Wave–based Mechanical Modeling Method For Complicated Piping System And Corresponding Spectral Calculation Method Of Energy And Power

The pipe system is important in industry and civil engineering. The vibration of pipe receives board interests because it can induce noise and fatigue failure. In especial areas, such as power station, marine and aerospace, it requires more severe demands in vibration control. So far, the Finite Element Method is widely used in the static and dynamic analysis of pipe. Although it is proved that FEM is successful in conventional engineering analysis, there are still some challenges in mid-/high-frequency range and active wave control. Recently, the wave-based method is begin to be used widely and is considered as an effective way to solve mid-/high-frequency range vibration, noise and control. The wave-based method depicts the structural dynamics in the view point of elastic wave propagation. However, there is still no simple and effective modeling and calculation framework based on wave methods, which can solve not only mid-/high-frequency wave propagation analysis but also solve conventional pipe analysis, such as statics, buckling and modal analysis. Considering that, in order to take both high-frequency vibration/wave analysis and modeling difficulty into account, the pipe is simplified as Timoshenko beam model.In this sense, the present work deeply investigates the application of the wavebased method in complex piping system. In computer automatic modelling and energy, power flow spectral calculation methods, the author achieved creative results. These achievements give theoretical reference and computing tools for wave-based vibration control and analysis of pipe.The research work of the present works are as follows:1. Design and realize automatic modelling and calculation frame work based on structural node method and wave solutions of Timoshenko beam. This frame work uses spectral coefficients of travelling wave, near field vibrations as basic unknowns and thus is suitable for wave propagation analysis in mid-/high frequency ranges. The basic equations are divided into type:nodal force balance and displacements compatibility. These modelling equations are simple, easy programming and can be used in conventional pipe analysis.2. Based on above calculation frame work, the multiple solving modulus have been developed for complicated piping system’s statics and dynamics. The modulus includes: statics, buckling, modal analysis, harmonic analysis,distributed calculations and structural wave propagation analysis.3. Derive the spectral coefficients formulas for Timoshenko beam’s energy and power flow calculations and simplify the expression effectively. In the viewpoint of quadratic matrix of energy and power formulas, investigate the energy transmission mechanism of near field vibrations. Comparing with standing wave and travelling wave of acoustic wave, the general wave concept has been proposed in order to explain the energy transmission mechanism of near field vibration. These results give an important theoretical reference for Timoshenko beam’s energy flow analysis and wave-based active control analysis and design.4. Deeply investigate the energy and power coupling effects of Timoshenko beam’s travelling wave modes and near field vibrations. The coupling effect and mechanism is explained in the view point of additivity of timeaveraged energy and power functions. It has been proved that the travelling mode and near field mode are decoupled in the energy and power functions. This result enhances the wave-based theory of energy and power flow analysis and can give introductory for mid-/high frequency active controller design.5. Execute numerical and experimental verifications for proposed calculation frame work and energy and power spectral formulas. An active wavebased control example has been given intentionally given. In this example,the active control force has been calculated for no reflection control. The“perfect wave-absorber” has been realized in order to illustrate the superiority of the present method in wave-based controller design and analysis.