The Experts below are selected from a list of 4203 Experts worldwide ranked by ideXlab platform
Guoyong Jin - One of the best experts on this subject based on the ideXlab platform.
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acoustic modeling of a three dimensional rectangular opened enclosure coupled with a semi infinite exterior field at the baffled opening
Journal of the Acoustical Society of America, 2016Co-Authors: Guoyong Jin, Shuangxia Shi, Zhigang LiuAbstract:A modeling method is proposed for the acoustic analysis of a three-dimensional (3D) rectangular opened enclosure coupled with a semi-infinite exterior field by a rectangular opening of arbitrary size, and with general wall impedance. In contrast to existing modeling methods that solve the differential equations, the energy principle in combination with a 3D modified Fourier Cosine Series is employed in the present method for the modeling of this system. Under this theoretical framework, the effect of an opening in the wall of a rectangular enclosure is taken into account via the work done by the sound pressure acting on the opening between the finite enclosure and exterior domain. The sound pressure inside the opened enclosure is expressed as the combination of a 3D trigonometric Cosine Series and one supplementary 2D expansion introduced to ensure uniform convergence of the solution over the entire solution domain including opening boundary. The acoustic responses of the opened enclosure are obtained bas...
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vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions
Smart Materials and Structures, 2016Co-Authors: Guoyong JinAbstract:The paper presents a unified solution for free and transient vibration analyses of a functionally graded piezoelectric curved beam with general boundary conditions within the framework of Timoshenko beam theory. The formulation is derived by means of the variational principle in conjunction with a modified Fourier Series which consists of standard Fourier Cosine Series and supplemented functions. The mechanical and electrical properties of functionally graded piezoelectric materials (FGPMs) are assumed to vary continuously in the thickness direction and are estimated by Voigt's rule of mixture. The convergence, accuracy and reliability of the present formulation are demonstrated by comparing the present solutions with those from the literature and finite element analysis. Numerous results for FGPM beams with different boundary conditions, geometrical parameters as well as material distributions are given. Moreover, forced vibration of the FGPM beams subjected to dynamic loads and general boundary conditions are also investigated.
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free vibration analysis of laminated composite and functionally graded sector plates with general boundary conditions
Composite Structures, 2015Co-Authors: Guoyong Jin, Xueren WangAbstract:Abstract A modified Fourier Series method is applied to study the free vibration of laminated composite and four-parameter functionally graded sector plates with general boundary conditions. The first-order shear deformation plate theory is employed to include the effects of rotary inertias and shear deformation. Regardless of the boundary conditions, each of the displacement and rotation components of the sector plates is described as a linear superposition of a double Fourier Cosine Series and several supplementary functions introduced to accelerate the convergence of Series representations. The Rayleigh–Ritz procedure based on the energy functions of the sector plates is adopted to solve the exact solutions. In order to verify the accuracy and reliability of the present method, comparisons of the present results with those published are presented. New numerical results for laminated composite and functionally graded sector plates with elastic restraints are given. The effects of the boundary conditions and material and geometrical properties on the frequencies of the sector plates are investigated.
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free vibration analysis of moderately thick functionally graded open shells with general boundary conditions
Composite Structures, 2014Co-Authors: Guoyong JinAbstract:Abstract This paper presents the free vibration analysis of functionally graded open shells including cylindrical, conical and spherical ones with arbitrary subtended angle and general boundary conditions. The material properties of the open shells have continuous and smooth variation in the thickness direction based on general four-parameter power-law distributions in terms of volume fractions of the constituents. The formulation is derived by the modified Fourier Series in conjunction with Rayleigh–Ritz method according to the first-order shear deformation shell theory. The modified Fourier Series is expressed in the form of the linear superposition of a double Cosine Series and auxiliary functions which are introduced to ensure and accelerate the convergence of the Series representations. The comprehensive investigations concerning the convergence and accuracy of the present method are performed by a number of numerical tests and comparisons. Some new results of FGM open shells with elastic restraints are presented. Parametric studies are carried out for FGM open shells with respect to the boundary conditions, material profiles and geometrical parameters.
