On similitude law of sub-systems

Based on Buckingham＇s π-Theorem, dimensional analysis has achieved considerable success over the past near-century. Model testing has long been a powerful tool in both scientific studies and engineering applications. However, the prototype objects are becoming more and more complicated nowadays, and many of the prototype systems can contain several sub-systems. The conventional theories on model-prototype similarity and dimensional analysis have only limited application since the π-Theorem itself does not distinguish between the original system and subsystems. This is particularly true in the field of structural dynamics, where the structure is often modeled as a multi-degree-of-freedom system. In this paper, we attempt to show that, if a system can be decoupled into several nontrivial subsystems, then, in each subsystem, the number of π-terms will be reduced and therefore simplify the model testing. On the other hand, if a system cannot be decoupled into subsystems, then using model testing with reduced π-term analysis, both experimentally and theoretically, may introduce severe errors.

Study on Energy Law of Similitude for Laser Propulsion in Repetitively-pulsed Mode

Energy law of similitude for laser propulsion refers to the law that there is an optimum nozzle configuration for the largest value of impulse coupling coefficient at certain incident laser energy. A dimensionless factor combined with incident laser energy, nozzle configuration parameters and working gas parameters is introduced. Energy law of similitude is established by means of theoretical analysis, experimental study and numerical simulation of radiation gas-dynamics. The qualitative results obtained from theoretical analysis are verified by experimental and numerical results. Physical meaning and engineering application of dimensionless factor and energy law of similitude are analyzed. Results indicate that ① impulse coupling coefficient has a maximurn value with dimensionless factor of about 0.4; ② impulse coupling coefficient is independent of incident laser energy when dimensionless factor is constant. Conclusions and recognitions acquired in this article can not only present optimum nozzle configurations for the present laser energy level, but also provide a good guide for the optimum nozzle configuration design once the laser energy is amplified to a high level.

Shaking Table Test of Pile-Water-Pier Superstructure

The model test of seismic simulation shaking table is an important method to study the seismic design of bridge structure. In order to evaluate the seismic response and dynamic characteristics of pile-water-pier system for developing more reliable design procedures, shaking table model tests of a submerged bridge pier system, including pile groups-cap-pier and inertia mass, were conducted. Since different similitude laws corresponding to different test objectives affected the validity of test results, the similitude law with the aim to consider the effect of hydrodynamic pressure was proposed and confirmed through an actual example. Based on the test results, the effect of water around model on seismic response under seismic excitation input was analyzed and the failure level was judged by observing the variation of basic frequency. The test results indicate that the transfer function of analytical model with water is different from that without water, the natural frequency without water is always higher than that with water, and the first modal shapes are various. It is also concluded that the similitude law is suitable for practical application and the dynamic characteristics and seismic response of the structure system can be changed because of the existence of the surrounding water, which should be paid much attention in the further investigation.