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• Open Access

ARTICLE

### Numerical Computation of Space Derivatives by the Complex-Variable-Differentiation Method in the Convolution Quadrature Method Based BEM Formulation

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 123-132, 2008, DOI:10.3970/cmes.2008.030.123

Abstract This paper is concerned with the numerical computation of space derivatives of a time-domain (TD-) Boundary Element Method (BEM) formulation for the analysis of scalar wave propagation problems. In the present formulation, the Convolution Quadrature Method (CQM) is adopted, i.e., the basic integral equation of the TD-BEM is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multi-step method. In order to numerically compute space derivatives, the present work properly transforms the quadrature weights of the CQM-BEM, adopting the so-called Complex-Variable-Differentiation Method (CVDM). More >

• Open Access

ARTICLE

### General Corotational Rate Tensor and Replacement of Material-time Derivative to Corotational Derivative of Yield Function

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 55-62, 2007, DOI:10.3970/cmes.2007.017.055

Abstract Constitutive equation describing the mechanical properties of material has to be formulated in an identical form independent of coordinate systems by which it is described even if there exist any mutual configuration and/or mutual rotation between the material and coordinate systems. This mechanical requirement is attained by describing rate variables as corotational rate tensors with objectivity in constitutive equations in rate form. Besides, in order to use the material-time derivative of yield condition as a consistency condition it has to be replaced to the corotational derivative. In this note a general corotational rate for tensors More >

• Open Access

ARTICLE

### Fractional Order Derivative Model of Viscoelastic layer for Active Damping of Geometrically Nonlinear Vibrations of Smart Composite Plates

CMC-Computers, Materials & Continua, Vol.49-50, No.1, pp. 47-80, 2015, DOI:10.3970/cmc.2015.049.047

Abstract This paper deals with the implementation of the one dimensional form of the fractional order derivative constitutive relation for three dimensional analysis of active constrained layer damping (ACLD) of geometrically nonlinear laminated composite plates. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composites (PZCs). The von Kármán type nonlinear strain displacement relations are used to account for the geometric nonlinearity of the plates. A nonlinear smart finite element model (FEM) has been developed. Thin laminated substrate composite plates with various boundary conditions and stacking sequences are analyzed to More >

• Open Access

ARTICLE

### Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 179-208, 2009, DOI:10.3970/cmc.2009.009.179

Abstract The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on More >

• Open Access

ARTICLE

### Solving Fractional Integro-Differential Equations by Using Sumudu Transform Method and Hermite Spectral Collocation Method

CMC-Computers, Materials & Continua, Vol.54, No.2, pp. 161-180, 2018, DOI:10.3970/cmc.2018.054.161

Abstract In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method. The fractional derivatives are described in the Caputo sense. The applications related to Sumudu transform method and Hermite spectral collocation method have been developed for differential equations to the extent of access to approximate analytical solutions of fractional integro-differential equations. More >

• Open Access

ARTICLE

### The Fictitious Time Integration Method to Solve the Space- and Time-Fractional Burgers Equations

CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 221-240, 2010, DOI:10.3970/cmc.2010.015.221

Abstract We propose a simple numerical scheme for solving the space- and time-fractional derivative Burgers equations: Dtαu + εuux = vuxx + ηDxβu, 0 < α, β ≤ 1, and ut + D*β(D*1-βu)2/2 = vuxx, 0 < β ≤ 1. The time-fractional derivative Dtαu and space-fractional derivative Dxβu are defined in the Caputo sense, while D*βu is the Riemann-Liouville space-fractional derivative. A fictitious time τ is used to transform the dependent variable u(x,t) into a new one by (1+τ)γu(x,t) =: v(x,t,τ), where 0 < γ ≤ 1 is a parameter, such that the original equation is written as a new functional-differential type partial differential equation More >

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