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a general fourier solution for the vibration analysis of composite laminated structure elements of revolution with general elastic restraints
Composite Structures, 2014Co-Authors: Guoyong Jin, Xingzhao Jia, Siyang GaoAbstract:Abstract A unified modified Fourier solution based on the first order shear deformation theory is developed for the vibrations of various composite laminated structure elements of revolution with general elastic restraints including cylindrical, conical, spherical shells and annular plates. Regardless of boundary conditions, each displacement and rotation component of the structures is invariantly expressed as the superposition of a Fourier Cosine Series and two supplementary functions introduced to remove any potential discontinuous of the original displacements and their derivatives. On the basis of energy functional of structure elements, the exact Series solutions are obtained using the Rayleigh–Ritz procedure. The accuracy and convergence of the proposed modified Fourier Series solution are demonstrated by the comprehensive numerical examples. A variety of new vibration results including frequencies and mode shapes for composite laminated cylindrical, conical, spherical shells and annular plates with classical and elastic restraints as well as different geometric and material parameters are presented, which may serve as benchmark solution for future researches. The effects of the elastic restraint parameters, layout orientations, number of layers, conical angles and degrees of anisotropic on the vibration frequencies of the structures are illustrated.
Cornelis W. Oosterlee - One of the best experts on this subject based on the ideXlab platform.
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on the fourier Cosine Series expansion method for stochastic control problems
Numerical Linear Algebra With Applications, 2013Co-Authors: Marjon Ruijter, Cornelis W. Oosterlee, R F T AalbersAbstract:SUMMARY We develop a method for solving stochastic control problems under one-dimensional Levy processes. The method is based on the dynamic programming principle and a Fourier Cosine expansion method. Local errors in the vicinity of the domain boundaries may disrupt the algorithm. For efficient computation of matrix–vector products with Hankel and Toeplitz structures, we use a fast Fourier transform algorithm. An extensive error analysis provides new insights based on which we develop an extrapolation method to deal with the propagation of local errors. Copyright © 2013 John Wiley & Sons, Ltd.
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two dimensional fourier Cosine Series expansion method for pricing financial options
SIAM Journal on Scientific Computing, 2012Co-Authors: Marjon Ruijter, Cornelis W. OosterleeAbstract:The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826--848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27--62]. In this paper, we extend the method to higher dimensions, with a multidimensional asset price process. The algorithm can be applied to, for example, pricing two-color rainbow options but also to pricing under the popular Heston stochastic volatility model. For smooth density functions, the resulting method converges exponentially in the number of terms in the Fourier Cosine Series summations; otherwise we achieve algebraic convergence. The use of an FFT algorithm, for asset prices modeled by Levy processes, makes the algorithm highly efficient. We perform extensive numerical experiments.
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a fourier based valuation method for bermudan and barrier options under heston s model
Siam Journal on Financial Mathematics, 2011Co-Authors: F Fang, Cornelis W. OosterleeAbstract:We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier Cosine Series expansion, as in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826-848, F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27-62], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error convergence.
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pricing options under stochastic volatility with fourier Cosine Series expansions
2010Co-Authors: F Fang, Cornelis W. OosterleeAbstract:An option pricing method for European options based on the FourierCosine Series, called the COS method, is presented. It can cover underlying asset processes for which the characteristic function is known, and in this paper, in particular, we consider stochastic volatility dynamics.
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pricing early exercise and discrete barrier options by fourier Cosine Series expansions
Numerische Mathematik, 2009Co-Authors: F Fang, Cornelis W. OosterleeAbstract:We present a pricing method based on Fourier-Cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Levy asset price models. The error convergence is exponential for processes characterized by very smooth ($${{\rm{C}}^{\infty}[a,b]\in\mathbb {R}}$$) transitional probability density functions. The computational complexity is O((M − 1)N log N) with N a (small) number of terms from the Series expansion, and M, the number of early-exercise/monitoring dates. This paper is the follow-up of (Fang and Oosterlee in SIAM J Sci Comput 31(2):826–848, 2008) in which we presented the impressive performance of the Fourier-Cosine Series method for European options.
F Fang - One of the best experts on this subject based on the ideXlab platform.
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a fourier based valuation method for bermudan and barrier options under heston s model
Siam Journal on Financial Mathematics, 2011Co-Authors: F Fang, Cornelis W. OosterleeAbstract:We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier Cosine Series expansion, as in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826-848, F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27-62], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error convergence.
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pricing options under stochastic volatility with fourier Cosine Series expansions
2010Co-Authors: F Fang, Cornelis W. OosterleeAbstract:An option pricing method for European options based on the FourierCosine Series, called the COS method, is presented. It can cover underlying asset processes for which the characteristic function is known, and in this paper, in particular, we consider stochastic volatility dynamics.
