The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Chenghung Huang - One of the best experts on this subject based on the ideXlab platform.
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an inverse Vibration Problem in estimating the spatial and temporal dependent external forces for cutting tools
Applied Mathematical Modelling, 2009Co-Authors: Chenghung Huang, Chih Chun Shih, Sin KimAbstract:Abstract An inverse forced Vibration Problem, based on the conjugate gradient method (CGM), (or the iterative regularization method), is examined in this study to estimate the unknown spatial and temporal-dependent external forces for the cutting tools by utilizing the simulated beam displacement measurements. The tool is represented by an Euler–Bernoulli beam. The accuracy of the inverse analysis is examined by using the simulated exact and inexact displacement measurements. The numerical experiments are performed to test the validity of the present algorithm by using different types of external forces, sensor arrangements and measurement errors. Results show that excellent estimations on the external forces can be obtained with any arbitrary initial guesses.
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a generalized inverse force Vibration Problem for simultaneously estimating the time dependent external forces
Applied Mathematical Modelling, 2005Co-Authors: Chenghung HuangAbstract:The conjugate gradient method (CGM) with adjoint equations was applied to a generalized inverse force Vibration Problem to simultaneously estimate the unknown time-dependent external forces in a multiple-degree-of-freedom damped system with time-dependent system parameters by using the simulated measured system displacement. The accuracy of the inverse analysis for a two-degree-of-freedom Problem is examined by using the simulated exact and inexact displacement measurements in the numerical experiments. Results have shown that the excellent estimations on the external forces can be obtained with any arbitrary initial guesses within a very short CPU time on a Pentium III-500 MHz PC.
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a nonlinear inverse Problem in estimating simultaneously the external forces for a Vibration system with displacement dependent parameters
Journal of The Franklin Institute-engineering and Applied Mathematics, 2005Co-Authors: Chenghung HuangAbstract:The conjugate gradient method (CGM), or the iterative regularization method, is applied to a generalized inverse nonlinear force Vibration Problem, (i.e. system parameters are function of displacement), to simultaneously estimate the unknown time-dependent external forces for a multiple-degree-of-freedom damped system by using the measured displacements. The system parameters of the present study are considered function of displacement, thus it is classified as a genuine nonlinear inverse Vibration Problem. The numerical experiments are performed to test the validity of CGM by using different types of system parameters, external forces and measurement errors in this study.
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a non linear inverse Vibration Problem of estimating the external forces for a system with displacement dependent parameters
Journal of Sound and Vibration, 2001Co-Authors: Chenghung HuangAbstract:The conjugate gradient method, i.e., the iterative regularization method, is used in an inverse non-linear force Vibration Problem of estimating the unknown time-dependent external forces in a damped system with the displacement-dependent spring constant and damping coefficients. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements. Since the system parameters are functions of displacement, the present study, from a purely mathematical viewpoint, is thus a genuine non-linear inverse Vibration Problem. The numerical simulations are performed to test the validity of the present algorithm by using different types of system parameters, external forces and measurement errors. Results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses with a couple of second's CPU time at Pentium III-500 MHz PC.
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an inverse non linear force Vibration Problem of estimating the external forces in a damped system with time dependent system parameters
Journal of Sound and Vibration, 2001Co-Authors: Chenghung HuangAbstract:Abstract An inverse non-linear force Vibration Problem based on the iterative regularization method, i.e., the conjugate gradient method (CGM), is used to estimate the unknown time-dependent external forces in a damped system having time-dependent system parameters by using the measured system displacement. It is assumed that no prior information is available on the functional form of the unknown external forces in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements. The numerical simulations are performed to test the validity of present algorithm by using different types of external forces and measurements. Results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses within a couple of seconds of CPU time at Pentium II-300 MHz PC.
Rodolfo Rodríguez - One of the best experts on this subject based on the ideXlab platform.
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Acoustic Vibration Problem for dissipative fluids
arXiv: Numerical Analysis, 2016Co-Authors: Felipe Lepe, Salim Meddahi, David Mora, Rodolfo RodríguezAbstract:In this paper we analyze a finite element method for solving a quadratic eigenvalue Problem derived from the acoustic Vibration Problem for a heterogeneous dissipative fluid. The Problem is shown to be equivalent to the spectral Problem for a noncompact operator and athorough spectral characterization is given. The numerical discretization of the Problem is based on Raviart-Thomas finite elements. The method is proved to be free of spurious modes and to converge with optimal order. Finally, we report numerical tests which allow us to assess the performance of the method.
