**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**18

# Search results for: Laplace Transform

##### 18 Three-Dimensional Generalized Thermoelasticity with Variable Thermal Conductivity

**Authors:**
Hamdy M. Youssef,
Mowffaq Oreijah,
Hunaydi S. Alsharif

**Abstract:**

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

**Keywords:**
Fourier Transforms,
Thermal Conductivity,
thermoelasticity,
three-dimensional,
Laplace transforms

##### 17 A Numerical Study on Semi-Active Control of a Bridge Deck under Seismic Excitation

**Authors:**
A. Yanik,
U. Aldemir

**Abstract:**

This study investigates the benefits of implementing the semi-active devices in relation to passive viscous damping in the context of seismically isolated bridge structures. Since the intrinsically nonlinear nature of semi-active devices prevents the direct evaluation of Laplace transforms, frequency response functions are compiled from the computed time history response to sinusoidal and pulse-like seismic excitation. A simple semi-active control policy is used in regard to passive linear viscous damping and an optimal non-causal semi-active control strategy. The control strategy requires optimization. Euler-Lagrange equations are solved numerically during this procedure. The optimal closed-loop performance is evaluated for an idealized controllable dash-pot. A simplified single-degree-of-freedom model of an isolated bridge is used as numerical example. Two bridge cases are investigated. These cases are; bridge deck without the isolation bearing and bridge deck with the isolation bearing. To compare the performances of the passive and semi-active control cases, frequency dependent acceleration, velocity and displacement response transmissibility ratios *T _{a}*(

*w*),

*T*(

_{v}*w*), and

*T*(

_{d}*w*) are defined. To fully investigate the behavior of the structure subjected to the sinusoidal and pulse type excitations, different damping levels are considered. Numerical results showed that, under the effect of external excitation, bridge deck with semi-active control showed better structural performance than the passive bridge deck case.

**Keywords:**
Seismic,
Bridge Structures,
Passive Control,
viscous damping,
semi-active control

##### 16 Mathematical Modeling and Analysis of Forced Vibrations in Micro-Scale Microstretch Thermoelastic Simply Supported Beam

**Authors:**
Geeta Partap,
Nitika Chugh

**Abstract:**

**Keywords:**
microstretch,
deflection,
exponential load,
residue theorem,
simply supported,
Laplace
transforms

##### 15 Study of Heat Transfer in the Absorber Plates of a Flat-Plate Solar Collector Using Dual-Phase-Lag Model

**Authors:**
Yu-Ching Yang,
Haw-Long Lee,
Win-Jin Chang

**Abstract:**

The present work numerically analyzes the transient heat transfer in the absorber plates of a flat-plate solar collector based on the dual-phase-lag (DPL) heat conduction model. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods is used to solve the linear hyperbolic heat conduction equation. This work also examines the effect of different medium parameters on the behavior of heat transfer. Results show that, while the heat-flux phase lag induces thermal waves in the medium, the temperature-gradient phase lag smoothens the thermal waves by promoting non-Fourier diffusion-like conduction into the medium.

**Keywords:**
Solar Collector,
absorber plates,
dual-phase-lag,
non-Fourier

##### 14 Transient Heat Transfer of a Spiral Fin

**Authors:**
Sen-Yung Lee,
Li-Kuo Chou,
Chao-Kuang Chen

**Abstract:**

**Keywords:**
Heat Transfer,
transient response,
Laplace transforms/Adomian decomposed method- Padé

##### 13 Dynamic Analysis of Viscoelastic Plates with Variable Thickness

**Authors:**
Gülçin Tekin,
Fethi Kadıoğlu

**Abstract:**

In this study, the dynamic analysis of viscoelastic plates with variable thickness is examined. The solutions of dynamic response of viscoelastic thin plates with variable thickness have been obtained by using the functional analysis method in the conjunction with the Gâteaux differential. The four-node serendipity element with four degrees of freedom such as deflection, bending, and twisting moments at each node is used. Additionally, boundary condition terms are included in the functional by using a systematic way. In viscoelastic modeling, Three-parameter Kelvin solid model is employed. The solutions obtained in the Laplace-Carson domain are transformed to the real time domain by using MDOP, Dubner & Abate, and Durbin inverse transform techniques. To test the performance of the proposed mixed finite element formulation, numerical examples are treated.

