However, some basic but crucial problems still remain unsettled: in the aspect of plate bending element, there exists the problem of imbalance between the development of plane elasticity elements and that of plate bending elements, which is not compatible with the similarity theory between plane elasticity and plate bending, for according to the theory the two systems, plane elasticity and plate bending, are isomorphic;

In the first place, with the similarity theory, a bridge is set up between plane elasticity and plate bending to transform those good plane elasticity elements into plate bending elements;

Physical and mathematical methods are applied to the further study on dimensional analysis, including water flows in a channel, the moving of round exploding waves and the flow of viscous fluid.

Based on the analogies between plane elasticity and thin plate bending problem,the thin plate bending under symplectic geometry form was solved by direct method.

The problem of vapor diffusion toward a droplet nucleated and growing in the diffusion regime is exactly solved using the similarity theory.

Based on the similarity theory, the parameters of similitude are invoked for orbits and perturbations.

Most engineering methods for calculating the properties of plasma generators use similarity theory to derive dimensionless equations to generalize experimental results [1].

A general functional dependence of the engine current on the basic dimensionless parameters is obtained on the basis of similarity theory and dimensional analysis.

The approach is based on modern theoretical notions concerning the dependence of mass transfer on conjugated effects of concentration polarization, such as electroconvection and the exaltation effect and makes use of the similarity theory principles.

In this paper,the first approximation solution of incompressiable axis - symmetrical turbulentwake flow using theory of pseudo - similarity has been given. We consider the continuity equation,the mean motion equations and the equations of the double velocity correlations with ignoring thetriple velocity correlations correlation equations. We introduce the hypothesis of the self preservation,and have gotten the theoretical results of the mean velocities the double velocitycorrelations and the turbulent micro...

In this paper,the first approximation solution of incompressiable axis - symmetrical turbulentwake flow using theory of pseudo - similarity has been given. We consider the continuity equation,the mean motion equations and the equations of the double velocity correlations with ignoring thetriple velocity correlations correlation equations. We introduce the hypothesis of the self preservation,and have gotten the theoretical results of the mean velocities the double velocitycorrelations and the turbulent micro - scale,etc. by using the method of second substitution. Theyare identical with the experimental results.

The experiments of aerodynamic-aeroacoustic performance in axial fans in non-self-stimulated and self-stimulated domain are carried out. Compare enlarged model fans in self-stimulated domain and small-scale fans in non-self-stimulated domain, their aerodynamic-aeroacoustic performances are not almost similar, So aerodynamic-aeroacoustic similarity are perfected and revised. The corrected formula of similarity are obtained. Testing shows that fans with skewed-swept rotating blades in non-self-stimulated domain...

The experiments of aerodynamic-aeroacoustic performance in axial fans in non-self-stimulated and self-stimulated domain are carried out. Compare enlarged model fans in self-stimulated domain and small-scale fans in non-self-stimulated domain, their aerodynamic-aeroacoustic performances are not almost similar, So aerodynamic-aeroacoustic similarity are perfected and revised. The corrected formula of similarity are obtained. Testing shows that fans with skewed-swept rotating blades in non-self-stimulated domain has advantages of high-refficiency and low-noise.

The governing equation for plate bending is biharmonic equation, the traditionalsolution methodology is the semi-inverse one that causes limitations. The Airy stress function isusually applied traditionally for plane elasticity problems, it also satisfies biharmonic equation.The analogy between plate bending and plane elasticity problems had been noticed long before,but their solution systems are different each other, and the analogy relationship had not been usedsystematically. In this paper, the analogy is...

The governing equation for plate bending is biharmonic equation, the traditionalsolution methodology is the semi-inverse one that causes limitations. The Airy stress function isusually applied traditionally for plane elasticity problems, it also satisfies biharmonic equation.The analogy between plate bending and plane elasticity problems had been noticed long before,but their solution systems are different each other, and the analogy relationship had not been usedsystematically. In this paper, the analogy is set up and perfect further.The deflection w for plate bending correspond to the Airy stress function in plane elasticity,conversely, the displacements in plane elasticity correspond to two bending moment functionsop. I gb. in plate bending. Based on the analogy between plate bending and plane elasticity problems,Hamiltonian system can also be applied to plate bending problem, that is, the problem can be solvedin symplectic space that consists of curvatures and bending moment functions. So correspondingto the principle of minimum potential energy and the Hellinger-Reissuer variational principle forplane elasticity, the new variational principles of minimum complementary energy and the Pro-H-R in terms of bending moment for plate bending can be proposed respectively. Carrying outthe variations, a set of new governing equations and solution for plate bending clajssical theory ispresented.The new methodology presents the analytical solutions in plate strip via the methods ofseparation of variables and eigenfunction-vector expansion, it breaks through the limit of traditionalsemi-inverse solution. The new one for plate simply support on both sides is equivalent to the Levysingle trigonometrical series expansion method, but it is not the same as the classical semi-inverseone, is derived rationally and analytical. Therefore it can easily be applied to other lateral boundaryconditions, which is very difficult for semi-inverse method, such as the both sides free plate givenin this paper. The results show that the new methodology will have vast application vista.