National Taiwan Ocean University Research Hubhttps://scholars.ntou.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 13 Sep 2024 10:33:06 GMT2024-09-13T10:33:06Z5091Dynamic Green's functions for multiple elliptical inclusions with imperfect interfaceshttp://scholars.ntou.edu.tw/handle/123456789/2508Title: Dynamic Green's functions for multiple elliptical inclusions with imperfect interfaces
Authors: Lee, W. M.; Jeng-Tzong Chen
Abstract: The problem of an unbounded elastic solid with multiple elliptical inclusions subjected to a time-harmonic anti-plane concentrated force is semi-analytically solved by using the collocation multipole method. The displacement of matrix and inclusion are represented by angular and radial Mathieu functions. The imperfect interface between the matrix and the inclusion is characterized as a linear spring model with vanishing thickness. It is the derivative that the imperfect condition is involved. The addition theorem of Mathieu function is frequently used to solve multiply-connected domain problems in the traditional multipole method. An alternate here is a direct computation. The associated normal derivative with respect to a non-local elliptical coordinate system is developed by means of directional derivative. Besides simple computation, no truncation error is caused. The displacement field is determined by using the imperfect interface conditions through collocating points along the interface. Several numerical experiments are done to investigate the effects of the driving frequency of the concentrated force, imperfect interface and the convexity of elliptical inclusions on the dynamic Green's functions.
Tue, 01 Sep 2020 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/25082020-09-01T00:00:00ZDerivation of Green's function using addition theoremhttp://scholars.ntou.edu.tw/handle/123456789/2362Title: Derivation of Green's function using addition theorem
Authors: Jeng-Tzong Chen; Chou, K. H.; Kao, S. K.
Abstract: Following the success of null-field integral equation to solve the BVP of the Laplace equation, this paper employs the addition theorem and superposition technique to revisit the Green’s function of Laplace problems with circular boundaries. The Green’s function is decomposed into two parts, one is the fundamental solution and the other is an infinite plane of circular boundaries subject to the specified boundary conditions derived from the addition theorem. After superimposing the two solutions, the governing equation and boundary condition are both satisfied. Some examples are demonstrated to see the validity of the present method.
Wed, 01 Apr 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23622009-04-01T00:00:00ZDegenerate scale for multiply connected Laplace problemshttp://scholars.ntou.edu.tw/handle/123456789/2446Title: Degenerate scale for multiply connected Laplace problems
Authors: Jeng-Tzong Chen; Wen-Cheng Shen
Abstract: The degenerate scale in the boundary integral equation (BIE) or boundary element method (BEM) solution of multiply connected problem is studied in this paper. For the mathematical analysis, we use the null-field integral equation, degenerate kernels and Fourier series to examine the solvability of BIE for multiply connected problem in the discrete system. Two treatments, the method of adding a rigid body term and CHEEF concept (Combined Helmholtz Exterior integral Equation Formulation), are applied to remedy the non-unique solution due to the critical scale. The efficiency and accuracy of the two regularizations are also addressed. For simplicity without loss of generality, the eccentric case is considered to demonstrate the occurring mechanism of degenerate scale.
Mon, 01 Jan 2007 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/24462007-01-01T00:00:00ZFictitious frequency for the exterior Helmholtz equation subject to the mixed-type boundary condition using BEMshttp://scholars.ntou.edu.tw/handle/123456789/2441Title: Fictitious frequency for the exterior Helmholtz equation subject to the mixed-type boundary condition using BEMs
Authors: Jeng-Tzong Chen; Tzong-Wey Lin; I-Lin Chen; Yang-Jye Lee
Abstract: Boundary integral equations and boundary element methods were employed analytically, semi-analytically and numerically to study the occurrence of fictitious frequency for the exterior Helmholtz equations subject to the mixed-type boundary conditions. A semi-infinite rod and a circular radiator of problems were addressed. Degenerate kernel of the fundamental solution and Fourier series for boundary density were utilized in the null-field integral equation to examine the occurrence of fictitious frequency semi-analytically. The BEM was utilized to solve the solution numerically. The CHIEF technique and Burton and Miller method were adopted to suppress the occurrence of the fictitious frequency. It is emphasized that the occurrence of fictitious frequency depend on the adopted method (singular or hypersingular formulation) no matter what the given type of boundary condition for the problem is. The illustrative examples were tested to verify this finding successfully.
Sat, 01 Jan 2005 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/24412005-01-01T00:00:00ZA new concept of modal participation factor for numerical instability in the dual BEM for exterior acousticshttp://scholars.ntou.edu.tw/handle/123456789/2353Title: A new concept of modal participation factor for numerical instability in the dual BEM for exterior acoustics
Authors: Jeng-Tzong Chen; Chen, K. H.; Chen, I. L.; Liu, L. W.
Abstract: This paper presents the occurring mechanism why irregular frequencies are imbedded in the exterior acoustics using the dual boundary element method (BEM). The modal participation factor which dominates the numerical instability is derived for continuous and discrete systems. In addition, the irregular (fictitious) frequencies embedded in the singular or hypersingular integral equations are discussed, respectively. It is found that the irregular values depend on the kernels in the integral representation for the solution. A two-dimensional dual BEM program for the exterior acoustics was developed. Numerical experiments are conducted to verify the concept of modal participation factor.
Sat, 01 Mar 2003 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23532003-03-01T00:00:00ZOn fictitious frequencies using dual BEM for non-uniform radiation problems of a cylinderhttp://scholars.ntou.edu.tw/handle/123456789/2341Title: On fictitious frequencies using dual BEM for non-uniform radiation problems of a cylinder
Authors: Jeng-Tzong Chen; Chen, C. T.; Chen, K. H.; Chen, I. L.
Wed, 01 Nov 2000 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23412000-11-01T00:00:00ZOn fictitious frequencies using circulants for radiation problems of a cylinderhttp://scholars.ntou.edu.tw/handle/123456789/2389Title: On fictitious frequencies using circulants for radiation problems of a cylinder
Authors: Jeng-Tzong Chen; Kuo, S. R.
Sat, 01 Jan 2000 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23892000-01-01T00:00:00ZOn fictitious frequencies using dual series representationhttp://scholars.ntou.edu.tw/handle/123456789/2333Title: On fictitious frequencies using dual series representation
Authors: Jeng-Tzong Chen
Tue, 01 Sep 1998 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/23331998-09-01T00:00:00ZFree vibration of a SDOF system with hysteretic dampinghttp://scholars.ntou.edu.tw/handle/123456789/16536Title: Free vibration of a SDOF system with hysteretic damping
Authors: L.Y. Chen; Jeng-Tzong Chen; C.H. Chen; H.-K. Hong
Tue, 01 Nov 1994 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/165361994-11-01T00:00:00Z