**Keywords:**
Dynamic Analysis,
inverse laplace transform techniques,
mixed finite element formulation,
viscoelastic plate with variable thickness

##### 12 Numerical Inverse Laplace Transform Using Chebyshev Polynomial

**Authors:**
Vinod Mishra,
Dimple Rani

**Abstract:**

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

**Keywords:**
chebyshev polynomial,
Numerical inverse Laplace transform,
Odd cosine series

##### 11 Laplace Technique to Find General Solution of Differential Equations without Initial Conditions

**Authors:**
Adil Al-Rammahi

**Abstract:**

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

**Keywords:**
Differential Equations,
Laplace Transformations

##### 10 Dynamic Response of Nano Spherical Shell Subjected to Termo-Mechanical Shock Using Nonlocal Elasticity Theory

**Authors:**
J. Ranjbarn,
A. Alibeigloo

**Abstract:**

**Keywords:**
nano-scale spherical shell,
thermomechanical shock,
nonlocal elasticity
theory

##### 9 Generalized Stokes’ Problems for an Incompressible Couple Stress Fluid

**Authors:**
M.Devakar,
T.K.V.Iyengar

**Abstract:**

In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.

**Keywords:**
Laplace transform,
couple stress fluid,
Generalized Stokes’ problems,
Numerical inversion

##### 8 A Modified Laplace Decomposition Algorithm Solution for Blasius’ Boundary Layer Equation of the Flat Plate in a Uniform Stream

**Authors:**
M. A. Koroma,
Z. Chuangyi,
A. F.,
Kamara,
A. M. H. Conteh

**Abstract:**

In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

**Keywords:**
Numerical Solution,
Modified Laplace decomposition algorithm,
Boundary
layer equation,
Padé approximant

##### 7 Stability Analysis in a Fractional Order Delayed Predator-Prey Model

**Authors:**
Changjin Xu,
Peiluan Li

**Abstract:**

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

**Keywords:**
Laplace transform,
characteristic equation,
Fractional predator-prey model

##### 6 Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method

**Authors:**
Changqing Yang,
Jianhua Hou

**Abstract:**

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

**Keywords:**
fractional derivative,
Laplace transform,
integro-differential equations,
adomian polynomials,
pade appoximants

##### 5 A Laplace Transform Dual-Reciprocity Boundary Element Method for Axisymmetric Elastodynamic Problems

**Authors:**
B. I. Yun

**Abstract:**

**Keywords:**
boundary element method,
Laplace transform,
Axisymmetric elasticity,
dual-reciprocity method

##### 4 Transient Currents in a Double Conductor Line above a Conducting Half-Space

**Authors:**
Valentina Koliskina,
Inta Volodko

**Abstract:**

**Keywords:**
Laplace transform,
Transient eddy currents,
double
conductor line

##### 3 Closed Form Solution to problem of Calcium Diffusion in Cylindrical Shaped Neuron Cell

**Authors:**
Amrita Tripathi,
Neeru Adlakha

**Abstract:**

**Keywords:**
reaction diffusion equation,
diffusion coefficient,
Laplace transform,
Modified Bessel function,
excess buffer,
calcium influx

##### 2 Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach

**Authors:**
Lianglin Xiong,
Yun Zhao,
Tao Jiang

**Abstract:**

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

**Keywords:**
Laplace transform,
characteristic equation,
Fractional neutral differential equation

##### 1 Laplace Transformation on Ordered Linear Space of Generalized Functions

**Authors:**
K. V. Geetha,
N. R. Mangalambal

**Abstract:**

**Keywords:**
Laplace transformable generalized function,
positive cone,
topology of bounded convergence