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pricing early exercise and discrete barrier options by fourier Cosine Series expansions
Numerische Mathematik, 2009Co-Authors: F Fang, Cornelis W. OosterleeAbstract:We present a pricing method based on Fourier-Cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Levy asset price models. The error convergence is exponential for processes characterized by very smooth ($${{\rm{C}}^{\infty}[a,b]\in\mathbb {R}}$$) transitional probability density functions. The computational complexity is O((M − 1)N log N) with N a (small) number of terms from the Series expansion, and M, the number of early-exercise/monitoring dates. This paper is the follow-up of (Fang and Oosterlee in SIAM J Sci Comput 31(2):826–848, 2008) in which we presented the impressive performance of the Fourier-Cosine Series method for European options.
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a novel pricing method for european options based on fourier Cosine Series expansions
SIAM Journal on Scientific Computing, 2008Co-Authors: F Fang, Cornelis W. OosterleeAbstract:Here we develop an option pricing method for European options based on the Fourier-Cosine Series and call it the COS method. The key insight is in the close relation of the characteristic function with the Series coefficients of the Fourier-Cosine expansion of the density function. In most cases, the convergence rate of the COS method is exponential and the computational complexity is linear. Its range of application covers underlying asset processes for which the characteristic function is known and various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal with European options in particular. In a follow-up paper we will present its application to options with early-exercise features.
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on an option pricing method based on fourier Cosine Series expansions
Reports of the Department of Applied Mathematical Analysis, 2008Co-Authors: F Fang, Cornelis W. OosterleeAbstract:Here we develop an option pricing method for European options based on the Fourier-Cosine Series, and call it the COS method. The convergence rate of the COS method is exponential and the computational complexity is linear. It has a wide range of applicability for different underlying dynamics, including Levy processes and Heston’s stochastic volatility model, and for various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal in particular with European options. In a follow-up paper, part II, we will present its application to options with early-exercise features.
Jiaquan Deng - One of the best experts on this subject based on the ideXlab platform.
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deflection of a cantilever rectangular plate induced by surface stress with applications to surface stress measurement
Journal of Applied Physics, 2012Co-Authors: Xianwei Zeng, Jiaquan DengAbstract:Surface stress plays important roles in the fabrication and applications of thin-film substrate systems. Bending test of cantilever microbeams has been commonly applied to characterize the surface stress. Stoney’s equation, ideally valid for completely unconstrained plates, is typically used to convert the measured deflection to a surface stress. To assess the validity of Stoney’s equation for the more complicated case of a plate with a clamped end, an analytical solution has been obtained in this study for the deflection of a cantilever rectangular plate due to surface stresses at its upper and lower surfaces. The analytical solution is given by the summation of single Fourier Cosine Series in the length and the width directions of the plate and a lower order polynomial. Numerical results for the deflection, slope, and curvature for the midpoint of the free end are presented for cantilever plates with aspect ratios ranging from 0.1 to 10 and for different Poisson’s ratios. In most practical measurements ...
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deflection of a cantilever rectangular plate induced by surface stress with applications to surface stress measurement
Journal of Applied Physics, 2012Co-Authors: Xianwei Zeng, Jiaquan DengAbstract:Surface stress plays important roles in the fabrication and applications of thin-film substrate systems. Bending test of cantilever microbeams has been commonly applied to characterize the surface stress. Stoney’s equation, ideally valid for completely unconstrained plates, is typically used to convert the measured deflection to a surface stress. To assess the validity of Stoney’s equation for the more complicated case of a plate with a clamped end, an analytical solution has been obtained in this study for the deflection of a cantilever rectangular plate due to surface stresses at its upper and lower surfaces. The analytical solution is given by the summation of single Fourier Cosine Series in the length and the width directions of the plate and a lower order polynomial. Numerical results for the deflection, slope, and curvature for the midpoint of the free end are presented for cantilever plates with aspect ratios ranging from 0.1 to 10 and for different Poisson’s ratios. In most practical measurements of surface stress, the aspect ratio is greater than one and the maximum percentage errors of Stoney’s equation for the deflection, slope, and curvature for the midpoint of the free end are 16%, 16%, and 10%, respectively. The present analytical solution based on Fourier Cosine Series with the first two leading terms can provide a significant improvement over Stoney’s equation. The maximum percentage errors for the deflection, slope, and curvature for the midpoint of the free end are reduced to 3%, 2%, and 3%, respectively.
Qingshan Wang - One of the best experts on this subject based on the ideXlab platform.