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A virtual element method for the acoustic Vibration Problem
arXiv: Numerical Analysis, 2016Co-Authors: Lourenço Beirão Da Veiga, David Mora, Gonzalo Rivera, Rodolfo RodríguezAbstract:We analyze in this paper a virtual element approximation for the acoustic Vibration Problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of H(div) virtual elements with vanishing rotor. Under standard assumptions on the meshes, we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates. With this end, we prove approximation properties of the proposed virtual elements. We also report some numerical tests supporting our theoretical results.
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A modal synthesis method for the elastoacoustic Vibration Problem
ESAIM: Mathematical Modelling and Numerical Analysis, 2002Co-Authors: Alfredo Bermúdez, L. Hervella-nieto, Rodolfo RodríguezAbstract:A modal synthesis method to solve the elastoacoustic Vibration Problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue Problem is introduced. Finite element discretizations with Lagrangian elements are considered for solving the uncoupled Problems. Convergence for eigenvalues and eigenfunctions is proved, error estimates are given, and numerical experiments exhibiting the good performance of the method are reported.
Daniel J. Inman - One of the best experts on this subject based on the ideXlab platform.
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symmetric inverse eigenvalue Vibration Problem and its application
Mechanical Systems and Signal Processing, 2001Co-Authors: Ladislav Starek, Daniel J. InmanAbstract:Abstract This paper summarises the authors' previous effort on inverse eigenvalue Problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices and non-proportional damping. The inverse Problem of interest here is that of determining real symmetric coefficient matrices assumed to represent mass normalised velocity and position coefficient matrices, given a set of specified complex eigenvalues and eigenvectors. There are given two solutions of a symmetric inverse eigenvalue Problem presented by Starek and Inman [1, 2]. The theory of inverse eigenvalue Problem is applied to the model updating Problem. The goal of this paper is to recognise that the model updating Problem is a subset of the inverse eigenvalue Problem. The approach proposed here is to use the results of inverse eigenvalue Problem to develop methods for model updating. Comments are made on how their procedure may be used to solve the damage detection Problem.
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A symmetric inverse Vibration Problem for nonproportional underdamped systems
Journal of Applied Mechanics, 1997Co-Authors: Ladislav Starek, Daniel J. InmanAbstract:This paper considers a symmetric inverse Vibration Problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices and nonproportional damping. The inverse Problem of interest here is that of determining real symmetric, coefficient matrices assumed to represent the mass normalized velocity and position coefficient matrices, given a set of specified complex eigenvalues and eigenvectors. The approach presented here gives an alternative solution to a symmetric inverse Vibration Problem presented by Starek and Inman (1992) and extends these results to include noncommuting (or commuting) coefficient matrices which preserve eigenvalues, eigenvectors, and definiteness. Furthermore, if the eigenvalues are all complex conjugate pairs (underdamped case) with negative real parts, the inverse procedure described here results in symmetric positive definite coefficient matrices. The new results give conditions which allow the construction of mass normalized damping and stiffness matrices based on given eigenvalues and eigenvectors for the case that each mode of the system is underdamped. The result provides an algorithm for determining a nonproportional (or proportional) damped system which will have symmetric coefficient matrices and the specified spectral and modal data.
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a symmetric inverse Vibration Problem with overdamped modes
Journal of Sound and Vibration, 1995Co-Authors: Ladislav Starek, Daniel J. InmanAbstract:Abstract Several previously published results have addressed the inverse eigenvalue Problem for lumped parameter non-conservative systems. These inverse results give conditions which allow the construction of mass normalized, velocity and position coefficient matrices based on given eigenvalues and eigenvectors. Previous theories have examined the construction of symmetric coefficients given complex and zero eigenvalues (rigid bodies). Here, the theory of real symmetric inverse eigenvalue Problems is extended to include the possibility of specifying real eigenvalues, corresponding to overdamped modes. Specifically, conditions are given that allow the construction of real, symmetric, mass normalized damping and stiffness matrices given specified eigenvalues and eigenvectors, some of which may correspond to overdamped modes.
