Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d＇Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d＇Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.

DYNAMICAL BEHAVIOR OF NONLINEAR VISCOELASTIC BEAMS

The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established. The material of the beams obeys the Leaderman nonlinear constitutive relation. rn the case of two simply supported ends, the mathematical model is simplified into an integro-differential equation after a 2nd-order truncation by the Galerkin method. Then the equation is further reduced to an ordinary differential equation which is convenient to carry out numerical experiments. Finally, the dynamical behavior of Ist-order and 2nd-order truncation are numerically compared.

声学浮标正弦垂直运动抑制及流噪声计算

The flow noise associated with sinusoidal vertical motion of a sonobuoy restrains its working performance.In practice,a suspension system consisting of elastic suspension cable and isolation mass is adopted to isolate the hydrophone from large vertical motions of the buoy on the ocean surface.In the present study,a theoretical model of vertical motion based on the sonobuoy suspension system was proposed.The vertical motion velocity response of the hydrophone of a sonobuoy can be obtained by solving the theoretical model with Runge-Kutta algorithm.The flow noise of the hydrophone at this response motion velocity was predicted using a hybrid computational fluid dynamics(CFD)-Ffowcs Williams-Hawkings(FW-H)technique.The simulation results revealed that adding the elastic suspension cable with an appropriate elastic constant and counterweight with an appropriate mass have a good effect on reducing the flow noise caused by the sonobuoy vertical motion.The validation of this hybrid computational method used for reliable prediction of flow noise was also carried out on the basis of experimental data and empirical formula.The finds of this study can supply the deep understandings of the relationships between flow noise reduction and sonobuoy optimization.