Nonlinear vibration and dynamic stability analysis of composite plates

The thermo-mechanical nonlinear dynamics of a buckled axially moving beam is numerically investigated, with special consideration to the case with a three-to-one internal resonance between the first two modes. The equation of motion of the system traveling at a constant axial speed is obtained using Hamilton’s principle. A closed form solution is developed for the post-buckling configuration for the system with an axial speed beyond the first instability. The equation of motion over the buckled state is obtained for the forced system. The equation is reduced into a set of nonlinear ordinary differential equations via the Galerkin method. This set is solved using the pseudo-arclength continuation technique to examine the frequency response curves and direct-time integration to construct bifurcation diagrams of Poincare maps. The vibration characteristics of the system at points of interest in the parameter space are presented in the form of time histories, phase-plane portraits, and Poincare sections.

Thermo-mechanical nonlinear dynamics of a buckled axially moving beam

Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities

Background/purpose This paper deals with analysis of biaxial buckling behavior of double-orthotropic microplate system including in-plane magnetic field, using strain gradient theory. Methods Two Kirchhoff microplates are coupled by an internal elastic medium and also are limited to the external Pasternak elastic foundation. Utilizing the principle of total potential energy, the equilibrium equations of motion for three cases (out-of-phase buckling, in-phase buckling and buckling with a plate) are acquired. In this study, we assumed boundary conditions of all the edges are simply supported. In order to get exact solution for buckling load of system, Navier approach which satisfies the simply supported boundary conditions is applied. Results Variations of the buckling load of double-microplate system subjected to biaxial compression corresponding to various values of the thickness, length scale parameter, magnetic field, stiffness of internal and external elastic medium, aspect ratio, shear stiffness of the Pasternak foundation and biaxial compression ratio are investigated. Furthermore, influence of higher modes on buckling load is shown. By comparing the numerical results, it is found that dimensionless buckling load ratio for in-phase mode is more than those of out of phase and one microplate fixed. Also it is shown that the value of buckling load ratio reduces, when non-dimensional length scale parameter increases. Conclusion However, we found when properties of plate are orthotropic the buckling load ratio is more than isotropic state. Also, by considering the effect of magnetic field, non-dimensional buckling load ratio reduces.

Biaxial buckling analysis of double-orthotropic microplate-systems including in-plane magnetic field based on strain gradient theory

Guan-Yuan Wu

Papers

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