Methods for Automated Dynamic Analysis of Discrete Mechanical Systems

1973 ◽  
Vol 40 (3) ◽  
pp. 809-811 ◽  
Author(s):  
Y. O. Bayazitoglu ◽  
M. A. Chace
Keyword(s):  
Differential Equations ◽  
Dynamic Analysis ◽  
Ordinary Differential Equations ◽  
Mechanical System ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Constrained Systems ◽  
Lower Pair ◽  
Linear And Nonlinear

The equations of motion for any discrete, lower pair mechanical system can be obtained by analyzing a branched, three-dimensional compound pendulum of indefinite length. In this paper, a set of expressions which provides the equations of motion of arbitrary mechanical dynamic systems directly as ordinary differential equations are presented. These expressions and the associated technique is applicable to linear and nonlinear unconstrained dynamic systems, kinematic systems and multidegree-of-freedom constrained systems.

Development and Application of a Generalized d’Alembert Force for Multifreedom Mechanical Systems

1971 ◽  
Vol 93 (1) ◽  
pp. 317-326 ◽  
Author(s):  
M. A. Chace ◽  
Y. O. Bayazitoglu
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Lagrange Equations ◽  
Second Order Differential Equations ◽  
Dimensional Version ◽  
Mechanical Networks ◽  
Geometric Effects

A set of expressions termed the generalized d’Alembert force is determined for application to two and three-dimensional dynamic analysis of discrete, nonlinear, multifreedom, constrained, mechanical dynamic systems. These expressions greatly simplify the task of developing a correct set of second order differential equations of motion for mechanical systems which are nonlinear because of large deflections or other geometric effects. They apply to both constrained and unconstrained mechanical systems via the method of Lagrange equations with constraint. The two-dimensional version of the expressions has been successfully applied in a type-varient computer program for the dynamic analysis of mechanical networks, and example problems simulated with this program are discussed.

Dynamic Thermal Analysis of Laminated Cylinder with a Piezoelectric Layer Based on Three-Dimensional Elasticity Solution

2012 ◽  
Vol 186 ◽  
pp. 16-25
Author(s):  
A.R. Daneshmehr ◽  
S. Akbari ◽  
A. Nateghi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Piezoelectric Layer ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Elasticity Solution ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Three Dimensional Elasticity

Three-dimensional elasticity solution is presented for finite length, simply supported, laminated cylinder with a piezoelectric layer under dynamic thermal load and pressure. The piezoelectric layer can be used as an actuator or a sensor. The ordinary differential equations are obtained from partial differential equations of motion by means of trigonometric function expansion in longitudinal direction. Galerkin finite element method is used to solve the resulting ordinary differential equations. Finally numerical results are discussed for different situations.

Nonsteady Three-Dimensional Stagnation-Point Flow

1971 ◽  
Vol 38 (1) ◽  
pp. 282-287 ◽  
Author(s):  
E. H. W. Cheng ◽  
M. N. O¨zis¸ik ◽  
J. C. Williams
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Potential Flow ◽  
Blunt Body ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Special Cases ◽  
Layer Flow ◽  
Two Parameters

The equations of motion for the three-dimensional nonsteady flow of incompressible viscous fluid in the vicinity of a forward stagnation point are reduced to three ordinary differential equations for a potential flow field chosen to vary inversely as a linear function of time. The resulting ordinary differential equations contain two parameters C and D, the former characterizes the type of curvature of the surface around the stagnation point and the latter the degree of acceleration or deceleration of the potential flow. The simple stagnation-point problems which have been studied previously are obtainable as special cases of the present analysis by assigning particular values to C and D. Exact solutions have been computed numerically for the velocity field and the pressure distribution in the boundary-layer flow around the stagnation point of a three-dimensional blunt body for the values of the parameter C from 0–1.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

2020 ◽  
Vol 98 (1) ◽  
pp. 32-38 ◽  
Author(s):  
S. Nadeem ◽  
M.Y. Malik ◽  
Nadeem Abbas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Surface Temperature ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equations ◽  
Exponential Order ◽  
Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

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