Theoretical Studies On The Stiffness Monitoring Of Cable-strut Tensile Structures Using Dynamic Method

It is over 30 years since the oldest large-span cable-strut tensile structure was erected.However,few studies have referred to the structural health monitoring and performance evaluation of such structures so far,let alone deep discussions.Compared with conventional structures,cable-strut tensile stuctures present distinct composition mechanisms of structural stiffness because they depend on the pretensions to provide the geometrical stiffness and maintain the structural stability.According to the experience,the design of cable-strut tensile structures is normally controlled by the structural stiffness checking.By comparison,it is generally easy for the structural strength performance to be satisfied.Because of the concern about the possiblely great structural stiffness degeneration,the pretensions are focused on for the stiffness monitoring of the existing cable-strut tensile structures.In the current practices,the pretensions are usually monitored by directly testing the cable forces,but the effective assessment of the variations of the integeral pretensions and structural stiffness can hardly be obtained by the finite measured cable forces.A novel way to directly monitor the structural stiffness of cable-strut structures by the conventional dynamic testing method is proposed in this dissertation.Due to the dense distribution of modal frequencies and the high sensitivity of modal parameters to pretension deviations in cable-strut structures,some key theoretical issues on the stiffness monitoring by the dynamic testing method are discussed.Five aspects are detailed as follows:(1)Whether the various stiffness components can provide main resistance to the deformation caused by a specific load should be quantitatively analyzed.The analysis is conducive to finding the force-transfering paths and supplying reference for conducting effective stiffness monitoring.An index to the contributions of various stiffness components of cable-strut tensile stuctures in the form of energy is put forward in this dissertation.It can describe the contributions of the elastic and geometrical stiffnesses at both the structural and member levels.What is more,if the eigenvectors of the structural stiffness matrix which represent different stiffness directions are concerned,the resistance capacity of stiffness in different eigenvetor directions to the deformation caused by the specific load can also be evaluated by the index.Thus,the "key stiffness" which is the key point in the stiffness monitoring is finally extracted from the structural stiffness.(2)The dynamic testing is normally conducted based only on the modal information of the idealized structure(no pretension deviations)in the conventional methods,which are merely applicable for an exsting structure whose modal parameters change little.Because cable-strut tensile structures present dense distributions of modal frequencies and high sentivity of modal parameters to the pretension deviations,it is essential to consider the influences of random pretension deviations on the modal parameters(frequencies and mode shapes)of an existing structure.The sensitivity relationships between member length errors and modal eigenvalues as well mode shapes are established in this dissertation.By considering the influences of random pretension deviations,a method to estimate the variation amplitudes of modal parameters and a criterion to judge mode jumpings for cable-strut tensile structures are put forward.The general influence law of the dynamic characteristics of cable-strut tensile structures affected by random pretension deviations is drawn based on the analysis of two numerical examples.(3)Based on the contribution analysis of the stiffness directions described in the modal space,a method to determine the target modes for monitoring the key stiffness of cable-strut tensile structures by the dynamic testing method is put forward in this dissertation.Because of the high sensitivity of modal parameters to the pretension deviations,the target modes determined based only on the idealized structural model are normally insufficient to reflect the key stiffness of an existing structure.To solve this problem,an expansion strategy of target modes is put forward by considering the mode shape changes and mode jumpings caused by the pretension deviations.It is shown from the numerical examples that the determined target modes by the proposed expansion strategy can envelop the influences of random pretension deviations on the modal parameters of cable-strut tensile structures,and can sufficiently reflect the key stiffness of an existing structure.(4)Because of the high sensitivity of modal prarameters to the pretension deviations,the conventional mode shape expansion methods based only on the idealized structural models can easily lose effectiveness for cable-strut tensile structures.A novel mode shape expansion method for cable-strut tensile structures considering random pretension deviations is put forward in this dissertation,in which the real mode shape of the existing structure is approximately expressed as the linear combination of only a few idealized mode shapes of the idealized structure(i.e.,contribution modes).As long as the contribution modes are properly determined and their combination factors are best estimated,the expanded mode shape is naturally obtained.A method to determine the contribution modes by considering the mode shapes changes and mode jumpings is proposed.Additionally,an improved effective independence method(CMEI)is put forward to obtain the best estimates of the combination factors of the contribution modes,in which the optimal sensor locations are also gained.It is illustrated from the numerical examples that the mode shapes of cable-strut tensile structures containing random pretension deviations can be effectively expanded by the proposed expansion method.Even in cases of severe modal variations and high noise levels,the proposed expansion method can produce good enough results.(5)Poor accuracy is normally presented for the modal identification of closely spaced modes by the conventional modal testing methods in which the excitations are not optimized.In order to improve the accuracy,a modal testing method of closely spaced modes is put forward by optimizing step excitations which cooperates with the time domain modal identification methods.By means of optimizing the locations and amplitudes of step excitations,the modal contributions to the structural free vibration are simultaneously enhanced for the mode to be identified and suppressed for its adjacent modes.The optimization of step excitations is achieved by the Genetic Algorithm.The numerical analysis shows that the proposed modal testing method can transform the modal identification of closely spaced modes to that of sparsely spaced modes by optimizing step excitations,and effectively improve the modal identification accuracy.