David Mora - One of the best experts on this subject based on the ideXlab platform.
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a virtual element method for the Vibration Problem of kirchhoff plates
Mathematical Modelling and Numerical Analysis, 2018Co-Authors: David Mora, Gonzalo Rivera, Ivan VelasquezAbstract:The aim of this paper is to develop a virtual element method (VEM) for the Vibration Problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an H 2 (Ω ) conforming discretization by means of the VEM which is simple in terms of degrees of freedom and coding aspects. Under standard assumptions on the computational domain, we establish that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we report several numerical experiments illustrating the behaviour of the proposed scheme and confirming our theoretical results on different families of meshes. Additional examples of cases not covered by our theory are also presented.
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a virtual element method for the Vibration Problem of kirchhoff plates
arXiv: Numerical Analysis, 2017Co-Authors: David Mora, Gonzalo Rivera, Ivan VelasquezAbstract:The aim of this paper is to develop a virtual element method (VEM) for the Vibration Problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an $H^2(\Omega)$ conforming discretization by means of the VEM which is simple in terms of degrees of freedom and coding aspects. Under standard assumptions on the computational domain, we establish that the resulting schemeprovides a correct approximation of the spectrum and prove optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. The analysis restricts to simply connected polygonal clamped plates, not necessarily convex. Finally, we report several numerical experiments illustrating the behaviour of the proposed scheme and confirming our theoretical results on different families of meshes. Additional examples of cases not covered by our theory are also presented.
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Acoustic Vibration Problem for dissipative fluids
arXiv: Numerical Analysis, 2016Co-Authors: Felipe Lepe, Salim Meddahi, David Mora, Rodolfo RodríguezAbstract:In this paper we analyze a finite element method for solving a quadratic eigenvalue Problem derived from the acoustic Vibration Problem for a heterogeneous dissipative fluid. The Problem is shown to be equivalent to the spectral Problem for a noncompact operator and athorough spectral characterization is given. The numerical discretization of the Problem is based on Raviart-Thomas finite elements. The method is proved to be free of spurious modes and to converge with optimal order. Finally, we report numerical tests which allow us to assess the performance of the method.
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A virtual element method for the acoustic Vibration Problem
arXiv: Numerical Analysis, 2016Co-Authors: Lourenço Beirão Da Veiga, David Mora, Gonzalo Rivera, Rodolfo RodríguezAbstract:We analyze in this paper a virtual element approximation for the acoustic Vibration Problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of H(div) virtual elements with vanishing rotor. Under standard assumptions on the meshes, we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates. With this end, we prove approximation properties of the proposed virtual elements. We also report some numerical tests supporting our theoretical results.
Ivan Velasquez - One of the best experts on this subject based on the ideXlab platform.
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a virtual element method for the Vibration Problem of kirchhoff plates
Mathematical Modelling and Numerical Analysis, 2018Co-Authors: David Mora, Gonzalo Rivera, Ivan VelasquezAbstract:The aim of this paper is to develop a virtual element method (VEM) for the Vibration Problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an H 2 (Ω ) conforming discretization by means of the VEM which is simple in terms of degrees of freedom and coding aspects. Under standard assumptions on the computational domain, we establish that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we report several numerical experiments illustrating the behaviour of the proposed scheme and confirming our theoretical results on different families of meshes. Additional examples of cases not covered by our theory are also presented.
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a virtual element method for the Vibration Problem of kirchhoff plates
arXiv: Numerical Analysis, 2017Co-Authors: David Mora, Gonzalo Rivera, Ivan VelasquezAbstract:The aim of this paper is to develop a virtual element method (VEM) for the Vibration Problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an $H^2(\Omega)$ conforming discretization by means of the VEM which is simple in terms of degrees of freedom and coding aspects. Under standard assumptions on the computational domain, we establish that the resulting schemeprovides a correct approximation of the spectrum and prove optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. The analysis restricts to simply connected polygonal clamped plates, not necessarily convex. Finally, we report several numerical experiments illustrating the behaviour of the proposed scheme and confirming our theoretical results on different families of meshes. Additional examples of cases not covered by our theory are also presented.