Damage Identification under Incomplete Mode Shape Data Using Optimization Technique Based on Generalized Flexibility Matrix

A generalized flexibility–based objective function utilized for structure damage identification is constructed for solving the constrained nonlinear least squares optimized problem. To begin with, the generalized flexibility matrix (GFM) proposed to solve the damage identification problem is recalled and a modal expansion method is introduced. Next, the objective function for iterative optimization process based on the GFM is formulated, and the Trust-Region algorithm is utilized to obtain the solution of the optimization problem for multiple damage cases. And then for computing the objective function gradient, the sensitivity analysis regarding design variables is derived. In addition, due to the spatial incompleteness, the influence of stiffness reduction and incomplete modal measurement data is discussed by means of two numerical examples with several damage cases. Finally, based on the computational results, it is evident that the presented approach provides good validity and reliability for the large and complicated engineering structures.

Curvature of Flexibility Matrix for Damage Identification in Legs of Jacket Platforms

In this paper a new nondestructive damage identification method is introduced. The method based on flexibility matrix can be used to detect and locate structm＇al damage and evaluate the severity of damage in legs of jacket platforms by modal parameters of a structure. With the modal data for only the few lower modes in both the intact and damaged states, the one-dimensional and two-dimensional distributed curvatures can be used to analyze damage location and the severity. Instead of directly comparing the curvatures before and ＇after damage, the method here uses modal parameters only in the damaged structure to detect the damage and it consists of three parts. First, ilexibility matrix is obtained by use of the absolute maximum in each column. Second, because the legs of jacket platforms are the pipe-like structure, the circumferential flexibility curvature matrix is obtained by use of the circular curvature. At last, equivalent curvature ratio is defined and the curve meaning equivalent curvature ratio and the severity of damage relationship for one element is given through the data of damage severity from ten percent to ninety percent by numerical simulation. Many existing damage detection methods need two steps, locate the damage firstly and evaluate the severity of the damage. However, the method present- ed! in this paper can locate and then evaluate the severity of damage at the same time. The numerical analysis results in- dicate that the present method is effective, useful and only need the first and the second mode data of the structure.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

Damage localization under ambient vibration using changes in flexibility

In recent years,Structural Health Monitoring (SHM) has emerged as a new research area in civil engineering.Most existing health monitoring methodologies require direct measurement of input excitation for implementation.However,in many cases,there is no easy way to measure these inputs-or alternatively to externally excite the structure.Therefore,SHM methods based on ambient vibration have become important in civil engineering.In this paper,an approach is proposed based on the Damage Location Vector (DLV) method to handle the ambient vibration case.Here,this flexibility-matrix-based damage localization method is combined with a modal expansion technique to eliminate the need to measure the input excitation.As a by-product of this approach,in addition to determining the location of the damage,an estimate of the damage extent also can be determined.Finally,a numerical example analyzing a truss structure with limited sensors and noisy measurement is provided to verify the efficacy of the proposed approach.

Structural Damage Detection in Framed Structures Under Foundation Settlement/Rotation of Bases

This paper describes the damage detection in framed structures due to thevertical support settlement and rotation of footing bases. The damage detection procedureproposed by Nobahari et al. [Nobahari and Seyedpoor (2013)] is used to detect thedamage in the members of the frame. In the present study, instead of using the flexibilitymatrix (referred here as original flexibility matrix) method, the generalized flexibilitymatrix is used in the same algorithm and the results are compared. The algorithm usesflexibility matrix and strain energy concept to detect the damage in the members. Thebehaviour of the frame is discussed through changes observed in flexibility in theassociated degree of freedom. Finally, the results indicate that, the damage indexdetermined by generalized flexibility matrix method is more reliable than using theoriginal flexibility matrix based method for the problem of settlement and rotation offooting base.

Meshing stiffness property and meshing status simulation of harmonic drive under transmission loading

The multitooth meshing state of harmonic drive (HD) is an important basic characteristic of its high transformation precision and high bearing capacity. Meshing force distribution affects the load sharing of the tooth during meshing, and theoretical research remains insufficient at present. To calculate the spatial distributed meshing forces and loading backlashes along the axial direction, an iterative algorithm and finite element model (FEM) is proposed to investigate the meshing state under varied transmission loading. The displacement formulae of meshing point under tangential force are derived according to the torsion of the flexspline cylinder and the bending of the tooth. Based on the relationship of meshing forces and circumferential displacements, meshing forces and loading backlashes in three cross-sections are calculated with the algorithm under gradually increased rotation angles of circular spline, and the results are compared with FEM. Owing to the taper deformation of the cup-shaped flexspline, the smallest initial backlash and the earliest meshing point appear in the front cross-section far from the cup bottom, and then the teeth in the middle cross-section of the tooth rim enter the meshing and carry most of the loading. Theoretical and numerical research show that the flexibility is quite different for varied meshing points and tangential force amplitude because of the change of contact status between the flexspline and the wave generator. The meshing forces and torsional stiffness of the HD are nonlinear with the torsional angle.

The Input-Output Model and the Analysis of Profit and Tax of Product

With the combination of modern quantitative analysis method and enterprise inputoutput model,in this paper we make a scientific analysis on the effect to product profit tax from the change of internal and external important factors of enterprise,and some important results hare been given.