No abstract

a b s t r a c tIn this paper, the elastic wave propagation in phononic crystals with piezoelectric and piezomagnetic inclusions is investigated taking the magneto-electro-elastic coupling into account. The electric and magnetic fields are approximated as quasi-static. The band structures of three kinds of piezoelectric/piezomagnetic phononic crystals-CoFe 2 O 4 /quartz, BaTiO 3 /CoFe 2 O 4 and BaTiO 3 -CoFe 2 O 4 /polymer periodic composites are calculated using the plane-wave expansion method. The piezoelectric and piezomagnetic effects on the band structures are analyzed. The numerical results show that in CoFe 2 O 4 /quartz structures, only one narrow band gap exists along the C-X direction for the coupling of xy-mode and z-mode for the filling fraction f being 0.4; while in BaTiO 3 /CoFe 2 O 4 composites, only one narrow band gap exists along the C-X direction forxy-mode and no band gap exists for z-mode as the filling friction f is 0.5. Moreover, for the new type of magneto-electroelastic phononic crystal-BaTiO 3 -CoFe 2 O 4 /polymer periodic composite, the band gap characteristics are more superior in the whole considered frequency regions due to the big contrast of the material properties in the two constituents and the effects of the piezoelectricity and piezomagneticity on the band gap structures are remarkable.

The two-dimensional wave propagation and localization in disordered periodic layered 2-2 piezoelectric composite structures are studied by considering the mechanic-electric coupling. The transfer matrix between two consecutive sublayers is obtained based on the continuity conditions. Regarding the variables of mechanical and electrical fields as the elements of the state vector, the expression of the localization factors in disordered periodic layered piezoelectric composite structures is derived. Numerical results are presented for two cases-disorder of the thickness of the polymers and disorder of the piezoelectric and elastic constants of the piezoelectric ceramics. The results show that due to the piezoelectric effects, the characteristics of the wave localization in disordered periodic layered piezoelectric composite structures are different from those in disordered periodic layered purely elastic ones. The wave localization is strengthened due to the piezoelectricity. And the larger the piezoelectric constant is, the larger the wave localization factors are. It is found that slight disorder in the piezoelectric or elastic constants of the piezoelectric ceramics can lead to more prominent localization phenomenon.

No abstract

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

The homoclinic phenomena in doublelayered nanoplates (DLNP) are investigated. Based on the nonlocal continuum theory, the nonlinear dynamical equations for DLNP subjected to in-plane excitation are derived by double-mode Galerkin truncation. The extended Melnikov method is utilized to discuss the homoclinic phenomena and chaotic motion for the buckled DLNP system. The criterions for the existence of transverse homoclinic orbits are established under different four buckling cases (i.e., the first-and second-type synchronous buckling as well as asynchronous buckling). And the results derived by the abovementioned analysis are verified by molecular dynamics and Lyapunov exponent spectrum. Small-scale effect on the homoclinic motion is mainly inspected. From the result, it is rather novel that the transversality condition is independent of the nonlinear terms in the equations. This fact means that it is not necessary to distinguish whether the boundaries are movable or immovable for the in-plane parametric excitation DLNP. The parametric regime where homoclinic phenomena appear shrinks with the augment of nonlocal parameter for the first-type synchronous buckling case. However, this trend is just opposite for the other three buckling cases.Finally, it can be seen that homoclinic phenomena more likely occur on Mode I (i.e., lower mode) for the second-type synchronous and asynchronous buckling cases. However, the homoclinic motion for the firsttype asynchronous buckling most likely takes place on Mode III.

In this paper, the active vibration control of conical shells is studied using velocity feedback and linear quadratic regulator methods. Up to now, many researches on the active vibration control of beams, plates and cylindrical shells have been published, however, to our knowledge, few people have studied the active vibration control of conical shells. Normally, in the equation of motion of the conical shells, some coefficients are variables, which makes the equation of motion of the conical shells very complicated and difficult to solve analytically. In order to solve this problem, Hamilton's principle with the assumed mode method is employed to derive the equation of motion of the complex electromechanical coupling system. This equation of motion for the conical shell and piezoelectric patch system can be easily solved and effectively used for the structural active vibration control. Based on the traditional theory of structural dynamics, this method is easy to understand and is verified by numerical simulations. The forced vibration responses of the conical shells with two piezoelectric patches are computed to study the active vibration control. The optimal design for the locations of the piezoelectric patches is also developed by the genetic algorithm. From the results it can be seen that the control gain has a significant effect on the vibration control of the conical shell, but the effect of the size of the piezoelectric patches on controlling the vibration amplitudes is not so obvious. The overall vibration of the conical shell can be effectively reduced by the velocity feedback control method. With the increase of the control gain, the active damping characteristics of the conical shell are improved. Moreover, the optimal placement scheme of the piezoelectric patches obtained by the genetic algorithm can significantly reduce the vibration amplitudes of the conical shell.

An analytical methodology is presented to study the active vibration control of beams treated with active constrained layer damping (ACLD). This analytical method is based on the conventional theory of structural dynamics. The process of deriving equations is precise and easy to understand. Hamilton’s principle with the Rayleigh–Ritz method is used to derive the equation of motion of the beam/ACLD system. By applying an appropriate external control voltage to activate the piezoelectric constraining layer, a negative velocity feedback control strategy is employed to obtain the active damping and effective vibration control. From the numerical results it is seen that the damping performances of the beam can be significantly improved by the ACLD treatment. With the increase of the control gain, the active damping characteristics are also increased. By equally dividing one ACLD patch into two and properly distributing them on the beam, one can obtain better active vibration control results than for the beam with one ACLD patch. The analytical method presented in this paper can be effectively extended to other kinds of structures.