The equation of lattice vibration of one-dimensional monatomic lattice and the equation of longitudinal vibration of a uniform bar are discussed.Raplacing the spatial derivatives by spatial differences in the equation of the latter,we get the equation of the former.The dispersion laws of the two systems are compared.The Brillioun zone of discrete system is intimately connected with the interparticle distance.With the changing of mass distribution from discretization to continuum,the dispersion law of the lattice vibration changes to that of the longitudinal vibration of a uniform bar.
Soliton dynamics is simulated for trans-polyacetylene single-chain systems using the Su-Schrieffer-Heeger (SSH) model with an additional part to include an external electric field. It is shown that the soliton moves along the chain with a constant speed when an external electric field is applied.
In this work, an efficient topology optimization approach is proposed for a three-dimensional (3D) flexible multibody system (FMBS) undergoing both large overall motion and large deformation. The FMBS of concern is accurately modeled first via the solid element of the absolute nodal coordinate formulation (ANCF), which utilizes both nodal positions and nodal slopes as the generalized coordinates. Furthermore, the analytical formulae of the elastic force vector and the corresponding Jacobian are derived for efficient computation. To deal with the dynamics in the optimization process, the equivalent static load (ESL) method is employed to transform the topology optimization problem of dynamic response into a static one. Besides, the newly developed topology optimization method by moving morphable components (MMC) is used and reevaluated to optimize the 3D FMBS. In the MMC-based framework, a set of morphable structural components serves as the building blocks of optimization and hence greatly reduces the number of design variables. Therefore, the topology optimization approach has a potential to efficiently optimize an FMBS of large scale, especially in 3D cases. Two numerical examples are presented to validate the accuracy of the solid element of ANCF and the efficiency of the proposed optimization methodology, respectively.
Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein–Gordon/Fermi–Pasta–Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.
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