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Convolution Integral (convolution + integral)
Selected AbstractsStability and identification for rational approximation of frequency response function of unbounded soilEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2010Xiuli Du Abstract Exact representation of unbounded soil contains the single output,single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency-domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped-parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least-squares fitting problem using the hybrid genetic-simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil,structure-interaction examples. Copyright © 2009 John Wiley & Sons, Ltd. [source] Aeroelastic forces and dynamic response of long-span bridgesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2004Massimiliano Lazzari Abstract In this paper a time domain approach for predicting the non-linear dynamic response of long-span bridges is presented. In particular the method that leads to the formulation of aeroelastic and buffeting forces in the time domain is illustrated in detail, where a recursive algorithm for the memory term's integration is properly developed. Moreover in such an approach the forces' expressions, usually formulated according to quasi-static theory, have been substituted by expressions including the frequency-dependent characteristics. Such expressions of aeroelastic and buffeting forces are made explicit in the time domain by means of the convolution integral that involves the impulse functions and the structural motion or the fluctuating velocities. A finite element model (FEM) has been developed within the framework of geometrically non linear analysis, by using 3-d degenerated finite element. The proposed procedure can be used to analyze both the flutter instability phenomenon and buffeting response. Moreover, working in the geometrically non-linearity range, it verifies the possibility of strongly flexible structures of actively resisting the wind loading. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stability of linear time-periodic delay-differential equations via Chebyshev polynomialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2004Eric A. Butcher Abstract This paper presents a new technique for studying the stability properties of dynamic systems modeled by delay-differential equations (DDEs) with time-periodic parameters. By employing a shifted Chebyshev polynomial approximation in each time interval with length equal to the delay and parametric excitation period, the dynamic system can be reduced to a set of linear difference equations for the Chebyshev expansion coefficients of the state vector in the previous and current intervals. This defines a linear map which is the ,infinite-dimensional Floquet transition matrix U'. Two different formulas for the computation of the approximate U, whose size is determined by the number of polynomials employed, are given. The first one uses the direct integral form of the original system in state space form while the second uses a convolution integral (variation of parameters) formulation. Additionally, a variation on the former method for direct application to second-order systems is also shown. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. An extension of the method to the case where the delay and parametric periods are commensurate is also shown. Stability charts are produced for several examples of time-periodic DDEs, including the delayed Mathieu equation and a model for regenerative chatter in impedance-modulated turning. The results indicate that this method is an effective way to study the stability of time-periodic DDEs. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stability of global and exponential attractors for a three-dimensional conserved phase-field system with memoryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2009Gianluca Mola Abstract We consider a conserved phase-field system on a tri-dimensional bounded domain. The heat conduction is characterized by memory effects depending on the past history of the (relative) temperature ,, which is represented through a convolution integral whose relaxation kernel k is a summable and decreasing function. Therefore, the system consists of a linear integrodifferential equation for ,, which is coupled with a viscous Cahn,Hilliard type equation governing the order parameter ,. The latter equation contains a nonmonotone nonlinearity , and the viscosity effects are taken into account by a term ,,,,t,, for some ,,0. Rescaling the kernel k with a relaxation time ,>0, we formulate a Cauchy,Neumann problem depending on , and ,. Assuming a suitable decay of k, we prove the existence of a family of exponential attractors {,,,,} for our problem, whose basin of attraction can be extended to the whole phase,space in the viscous case (i.e. when ,>0). Moreover, we prove that the symmetric Hausdorff distance of ,,,, from a proper lifting of ,,,0 tends to 0 in an explicitly controlled way, for any fixed ,,0. In addition, the upper semicontinuity of the family of global attractors {,,,,,} as ,,0 is achieved for any fixed ,>0. Copyright © 2009 John Wiley & Sons, Ltd. [source] An efficient time-domain damping solvent extraction algorithm and its application to arch dam,foundation interaction analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2008Hong Zhong Abstract The dynamic structure,unbounded foundation interaction plays an important role in the seismic response of structures. The damping solvent extraction (DSE) method put forward by Wolf and Song has a great advantage of simplicity, with no singular integrals to be evaluated, no fundamental solution required and convolution integrals avoided. However, implementation of DSE in the time domain to large-scale engineering problems is associated with enormous difficulties in evaluating interaction forces on the structure,unbounded foundation interface, because the displacement on the corresponding interface is an unknown vector to be found. Three sets of interrelated large algebraic equations have to be solved simultaneously. To overcome these difficulties, an efficient algorithm is presented, such that the solution procedure can be greatly simplified and computational effort considerably saved. To verify its accuracy, two examples with analytical solutions were investigated, each with a parameter analysis on the domain size and amount of artificial damping. Then with the parameters suggested in the parameter study, the complex frequency,response functions and earthquake time history analysis of Morrow Point dam were presented to demonstrate the applicability and efficiency of DSE approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] A fast multi-level convolution boundary element method for transient diffusion problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005C.-H. Wang Abstract A new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods (BEM) for transient diffusion. This approach, which is based upon the multi-level multi-integration concepts of Brandt and Lubrecht, provides a fast, accurate and memory efficient time domain method for this entire class of problems. Conventional BEM approaches result in operation counts of order O(N2) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(N3/2) for three two-dimensional model problems using the multi-level convolution BEM. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||