Search

The dynamical model of multiple honeycomb plates connected by hinges, including the thermal–structural coupling effect, is investigated in this paper. Under the assumption of small deformations and strains, the classical plate theory is used to establish the dynamical model of the honeycomb plate. The Chebyshev polynomial is adopted to describe the deformation of the plate and the linear torsional spring to represent the elastic hinge. Using the Rayleigh–Ritz method, the characteristic equation of the honeycomb sandwich structure is derived, from which the natural frequencies are obtained. Considering the thermal effect of the plate, the thermal–structural coupling dynamical equation is obtained. The thermal conduction in the thickness direction is calculated by the finite difference method. The present model is validated by comparing with the result generated by an equivalent orthotropic plate model established by the finite element (FE) software MSC Patran. The response analysis reveals the important effect of the metal skin and the hinge stiffness on the dynamic characteristics of the honeycomb sandwich structure. Numerical simulations reveal thermal–structural coupling features for the multi-honeycomb-plate structure from the perspective of the change in dynamic characteristics and the distribution of the temperature gradient. The thermal–structural coupling calculation method adopted herein can be used to solve the thermal conduction of the plate. It serves as the theoretical method for analyzing the dynamical behavior of the solar panel subjected to the solar heat. [ABSTRACT FROM AUTHOR]

In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed planar hybrid piecewise-smooth systems. In this class, the switching manifold is a straight line which divides the plane into two zones, and the dynamics in each zone is governed by a smooth system. When a trajectory reaches the separation line, then a reset map is applied instantaneously before entering the trajectory in the other zone. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise-smooth homoclinic solution transversally crossing the switching manifold. Then, we study the persistence of the homoclinic orbit under a nonautonomous periodic perturbation and the reset map. To achieve this objective, we obtain the Melnikov function to measure the distance of the perturbed stable and unstable manifolds and present the theorem for homoclinic bifurcations for the class of planar hybrid piecewise-smooth systems. Furthermore, we employ the obtained Melnikov function to detect the chaotic boundaries for a concrete planar hybrid piecewise-smooth system. [ABSTRACT FROM AUTHOR]

In this paper, we extend the well-known Melnikov method for smooth systems to a class of planar hybrid piecewise-smooth systems, defined in three domains separated by two switching manifolds and . The dynamics in each domain is governed by a smooth system. When an orbit reaches the separation lines, then a reset map describing an impacting rule applies instantaneously before the orbit enters into another domain. We assume that the unperturbed system has a continuum of periodic orbits transversally crossing the separation lines. Then, we wish to study the persistence of the periodic orbits under an autonomous perturbation and the reset map. To achieve this objective, we first choose four appropriate switching sections and build a Poincaré map, after that, we present a displacement function and carry on the Taylor expansion of the displacement function to the first-order in the perturbation parameter near . We denote the first coefficient in the expansion as the first-order Melnikov function whose zeros provide us the persistence of periodic orbits under perturbation. Finally, we study periodic orbits of a concrete planar hybrid piecewise-smooth system by the obtained Melnikov function. [ABSTRACT FROM AUTHOR]

The extended Melnikov method is improved to investigate the nonautonomous nonlinear dynamical system in Cartesian coordinate. The multipulse chaotic dynamics of a simply supported functionally graded materials (FGM) rectangular plate subjected to transversal and in-plane excitations is investigated in this paper for the first time. The formulas of the FGM rectangular plate are two-degree-of-freedom nonautonomous nonlinear system with coupling of nonlinear terms including several square and cubic terms. The extended Melnikov method is improved to enable us to analyze directly the nonautonomous nonlinear dynamical system of the simply-supported FGM rectangular plate. The results obtained here indicate that multipulse chaotic motions can occur in the simply-supported FGM rectangular plate. Numerical simulation is also employed to find the multipulse chaotic motions of the simply-supported FGM rectangular plate. [ABSTRACT FROM AUTHOR]

In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed piecewise smooth planar system. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise smooth homoclinic solution transversally crossing the switching manifold. The Melnikov-type function is explicitly derived by using the Hamiltonian function to measure the distance of the perturbed stable and unstable manifolds. Finally, we apply the obtained results to study the chaotic dynamics of a concrete piecewise smooth system. [ABSTRACT FROM AUTHOR]