Time-varying Dynamics Of Supporting Structure Subjected To Long-displaced Moving Beam Under Sharp Impact

The most important development trend of gun system is high muzzle velocity, high precision and high moblity, which requests higher rigidity, strength, velocity and precision. The traditional non-time-varying dynamic theory can not suit this development demand. Therefore, it’s necessary to consider the effect of time-varying parameters during gun system’s launching process. Based on this background, and funded by the national basic research program of China,"Time-varying dynamics research of×××", finete elements method and dynamic stiffness matrix method were used to study the time-varying variables’s effects during gun barrel’s large displacement recoil process. The main contents were included as below.Firstly, according to the Euler-Bernoulli beam theory and finite elements method, time-varying dynamics models of beam subjected to moving force, moving mass, and moving oscillator with large displacement were constructed respectively. Dynamic responses of moving load systems with different velocity, acceleration, and mass were calculated. The time-varying dynamics experiment system of cantilever beam subjected to moving mass was designed and manufactured. Curves of strain and deflection of the cantilever beam versus time were measured. The proposed model was validated by comparing the experiment data and numerical results.Secondly, the exact shape function of beam element matrix was deduced for dynamic stiffness by using Euler-Bernoulli beam’s dynamics governing equation. The inertial force of moving load was treated as additional dynamic stiffness matrix of the bending beam. The dynamic stiffness matrix was formulated for the bending beam subjectd to moving load. Wittrick-Williams algorithm was applied to calculate the natural frequencies of beam system, and the effects of moving load’s position, mass, velocity and acceleration on natural frequencies of moving load system were summarized.Thirdly, the governing equation and boundary conditions of axially accelerated beam was established via extended Hamilton’s principle. In terms of solving axially accelerated beam’s governing equation in frequency domain, and by combining the displacement boundary conditions and force boundary conditions, the dynamic stiffness matrix of axially accelerated beam was developed, and finite elements model was set up by using Hermite shape function. The influences of velocity, acceleration, axial load on on natural frequencies of moving load system were induced. Fourthly, the interaction between gun barrel and cradle was simplified into two elastic supports. The stiffness of two supports varying with the frequency was retrieved by measuring dynamics response of gun barrel and using system idendification model based on spectral element method. The dynamic stiffness matrix of gun barrels was developed, in which the recoil displacement, velocity, acceleration of gun barrel, and axial loads were taken into consideration. The comparison between numerical results and data of modal experiment is conducted, and the influences of recoil displacement, velocity, acceleration of gun barrel, and axial loads on natural frequencies were discussed.Fifthly, the matrix of moving beam element was formulated by considering the effects of recoil velocity, acceleration of gun barrel, and axial loads. The cradle was treated as bending beam with non-uniform section, and the corresponding matrix was developed. The additional matrix due to coupling motion between gun barrel and cradle was formulated. By assembling the aboved matrices,2D time-varying dynamics model was established for supporting beam subjected to axially moving blending beam under impact load. Numerical computation of time-varying dynamics was performed for barrel recoil of a gun. In light of comparison between results from theoretical calculation and experiment of simulated barrel recoil, the deficiency of2D time-varying dynamics model in respresenting3D structural characteristics of cradle was pointed out.Sixthly,3D structure of gun barrel and cradle was discretized by uses of3D moving beam elements and plate elements, respectively. Data structure of finite elements was anatomized, and the requested modeling information was extracted automatically. In light of the method called’Finding the seat by the unique number’, elements of additional matrix due to coupling motion between gun barrel and cradle were assembled into the corresponding positions of elements of system mass matrix and stiffness matrix, and the time-varying system mass matrix and stiffness matrix were formulated.3D time-varying dynamics model was construced for cradle subjected to recoiling gun barrel with large displacement and under impact load. The codes for numerical calculation were developed by C++language.Finally, aiming at researching large displacement recoil of a gun barrel, the pushing force acted on piston rod due to buring of propellant in closed bomb was used to simulate the bore force during actual gun launch. Time-varying dynamics experiment of gun barrel with large displacement recoil was processed. The measured muzzle vertical displacement, velocity, and strain, vertical displacement of a tested point on cradle were compared with the results from3D time-varying dynamics model, FE model, and2D time-varying dynamics model, respectively, and which can illustrate that3D time-varying dynamics model can much exactly predict the dynamic response generated by large displacement recoil of gun barrel than other models.