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a modified fourier solution for sound vibration analysis for composite laminated thin sector plate cavity coupled system
Composite Structures, 2019Co-Authors: Hong Zhang, Qingshan WangAbstract:Abstract This paper applied the modified Fourier Series method to investigate the sound-vibration characteristics by establishing a composite laminated thin sector plate-cavity coupled model for the first time based on the classical plate theory (CPT) and Rayleigh-Ritz energy technique. The coupled system consists of an annular sector or circular sector plate backed by an acoustic cavity filled with air or water. Ignoring the influence of boundary conditions, displacements admissible functions of laminated sector plate and sound pressure admissible functions of cavity can be set up as a Fourier Series superposition, whose composition are the superposition of Fourier Cosine Series and supplementary functions. The addition of these supplementary polynomials can effectively eliminate the discontinuity or jump phenomenon on the boundary. The correctness of the established analytical model has been validated by being compared with the results achieved by the finite element method (FEM). On this basis, the coupling mechanism of the weakly coupled system and the strongly coupled system are discussed in detail. In addition, some new results and discussions are given, including the cavity depth, plate thickness, anisotropic degree, varying boundary conditions and so on, which could provide reference for future research.
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benchmark solution for free vibration of thick open cylindrical shells on pasternak foundation with general boundary conditions
Meccanica, 2017Co-Authors: Qingshan Wang, Fuzhen Pang, Dongyan Shi, Fazle AhadAbstract:In the present article, a new three-dimensional exact solution for free vibration of thick open cylindrical shells on Pasternak foundation with general boundary conditions is presented. The three-dimensional elasticity theory is employed to formulate the theoretical model. The admissible functions of the thick shells are described as a combination of a three-dimensional (3-D) Fourier Cosine Series and auxiliary functions. Compared with the traditional Fourier Series, the improved Fourier Series can eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions. The excellent accuracy and reliability of the current solutions are demonstrated by numerical examples and comparison of the present results with those available in the literature and obtained by using ABAQUS which is based on the finite element method. Numerous new results for thick open cylindrical shells on Pasternak foundation with elastic boundary conditions are presented. In addition, comprehensive studies on the effects of the elastic restraint parameters, geometric parameters and elastic foundation coefficients are also reported.
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an improved fourier Series solution for the dynamic analysis of laminated composite annular circular and sector plate with general boundary conditions
Journal of Composite Materials, 2016Co-Authors: Qingshan Wang, Qian Liang, Fazle AhadAbstract:In this article, the authors presented a unified solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. Regardless of the shapes of the plates and the types of boundary conditions, each displacement and rotation component of the elements is expanded as an improved Fourier Series expansion which is composed of a double Fourier Cosine Series and several auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of Series representations. Since the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the plates. The accuracy, reliability, and versatility of the current solution is fully demonstrated and verif...
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a unified spectro geometric ritz method for vibration analysis of open and closed shells with arbitrary boundary conditions
Shock and Vibration, 2016Co-Authors: Dongyan Shi, Qingshan Wang, Yunke Zhao, Xiaoyan Teng, Fuzhen PangAbstract:This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier Cosine Series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the Series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.
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a Series solution for the in plane vibration analysis of orthotropic rectangular plates with non uniform elastic boundary constraints and internal line supports
Archive of Applied Mechanics, 2015Co-Authors: Dongyan Shi, Qingshan Wang, Xianjie Shi, Fuzhen PangAbstract:In this investigation, the free in-plane vibration analysis of orthotropic rectangular plates with non-uniform boundary conditions and internal line supports is performed with a modified Fourier solution. The exact solution for the problem is obtained using improved Fourier Series method, in which both two in-plane displacements of the orthotropic rectangular plates are represented by a double Fourier Cosine Series and four supplementary functions, in the form of the product of a polynomial function and a single Cosine Series expansion, introduced to remove the potential discontinuities associated with the original displacement functions along the edges when they are viewed as periodic functions defined over the entire x–y plane. The unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh–Ritz procedure. The change of the boundary conditions can be easily achieved by only varying the stiffness of the two sets of the boundary springs at the all boundary of the orthotropic rectangular plates without the need of making any change to the solutions. The excellent accuracy of the current result is validated by comparison with those obtained from other analytical approach as well as the finite element method (FEM). Numerical results are presented to illustrate the current method that is applied not only to the homogeneous boundary conditions but also to other interesting and practically important boundary restraints on free in-plane vibrations of the orthotropic rectangular plates, including varying stiffness of boundary springs, point supported, partially supported boundary conditions and internal line supports. In addition to this, the effects of locations of line supports are also investigated and reported. New results for free vibration of moderately orthotropic rectangular plates with various edge conditions and internal line supports are presented, which may be used for benchmarking of researchers in the field.
