This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the magnetic and electric fields on the boundary as inputs and outputs. Suitable expressions for the energy stored in the region and the energy absorbed from the boundaries are introduced, and used to show that the FDTD system is dissipative under a generalized Courant-Friedrichs-Lewy condition. Based on the concept of dissipation, a powerful theoretical framework to investigate the stability of FDTD methods is devised. The new method makes FDTD stability proofs simpler, more intuitive, and modular. Stability conditions can indeed be given on the individual components (e.g. boundary conditions, meshes, embedded models) instead of the whole coupled setup. As an example of application, we derive a new subgridding method with material traverse, arbitrary grid refinement, and guaranteed stability. The method is easy to implement and has a straightforward stability proof. Numerical results confirm its stability, low reflections, and ability to handle material traverse.

Abstract-A miniaturized printed log-periodic fractal dipole antenna is proposed. Tree fractal structure is introduced in an antenna design and evolves the traditional Euclidean log-periodic dipole array into the log-periodic second-iteration tree-dipole array (LPT 2 DA) for the first time. Main parameters and characteristics of the proposed antenna are discussed. A fabricated proof-of-concept prototype of the proposed antenna is etched on a FR4 substrate with a relative permittivity of 4.4 and volume of 490 mm × 245 mm × 1.5 mm. The impedance bandwidth (measured VSWR < 2) of the fabricated antenna with approximate 40% reduction of traditional log-periodic dipole antenna is from 0.37 to 3.55 GHz with a ratio of about 9.59 : 1. Both numerical and experimental results show that the proposed antenna has stable directional radiation patterns and apparently miniaturized effect, which are suitable for various ultra-wideband applications.

The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be particularly challenging in scenarios where a setup is composed of multiple components, such as grids of different resolution, advanced boundary conditions, reduced-order models, and lumped elements. We propose a dissipation theory for 3-D FDTD inspired by the principle of energy conservation. We view the FDTD update equations for a 3-D region as a dynamical system, and show under which conditions the system is dissipative. By requiring each component of an FDTD-like scheme to be dissipative, the stability of the overall coupled scheme follows by construction. The proposed framework enables the creation of provably stable schemes in an easy and modular fashion, since conditions are imposed on the individual components, rather than on the overall coupled scheme as in existing approaches. With the proposed framework, we derive a new subgridding scheme with guaranteed stability, low reflections, support for material traverse and arbitrary (odd) grid refinement ratio.

e nonlinear dynamic responses of a wire rope under periodic excitation in a friction hoisting system are investigated.Longitudinal excitation experiments of different periodic excitation frequencies are performed. e nonlinear dynamic characteristics of the rope, including transverse, longitudinal, and coupled vibrations, are discussed with time-frequency analysis. e results show that the transverse vibration is a forced vibration following the excitation, while the longitudinal vibration shows a complex, random vibration state. e vibration amplitude and intensity deviate significantly from their linear trend (superharmonic resonance) at some excitation frequencies, and this deviation indicates the typical nonlinear multiorder natural frequency characteristics. e lifting motion can lead to additional corrugated high-order harmonics and cause a fundamental wave distortion of low-frequency excitation. Experimental evidence for the coupling characteristics of the transverse-longitudinal rope vibration in the lifting process is found.

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