Dynamic Load Identification Methods And Experimental Research Of Linear And Nonlinear Structures

Considering the vital role of loads in structure design, structural dynamic optimization and normal operation of structures, it is essential to acquire accurately the loads using proper testing methods. Loads measurement can be divided into two kinds,i.e., the direct measurement and the indirect measurement. The direct measurement method has many difficulties in reality. Firstly, the effect of loads on the structure is a kind of the energy transmission, while the diversity of actuating medium make the load measuring equipment and the test methods complicated due to the solid, liquid and gas in the actuating medium. Secondly, the load test equipments work in the condition of acid, alkali, salt, high temperature high pressure, etc., therefore the durability and reliability of the load test equipment should have much higher standard and performance. Specially, loads can not be measured directly due to the uncertainty of loads position, occurrence time and occasionlity of loads in many cases. In this case the measurement of loads is even more important for structural safety and reliability. In comparison with the direct loads measurement, the difficulties of response measurement are relatively much more smaller or even do not exist. Therefore, the indirect loads measurement have attacted much attention by observing the structural response to identify the load.The load identification method for linear structures under mutual independent loads is studied. Then the load identification method for linear structure under general load is given. Finally, the load identification method using exponential nonlinear function to express nonlinear restoring forece is proposed for nonlinear structures. Meanwhile, the corresponding experiments are conducted to verify the proposed load identification methods. The main contents are divided into five parts as follows:Firstly, the load is produced by the vibrating source, and the phycial process caused by one kind of load is independent with that caused by another if the vibrating sources have no relation. The differential equation method of load identification for linear structures is proposed which combines the load from the physical process with prior knowledge of the load independence. The external load acting on the structure can be decomposed into two variables, e.g., the waveform and the amplitude, and the two variables can be identified respectively. The load waveform can be expressed as a convolution of load separation functions and structural responses, and the independence of load can be mearsured by calculating the mutual information of the load waveform by minimizing the objective function of mutual information. The load separation functions can be iteratively updated by gradient descent algorithm and the objective function minimization, and the identified waveforms and the real loads are identical. The waveforms are normalized by the maximum loads and used as basis functions of loads. Therefore, the external loads can be expressed as the linear combination of basis functions of loads. Structural responses can be experssed as load combination coefficients by the first-order Taylor expansion, and the load combination coefficients can be achieved by using the least squares method, and then the real load can be identified. Finally, the numerical simulation results of space truss structures indicate that the method can identify the harmonic load, the triangular wave load and the random load accurately.Secondly, the integral equation method of load identification for linear structures is proposed in the case that any prior knowledge is not available. The dynamic differential equation can be transformed into the equivalent integral equations with a subsection integration to the equivalent integral equation by the virtual work principle. The function between the real force work on the virtual displacement and the virtual force work on the real displacement can be derived. The linear equations on load coefficient and displacement coefficient are established by using the moving least squares to fit the displacement, the velocity and the external load,. Finally, the external load can be identified by using optimization method to solve the linear equations. The numerical simulation and experimental results show that the moving least squares method can restrain the noise and reduce the computation. Using the optimization method to solve the linear equation can implove the stability of the solution. To improve the calculation efficiency, a feasible method is to add the window on the acquisition signal, and the dimension of linear equations is reduced effectively.Thirdly, the errors between the theoretical and actual model are not considered in the numerical simulations. To consider both the influences of the measurement noise and model errors on identified results, a space truss experiment is designed to verify the differential equation method of load identification for linear structures(Chapter 2) and the integral equation method of load identification for linear structure(Chapter 3). The experimental results show that the two methods have general features about the influences of load type and measurement noise on the identification precision. In respective of time domain, the identification effect of the continuous differentiable cycle load is usually best, and non-differentiable points affect the identification accuracy directly; in respective of frequency domain, low frequency load and the load with narrow frequency spectrum identification effect is better, and the frequency spectrum can be accurately identified; the two methods have certain amplification effect on the noise. Besides the common features, these two kinds of load identification methods also have their own different characteristics, i.e., the differential equation method of load identification for linear structure has larger error when load time desynchronization, but the integral equation method of load identification for linear structure identification error concentrates at the end of load time-history.Fourthly, the homotopy analysis method of load identification for nonlinear structure is proposed based on the continuous deformation in algebraic topology. High-order deformation equation is constructed using the weighted superposition through the equation of motion of linear and nonlinear structure. Taking the residual error between calculated response and the measured response as objective function, the residual error is redistributed to the 1st-order deformation equation proportionally, and the incremental load is identified using the load identification for linear structures, and then the external load is updated until the residual error of response converges to the error limit. Finally, a numerical example is simulated to verify the effectiveness of the proposed method by using these three different kinds of seismic excitation.Finally, to verify the homotopy analysis method of load identification for nonlinear structures(Chapter 5), a multi-degree-of-freedom nonlinear structure with cubic stiffness is designed. An experimental scheme to simulate the nonlinear stiffness with linear spring is proposed. According to the result of spring test, the restoring force of experimental structure meets the cubic nonlinear stiffness. Experimental identification results show that the homotopy analysis method of load identification can identify the excitation shape and the frequency spectrum range for aperiodic stochastic excitation than periodic excitation with much higher accuracy. For the harmonic excitation identification, the accuracy is very high; for the triangular wave excitation identification, although the accuracy is low, the excitation frequency can be accurately identified.