New Family of Explicit Structure-Dependent Integration Algorithms with Controllable Numerical Dispersion

Tang, Yu; Ren, Deqing; Qin, Hui; Luo, Chao

doi:10.1061/(asce)em.1943-7889.0001901

Cited by 6 publications

(4 citation statements)

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“…It is also observed that the left-shift values of the numerical resonance peak of TL-ϕ algorithms are smaller than those of other algorithms, indicating a smaller PE in the numerical solution. This property conforms to the findings presented in previous work [30]. In addition, the maximum values of D num for all the algorithms become larger with an increasing value of Ω than those of the exact solution.…”

Section: Frequency Response Under Arbitrary Excitationsupporting

confidence: 92%

“…Thus, the numerical characteristics of an algorithm applied in an MDOF system can be evaluated for each mode in the same way as for a single-degree-of-freedom (SDOF) system. The numerical characteristics of TL-ϕ algorithms under the free-vibration response have been fully investigated in the previous work [30]. This section focuses on the frequency response of TL-ϕ algorithms under arbitrary excitation with initial conditions of x 0 = 0 and ẋ0 = 0.…”

Section: Frequency Response Under Arbitrary Excitationmentioning

confidence: 99%

“…As only the mass matrix of the system is changed slightly, the convergence rate and stability property of the algorithm are maintained. Tang and Ren [30] presented a new family of explicit SDIM with controllable numerical dispersion based on the TL algorithm, known as TL-ϕ algorithms. By introducing a scaling parameter ϕ into the two integration parameters of TL algorithm, the values of PE at a certain structural natural frequency can be greatly diminished when compared to other well-developed algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…For an MDOF system, the calculation of ϕ depends on the critical frequency ω c = ω A that dominates the total responses of the original continuous system. In the previous work [30], the fundamental frequency ω 1 is regarded as ω c , so that ϕ becomes a constant scaling for all the modes of the system when calculating the integration parameters of the TL-ϕ algorithms. However, the first mode may not uniquely contribute to the dynamic responses of an MDOF system under a given external excitation, and the determination of ω c should take the numerical properties of both the original system and external excitation into consideration.…”

Section: Introductionmentioning

confidence: 99%

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Choices of the Critical Frequency for φ in TL-φ Algorithms When Applied to Multi-Degree of Freedom Systems

Tang

Luo

2022

Buildings

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TL-φ algorithms are newly developed explicit structure-dependent integration algorithms utilized for solving the temporally discretized equations of motion. In contrast to the existing algorithms, the most significant improvement of TL-φ algorithms is in diminishing the amount of period errors by introducing a precorrection coefficient φ into the integration parameters of TL-φ algorithms, which is related to the critical frequency of a system. In the previous work, the fundamental frequency of the system is deemed to be the critical frequency, so that φ is a constant scaling corresponding to the fundamental frequency for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. However, for a MDOF system, the first mode may not contribute to the total response more than other ones under a given external excitation, calculating φ only by the fundamental frequency will underestimate the contribution of the higher-frequency modes to structural dynamics. In this paper, choices of the critical frequency for φ when applying TL-φ algorithms to MDOF systems are investigated thoroughly. By considering the initial structural properties of the system and the frequency characteristics of the external excitation simultaneously, a calculation criterion of φ for MDOF systems under specific external excitations is proposed. Four numerical examples with different initial structure properties and loading conditions are designed, and the results demonstrate that the proposed criterion can be potentially used to solve structural dynamic problems of MDOF systems with a more desirable numerical dispersion performance.

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Section: Frequency Response Under Arbitrary Excitationsupporting

confidence: 92%

Section: Frequency Response Under Arbitrary Excitationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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