The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.
Band gap materials(i.e.phononic crystals) are the artificially periodic structures,which have the stop band characteristic for elastic waves.The elastic waves will be localized in phononic crystals with defects,which results in the energy being accumulated around the defects.As a result,it is important to analyze the wave propagation and localization in band gap materials,especially for the structures consisting of smart materials.For example,with the mechanical-electro and mechanical-electro-magneto coupling,the phononic crystals consisting of piezoelectric and magnetoelectroelastic materials can be applied widely.This sets the theoretical basis for the design of band gap materials with multi fields coupling.This paper reviews the recent development of the elastic wave propagation and localization in both ordered and disordered band gap materials.The discussion focuses on the stop band and localization characteristics of elastic waves.Analytical methods and important results are also presented.Finally,some problems for further studies are discussed.This work aims to present the basic properties of wave band gaps in phononic crystals and wave localization in disordered periodic structures(e.g.phononic crystals with definite and random defects and phononic quasicrystals).
As the typical systems of nano structures, nanotubes can be widely applied in mechanical electronics, mechanical manufacture and other fields at nano scales. The superior dynamical properties of nanotubes have become a hot topic. Furthermore, there are always complicated conditions for practical engineering (e.g. initial stress/strain, temperature change for external environment and the interaction between the structure and elastic matrix). Then, it is important to establish the proper model and apply the effective analysis method. By using the nonlocal continuum method, this paper reviews the recent progress of dynamical properties of micro structures at nano scales. The discussion is focused on dynamical behaviors of nanotubes, including vibration, wave propagation and fluid-structure interaction, etc. At last, conclusions and prospects in future studies are discussed.
The transient wave propagation in the finite rectangular Mindlin plate is investi- gated by the analytical and experimental methods. The generalized ray method （GRM） which has been successfully applied to study the transient responses of beams, planar trusses, space frames and infinite layered media is extended to investigate the transient wave propagation and early short time transient response in finite Mindlin plate. Combining the wave solution, the shock source and the boundary conditions, the ray groups transmitted in the finite rectangular plate can be determined. Numerical simulations and experiments are performed and compared with each other. The results show that the transient wave propagation and early short time transient responses in the finite plate can be studied using the GRM. The early short time transient acceler- ations are very large for the finite plate subjected to the unit impulse, while the early short time transient displacements are very small. The early short time transient accelerations under the unit impulse are much larger than those under the unit step impulse. The thickness and material characteristics have remarkable effects on the early short time transient responses.
The piezoelectric materials are used to investigate the active vibration control of ordered/disordered periodic two-span beams. The equation of motion of each sub-beam with piezoelectric patches is established based on Hamilton＇s principle with an assumed mode method. The velocity feedback control algorithm is used to design the controller. The free and forced vibration behaviors of the two-span beams with the piezoelectric actuators and sensors are analyzed. The vibration properties of the disordered two-span beams caused by misplacing the middle support are also researched. In addition, the effects of the length disorder degree on the vibration performances of the disordered beams are investigated. From the numerical results, it can be concluded that the disorder in the length of the periodic two-span beams will cause vibration localizations of the free and forced vibrations of the structure, and the vibration localization phenomenon will be more and more obvious when the length difference between the two sub-beams increases. Moreover, when the velocity feedback control is used, both the forced and the free vibrations will be suppressed. Meanwhile, the vibration behaviors of the two-span beam are tuned.
