Multi-Degrees of Freedom System and Hydrodynamic Principle

2021 ◽  
pp. 81-142
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Superposition Method ◽  
Modal Superposition ◽  
Damped System ◽  
Modal Superposition Method ◽  
Hydrodynamic Study

A system with one degree of freedom is far from reality, because we do not take into account all the degrees of freedom. In order to be close to the reality, it is necessary to use a system with several degrees of freedom. Efforts in this chapter are concentrated to the study of multi-degrees of freedom system, whether for a free undamped and forced damped system, by detailing the modal superposition method as well as a coupled coordinates. We finish the chapter with hydrodynamic study using Hozner method as well as some applications.

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.

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.

scholarly journals Excitation Force Identification of Multiple Devices in Railway Vehicles Based on Modal Superposition Method and Kalman Filter

2021 ◽  
Author(s):  
Jiangxue Chen ◽  
Jinsong Zhou ◽  
Dao Gong
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Superposition Method ◽  
Force Identification ◽  
Railway Vehicles ◽  
Active Devices ◽  
Modal Superposition ◽  
Modal Superposition Method ◽  
Multiple Devices ◽  
Excitation Force

Abstract The excitation force identification of multiple devices in railway vehicles is studied. The vertical dynamic coupling model between the flexible car body of high-speed train and the under-chassis active device with excitation itself is established based on the modal superposition method. The excitation force from device is identified based on Kalman filter. A modal order selection method is developed for improving the identification accuracy based on tolerance index. The identification effects of single and multiple active devices including single-frequency steady-state, multi-frequency steady-state, impact, sawtooth wave and square wave excitation forces are analyzed. An error limit range of 5% is defined to evaluate the identification results. The results show that the method is suitable for the identification of various steady-state and transient-state excitation forces, and the identification results of excitation forces of single and multiple active devices have good accuracy.

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