TIME INTEGRATION OF RECTANGULAR MEMBRANE FREE VIBRATIONUSING SPLINE-BASED DIFFERENTIAL QUADRATURE

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JAVIDPOOR SARA; ALE ALI NASSIM; KABI AMER

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Paper Information

Journal: JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS Year:2016 | Volume:2 | Issue:2 Page(s): 74-79

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Title

TIME INTEGRATION OF RECTANGULAR MEMBRANE FREE VIBRATIONUSING SPLINE-BASED DIFFERENTIAL QUADRATURE

Author(s)

JAVIDPOOR SARA | ALE ALI NASSIM | KABI AMER | Issue Writer Certificate

Keywords

RUNGE–KUTTA METHOD

SPLINE-BASED DIFFERENTIAL QUADRATURE METHOD

MEMBRANE VIBRATION

TIMEINTEGRATION

Abstract

In this paper, numerical spline-based differential quadrature is presented for solving the boundary andinitial value problems, and its application is used to solve the fixed rectangular MEMBRANE VIBRATIONequation. For the time integration of the problem, the Runge– Kutta and spline-based differential quadraturemethods have been applied. The Runge– Kutta method was unstable for solving the problem, with largeerrors in its results, but the SPLINE-BASED DIFFERENTIAL QUADRATURE METHOD obtained results that agree with theexact solution. The relative errors were calculated and investigated for different values of time and spatialnodes of discretisation. It seems that the SPLINE-BASED DIFFERENTIAL QUADRATURE METHOD is proper for the fullsimulation of MEMBRANE VIBRATION in both spatial and temporal solutions. For the time solving of themembrane vibration, conventional methods, such as the Runge– Kutta method, are not useful even if thetime steps are considered too small.

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APA: Copy

JAVIDPOOR, SARA, ALE ALI, NASSIM, & KABI, AMER. (2016). TIME INTEGRATION OF RECTANGULAR MEMBRANE FREE VIBRATIONUSING SPLINE-BASED DIFFERENTIAL QUADRATURE. JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, 2(2), 74-79. SID. https://sid.ir/paper/353163/en

Vancouver: Copy

JAVIDPOOR SARA, ALE ALI NASSIM, KABI AMER. TIME INTEGRATION OF RECTANGULAR MEMBRANE FREE VIBRATIONUSING SPLINE-BASED DIFFERENTIAL QUADRATURE. JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS[Internet]. 2016;2(2):74-79. Available from: https://sid.ir/paper/353163/en

IEEE: Copy

SARA JAVIDPOOR, NASSIM ALE ALI, and AMER KABI, “TIME INTEGRATION OF RECTANGULAR MEMBRANE FREE VIBRATIONUSING SPLINE-BASED DIFFERENTIAL QUADRATURE,” JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, vol. 2, no. 2, pp. 74–79, 2016, [Online]. Available: https://sid.ir/paper/353163/en

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