Theoretical Studies On The Stiffness Monitoring And Compensation For Flexible Tensile Structures Based On The Dynamic Testing

Different from conventional structures,the flexible tensile structure maintains its stability and deformation resistance substantially depending on the geometrical stiffness contributed by the pretension.As the most important structural performance,the stiffness should be regarded as the key point in monitoring an existing flexible tensile structure,while the inevitable pretension deviations caused by many factors will lead to the stiffness degradation.Because of the limited number and the problems associated with the accuracy and durability of cable force sensors,the traditional cable force measurement is usually difficult to effectively evaluate the structural integral pretension distribution and stiffness performance.Considering that the dynamic testing method has been well developed both theoretically and technically,the research on the stiffness monitoring of an existing flexible tensile structure is carried out based on the dynamic modal testing.The validity of the theories and methods proposed in this thesis is verified by taking the cable net structure as an example.The main works including five aspects are as follows:(1)The stiffness component,which provides the main resistance to the deformation caused by the dominant loads,is defined as the key stiffness.The target modes for monitoring the key stiffness can be selected according to the proportion of the work done by the dominant load in the direction of each mode shape to the total work.The variations of eigenvalues and mode shapes for the target modes corresponding to the initial(idealized)structural model are estimated based on the matrix perturbation theory.Considering the mode jumping and mode localization occurred between the target mode and its adjacent mode in the same dense-frequency region,a simple and rapid method for determining the target modes is established using the density index of modal eigenvalues.(2)A step excitation optimization method is put forward to improve the identification accuracy of dense modes.The modal energy in the induced free vibration response can be quantitatively evaluated by the work done by the step excitation load in the direction of this mode shape.Define the modes adjacent to the target mode as the suppressed modes,and a method for constructing the step excitation load is presented using the mode shapes of those unsuppressed modes,so that the energy of the suppressed modes in the structural vibration response can be completely eliminated.Referring to the idea of the effective independence(EI)method,an iterative algorithm is developed to select a given number of loaded degrees of freedom(DOFs)that can ensure the target mode has a relatively large energy proportion.The magnitude of the step excitation load is optimized based on the solution of generalized Rayleigh entropy to further improve the relative energy of the target mode to the other unsuppressed modes.(3)A testing strategy of the target modes is proposed to monitor the key stiffness of an existing flexible tensile structure.Due to the stiffness deviation,the target mode determined based on the initial structural model will change in its dense-frequency region,typical of mode jumping and mode localization.For each initial target mode in this frequency region,the corresponding step excitation load can be optimized to suppress the vibration of other modes in the same region.It is proved theoretically that all the target modes of the existing structure can be sufficiently excited if these optimized step excitation loads are applied one by one,thus their identification accuracies are guaranteed.The static displacement of the existing structure can be calculated using the identified parameters of the target modes,and employed to evaluate the variation of key stiffness.(4)The compensation method of key stiffness and selection strategy of re-stretched cables are discussed for an existing flexible tensile structure.Concerning the stiffness degradation caused by pretension deviations,a novel approach is proposed for compensating the structural key stiffness by rehabilitating the parameters of target modes.It is proved that the perturbation method using eigenvalue shift technique can be employed to estimate the variations of both isolated modes and dense modes resulting from stiffness deviation.The relationship between the rehabilitation of target modes and the compensation of key stiffness is expounded theoretically.The connection between the length adjustment of re-stretched cables and the variation of target modes is established based on the perturbation theory.When the number of re-stretched cables is limited,a strategy for selecting the optimal re-stretched cables is developed to improve the rehabilitation accuracy of modal parameters.(5)The feasibility of theories and methods discussed in this paper for monitoring the key stiffness of an existing flexible tensile structure is investigated through the dynamic modal testing of a saddle-shaped cable net experimental model.The key stiffness and target modes corresponding to the given dominant loads are solved based on the initial(numerical)structural model.The shape finding analysis of the existing model with pretension deviations introduced is carried out using the measured cable forces.Comparing the results of modal analysis based on the initial and existing model,the necessity of expanding the set of initial target modes is verified.According to the identification results of closely spaced target modes in the cases of optimized step excitation and hammer excitation,the validities of the proposed step excitation optimization method and modal testing strategy are investigated.Furthermore,the variation of key stiffness component can be evaluated using the identifiedparameters of the target modes.