Study On Dual Neural Network Method For Differential Equation Of Structural Vibration

Many engineering problems can be simplified as multi degree of freedom vibration problems to describe the main characteristics of mechanical system vibration,so the solution and analysis of multi degree of freedom vibration equation is very important.Most of the solutions to the multi degree of freedom vibration equations are integral numerical integration methods,which have some disadvantages in solving problems,such as the mode superposition method involves matrix inversion in the solution process,which is not applicable to large-scale;the direct integration method needs to select reasonable iteration steps,but it is not easy to operate;a large number of matrix calculation and matrix index calculation appear in the process of precise integration calculation,how to deal with these calculations is very important.Due to the rapid development of artificial intelligence,neural network as one of them,its theory has also made great progress,and has been applied to many fields.This paper discusses in detail the neural network method to solve the multi degree of freedom vibration equation.There are many numerical integration methods for solving the vibration equation that are not applicable because they involve a lot of matrix calculation and unsuitable selection of iterative process parameters.The advantage of this method is that it only needs a simple equivalent transformation of the vibration equation without a lot of matrix calculation,and only needs to adjust the parameters of the neural network to get the results.It is proved that the dual neural network is accurate and easy to operate.There are many continuous systems involved in the project,most of them can not give the analytical solution of the problem,so it is necessary to discretize the continuous system,and then transform the problem into the problem of multi degree of freedom system.This kind of problem is unable to give the specific multi degree vibration equation,and the general numerical integration method can not calculate this kind of problem without the specific equation.However,the neural network only needs to know the data points of the input samples and the output samples to realize the solution calculation,and there is no need to know the specific analytical formula of the function,which provides a method for the solution of the above problems.Firstly,the representative discrete points are selected according to the characteristics of the continuous system,and then the displacement of these discrete points at different times is known by using the finite element software simulation.Taking these conditions as the input and output of the neural network,the system can be solved.Finally,the feasibility of this method is verified by an example of aircraft wing.