Structure Vibration Control Optimization And Multi-dimensional Random Vibration Analysis

Civil engineering structures are often subjected to various random excitationsduring its service period, such as earthquakes, strong winds, sea waves and so on,Traditional dynamic calculation methods which taking the observed seismic waverecords as input can’t fully reflect the randomness and non-stationary characteristicsof the ground motion, It is critical to research the structural dynamic analysis underrandom seismic excitation. Based on continuous wavelet transform theory, theequivalent evolution random excitations of specific site conditions are constructed byequivalent excitation method, which can be a realistic simulation of ground motioncharacteristics.Structural vibration control technology is an effective measure of civilengineering structures to withstand earthquakes, strong winds, sea waves and anyother natural disasters, and reasonable placement of the controllers is the key toensure the control effect and economy of the vibration control system. In the past, theresearch of the optimization of active structural control focused on the optimization ofthe control force, less attention has been taken to the optimal placement of controllers;The dynamic analysis in the research of passive structural control always took theobserved seismic wave records as input, lacking appropriate random vibrationanalysis in time domain. In this paper, the dynamic analysis takes the equivalentevolution random excitations which take the random vibration analysis fromfrequency domain into the time domain as input. Based on genetic algorithm, theoptimal placement of controllers in active/passive random control structures areresearched in this article.The actual ground motion excitation should be multidimensional, the study ofthree-dimensional seismic excitation in this paper include two translationalcomponents in horizontal and a rotational component about vertical. At present, forthe lacking of reasonable equations of motion of a structure under multi-dimensionalseismic excitations, few research in the multi-dimensional ground motion, more less research in the random vibration analysis of multi-dimensional both at home andabroad. The latest equations of motion of a structure under multi-dimensional seismicexcitations is introduced in this paper, Numerical analysis program based on Matlablanguage is worked out to solve the equations of a three-tier frame structure, and thenobtain the dynamic response of the structure under the multi-dimensionalnon-stationary random seismic excitation.Based on the analysis above-mentioned, this paper mainly solves the followingaspects of the research work:1. Constructed equivalent evolutionary random seismic excitation load. Based onthe Continuous Wavelet Transform theory, applying the Equivalent Excitation Method,equivalent evolution random seismic excitations of one-dimensional andmulti-dimensional are constructed by the translational acceleration power spectraldensity function and rotational angular acceleration power spectral density function,which effectively simulate randomness and non-stationary characteristics of the actualground motion.2. Proposed the optimization modal which is adapted to the placement ofstructural vibration controllers. Based on numerical examples， and with theaforementioned equivalent evolution random seismic excitations of one-dimensionalas the input, the linear quadratic Gauss optimal control is applied to the structure.Then by applying the state space control theory, the Riccati equation is solved byprecise integral calculation, and the dynamic response of the structure is obtained. A0-1chromosome coding of genetic algorithm is used to simulate the specialarrangement of actuators and dampers, and then in the case that the number ofcontrollers is specified, the optimal schemes of arrangement of controllers controlledby different objective functions are achieved.3. Structural random vibration analysis under multi-dimensional non-stationaryexcitations. The latest equations of motion of a structure under multi-dimensionalseismic excitations are introduced in this paper, which have taken full account of thetorsional component of seismic excitation (i.e. the Coriolis acceleration). Theequations present a significant nonlinear characteristic. Based on numerical examples, and with the aforementioned multi-dimensional equivalent evolution random seismicexcitations as the input, the Matlab numerical analysis program has been used to solvethe nonlinear equations, and then the dynamic response of the structure under themulti-dimensional excitation is finished.