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 implementatio...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.展开更多
Let G be a simple connected graph with n vertices and m edges,L G be the line graph of G and λ 1(L G)≥λ 2(L G)≥...≥λ m(L G) be the eigenvalues of the graph L G.In this paper,the range of eigenvalues of a...Let G be a simple connected graph with n vertices and m edges,L G be the line graph of G and λ 1(L G)≥λ 2(L G)≥...≥λ m(L G) be the eigenvalues of the graph L G.In this paper,the range of eigenvalues of a line graph is considered.Some sharp upper bounds and sharp lower bounds of the eigenvalues of L G are obtained.In particular,it is proved that-2cos(πn)≤λ n-1 (L G)≤n-4 and λ n(L G)=-2 if and only if G is bipartite.展开更多
A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained....A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.展开更多
Let K be the quasi-Laplacian matrix of a graph G and B be the adjacency matrix of the line graph of G, respectively. In this paper, we first present two sharp upper bounds for the largest Laplacian eigenvalue of G by ...Let K be the quasi-Laplacian matrix of a graph G and B be the adjacency matrix of the line graph of G, respectively. In this paper, we first present two sharp upper bounds for the largest Laplacian eigenvalue of G by applying the non-negative matrix theory to the similar matrix D-1/2 KD 1/2 and U-1/2 BU 1/2, respectively, where D is the degree diagonal matrix of G and U=diag(dudv: uv ∈ E(G)).And then we give another type of the upper bound in terms of the degree of the vertex and the edge number of G. Moreover, we determine all extremal graphs which achieve these upper bounds. Finally,some examples are given to illustrate that our results are better than the earlier and recent ones in some sense.展开更多
文摘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.
文摘Let G be a simple connected graph with n vertices and m edges,L G be the line graph of G and λ 1(L G)≥λ 2(L G)≥...≥λ m(L G) be the eigenvalues of the graph L G.In this paper,the range of eigenvalues of a line graph is considered.Some sharp upper bounds and sharp lower bounds of the eigenvalues of L G are obtained.In particular,it is proved that-2cos(πn)≤λ n-1 (L G)≤n-4 and λ n(L G)=-2 if and only if G is bipartite.
文摘A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.
基金This work was supported by the Natural Science Foundation of Sichuan Province (Grant No.2006C040)
文摘Let K be the quasi-Laplacian matrix of a graph G and B be the adjacency matrix of the line graph of G, respectively. In this paper, we first present two sharp upper bounds for the largest Laplacian eigenvalue of G by applying the non-negative matrix theory to the similar matrix D-1/2 KD 1/2 and U-1/2 BU 1/2, respectively, where D is the degree diagonal matrix of G and U=diag(dudv: uv ∈ E(G)).And then we give another type of the upper bound in terms of the degree of the vertex and the edge number of G. Moreover, we determine all extremal graphs which achieve these upper bounds. Finally,some examples are given to illustrate that our results are better than the earlier and recent ones in some sense.
