sensitivities analysis of undamped system. In this study the truncation error of modal superposition is expressed by the first L orders eigenvalues and its eigenvectors explicitly. The epsilon algorithm is used to accelerate the convergence of the truncation errors. Numerical examples show that the present method is validity and effectiveness.

Sound Transmission in Dual-Coupling System of Elastic Plate and Acoustic Cavity Based on Modal Superposition Method

2013 ◽  
Vol 475-476 ◽  
pp. 1474-1478
Author(s):  
Hong Qiu Li ◽  
Guo Ping Chen
Keyword(s):  
Elastic Plate ◽  
Sound Transmission ◽  
Superposition Method ◽  
Acoustic Cavity ◽  
Modal Superposition ◽  
Coupling System ◽  
Modal Superposition Method ◽  
Cavity System ◽  
Coupling Characteristics ◽  
Plate System

This paper presents a study on the dual-coupling characteristics between elastic plate and acoustic cavity. Modal superposition method was employed to analyze sound transmission in the plate-cavity-plate system and cavity-plate-cavity system. Impedance and mobility methods were also adopted which were easy to investigate the characteristics between the structural and acoustic systems. The expression of sound transmission between plate-cavity-plate system and cavity-plate-cavity system were given.

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