arXiv subjects

Kaiping Yu

Publications and source records attributed to Kaiping Yu.

6 recordsLinked to original sources

arXiv2026

Order elevation of directly self-starting sub-step implicit integrators for transient dynamics

Directly self-starting implicit methods are attractive for transient analysis because they avoid auxiliary starting procedures while retaining the original first- or second-order governing equations. However, most existing formulations usually fix the last sub-step at the end of each time interval, which restricts the attainable order. This study develops a generalized $s$-sub-step implicit framework by releasing this constraint and treating all sub-step locations as design variables. The resulting methods admit a unified Runge--Kutta representation for both first- and second-order transient systems and preserve identical effective matrices over all sub-steps. Accuracy conditions are derived by simultaneously matching the numerical amplification factor and load operator, thereby accounting for both homogeneous and forced responses. For $s=1,~\cdots,~6$, two complementary families are obtained: $s$th-order members with user-controllable high-frequency numerical dissipation and adjustable sub-step locations, and $(s+1)$th-order members obtained by selecting the sub-step locations, with fixed dissipation. The latter reach up to seventh-order accuracy without increasing the number of sub-steps, although some high-order members are $A(\alpha)$-stable with stability angles extremely close to $90^\circ$. Analytical amplitude and phase errors further reveal parity-dependent superconvergence in undamped systems, and appropriate parameter selections can substantially increase either phase or amplitude accuracy beyond the formal order. Numerical benchmarks confirm the predicted convergence orders and the controllable suppression of spurious high-frequency responses.

math.NA↗

arXiv2022

High-order accurate multi-sub-step implicit integration algorithms with dissipation control for second-order hyperbolic problems

This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step and thus the trapezoidal rule is always employed in the first sub-step. This paper demonstrates for the first time that the proposed $ s $-sub-step implicit method with $ s\le6 $ can reach $ s $th-order accuracy when achieving dissipation control and unconditional stability simultaneously. Hence, this paper develops, analyzes, and compares four cost-optimal high-order implicit algorithms within the present $ s $-sub-step method using three, four, five, and six sub-steps. Each high-order implicit algorithm shares identical effective stiffness matrices to achieve optimal spectral properties. Unlike the published algorithms, the proposed high-order methods do not suffer from the order reduction for solving forced vibrations. Moreover, the novel methods overcome the defect that the authors' previous algorithms require an additional solution to obtain accurate accelerations. Linear and nonlinear examples are solved to confirm the numerical performance and superiority of four novel high-order algorithms.

math.NA↗

arXiv2021

Abnormal topological refraction into free medium at sub-wavelength scale in valley phononic crystal plates

In this work we propose a topological valley phononic crystal plate and we extensively investigate the refraction of valley modes into the surrounding homogeneous medium. This phononic crystal includes two sublattices of resonators (A and B) modeled by mass-spring systems. We show that two edge states confined at the AB/BA and BA/AB type domain walls exhibit different symmetries in physical space and energy peaks in the Fourier space. As a result, distinct refraction behaviors, especially through an armchair cut edge, are observed. On the other hand, the decay depth of these localized topological modes, which is found to be solely determined by the relative resonant strength between the scatterers, significantly affects the refraction patterns. More interestingly, the outgoing traveling wave through a zigzag interface becomes evanescent when operating at deep sub-wavelength scale. This is realized by tuning the average resonant strength. We show that the evanescent modes only exist along a particular type of outlet edge, and that they can couple with both topological interface states. We also present two designs of topological functional devices, including an elastic one-way transmission waveguide and a near-ideal monopole/dipole emitter, both based on our phononic structure.

physics.app-ph↗

arXiv2018

Topological spin-Hall edge states of flexural wave in perforated metamaterial plates

This paper investigates the pseudo-spin based edge states for flexural waves in a honeycomb perforated phononic plate, which behaves an elastic analogue of the quantum spin Hall effect. We utilize finite element method to analyse the dispersion for flexural waves based on Mindlin's plate theory. Topological transition takes place around a double Dirac cone at $\Gamma$ point by adjusting the sizes of perforated holes. We develop an effective Hamiltonian to describe the bands around the two doubly degenerated states and analyse the topological invariants. This further leads us to observe the topologically protected edge states localized at the interface between two lattices. We demonstrate the unidirectional propagation of the edge waves along topological interface, as well as their robustness against defects and sharp bends.

physics.app-ph↗

arXiv2017

Dial-in Topological Metamaterials Based on Bistable Stewart Platform

Recently, there have been significant efforts to guide mechanical energy in structures by relying on a novel topological framework popularized by the discovery of topological insulators. Here, we propose a topological metamaterial system based on the design of the Stewart Platform, which can not only guide mechanical waves robustly in a desired path, but also can be tuned in situ to change this wave path at will. Without resorting to any active materials, the current system harnesses bistablilty in its unit cells, such that tuning can be performed simply by a dial-in action. Consequently, a topological transition mechanism inspired by the quantum valley Hall effect can be achieved. We show the possibility of tuning in a variety of topological and traditional waveguides in the same system, and numerically investigate key qualitative and quantitative differences between them. We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range, topological waveguides are distinctive as they support robust, back scattering immune, one-way wave propagation.

cond-mat.mes-hall↗

arXiv2017

Generalized thermoelastic band structures of Rayleigh wave in one-dimensional phononic crystals

We investigate generalized band structures of Rayleigh wave in 1-D phononic crystals in the context of Green-Nagdhi thermoelastic (TE) theory. Solutions of the coupled equations included thermal field are obtained firstly. Then according to boundary conditions, phase velocity is derived. The transfer matrix methodology is adopted in order to formulate the band structures of generalized TE Rayleigh wave. It is demonstrated that the band structure of TE Rayleigh wave is comprised of elastic and thermal bands. For Aluminum-Epoxy phononic crystal, the thermoelasticity can influence the transmission ability of band gaps as well as narrow down the band gap width.

cond-mat.mtrl-sci↗