scholarly journals Exact solutions in Weyl-cubed gravity

2019 ◽  
Vol 34 (05) ◽  
pp. 1950036
Author(s):  
Mohammad A. Ganjali
Keyword(s):  
Exact Solutions ◽  
Order Term ◽  
Equations Of Motion ◽  
Classical Solutions ◽  
Conformally Flat ◽  
Third Order ◽  
Gravitational Action

In this paper, we will use a unitary gravitational action up to third-order of curvature with respect to the holographic a-theorem. In particular, its third-order term has a Weyl-cubed term. In this paper, we study this Weyl-cubed theory and find some of its exact classical solutions. We show that the theory admits conformally flat, Lifshitz, Schrödinger and also hyperscaling-violating backgrounds as the solutions of the equations of motion. Our analysis has been done for the pure Weyl-cubed gravity, Einstein plus Weyl-cubed term and gravity with matter.

CLASSICAL SOLUTIONS OF THE p-BRANES

1989 ◽  
Vol 04 (13) ◽  
pp. 1287-1295 ◽  
Author(s):  
D.T. STOYANOV
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
General Class ◽  
Broad Class ◽  
Equations Of Motion ◽  
Classical Solutions ◽  
Subsidiary Condition ◽  
Nonlinear Equations Of Motion

An appropriate subsidiary condition is introduced in the classical actions of the p-branes (p arbitrary). A general class of exact solutions of the resulting nonlinear equations of motion are obtained which yield a broad class of characteristics for the original covariant equations of the p-branes.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Chaotic Motion of a Functionally Graded Materials Square Thin Plate

2012 ◽  
Vol 531 ◽  
pp. 593-596
Author(s):  
Shuang Bao Li ◽  
Yu Xin Hao
Keyword(s):  
Thin Plate ◽  
Functionally Graded Materials ◽  
Chaotic Motion ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Steady State Heat ◽  
Steady State Heat Transfer

Chaotic motion of a simply supported functionally graded materials (FGM) square thin plate under one-to-two internal resonance is studied in this paper. The FGM plate is subjected to the transversal and in-plane excitations. Material properties are assumed to be temperature-dependent and change continuously throughout the thickness of the plate. The temperature variation is assumed to occur in the thickness direction only and satisfy the steady-state heat transfer equation. Based on the Reddy’s third-order plate theory and Hamilton’s principle, the nonlinear governing equations of motion for the FGM plate are derived by using the Galerkin’s method to describe the transverse oscillation in the first two modes Numerical simulations illustrate that there exist chaotic motion for the FGM rectangular plate.

scholarly journals Generalized Kudryashov Method for Time-Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Yusuf Pandir ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Third Order ◽  
Hilliard Equation ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Cahn Hilliard Equation

In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.

The Effects of Flare and Overhangs on the Motions of a Yacht in Head Seas

1993 ◽  
Author(s):  
John C. Kuhn ◽  
Eric C. Schlageter
Keyword(s):  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Order Effects ◽  
Third Order ◽  
Numerical Work ◽  
Strip Theory ◽  
Hull Forms ◽  
The Time Domain ◽  
The Impact

The coupled heave and pitch motions of hull forms with flare and overhangs are examined numerically. The presence of flare and overhangs is numerically modelled with nonlinear hydrostatic and Froude-Krylov forces based on integrals over the instantaneous wetted surface. Forces due to radiation and diffraction are computed with a linear strip-theory. These forces are combined in two coupled nonlinear differential equations of motion that are solved in the time domain with a fourth-order Runge-Kutta integration method. An assessment of the impact of flare and overhangs on motions is obtained by comparing these nonlinear solutions with solutions of the traditional linear equations of motion, which do not contain forces due to flare and overhangs. For an example based on an International America's Cup Class yacht design, it is found that the nonlinear heave and pitch motions are smaller than the linear motions. This is primarily due to reduced first-order response components, which are coupled with nonlinear response components. Comparisons of these results with towing tank data demonstrate that the nonlinear procedure improves prediction quality relative to linear results. In support of this numerical work, the hydrostatic and Froude­Krylov force integrals are expanded in Taylor series with respect to wave elevation. These results indicate how hydrostatic and Froude-Krylov forces change with changing flare and overhang angles, revealing that sectional slope has second and third-order effects on forces while sectional curvature and overhang angles produce third-order effects.

Modeling, Simulation, and Modal Analysis Hydraulic Valve Lifter With Oil Compressibility Effects

1989 ◽  
Author(s):  
T. Hatch ◽  
A. P. Pisano
Keyword(s):  
Differential Equations ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Check Valve ◽  
Linear Differential Equations ◽  
Third Order ◽  
Mode Behavior ◽  
Special Cases ◽  
Linear Differential ◽  
Hydraulic Valve

Abstract A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multi-mode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid In the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, non-linear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.

scholarly journals Approximately permanent electronic orbits and the origin of spectral series

1915 ◽  
Vol 91 (626) ◽  
pp. 156-170
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Experimental Work ◽  
Close Agreement ◽  
Equations Of Motion ◽  
Electronic Systems ◽  
Spectral Series ◽  
Simplifying Assumptions

The electrodynamical theory which we owe to Lorentz and Larmor provides theoretically a logical and consistent scheme whereby the equations of motion of electronic systems may be formulated. But, unfortunately, even most simple cases lead to equations of such complexity that the attempt to deduce exact solutions must at present be abandoned since there is no mathematical machinery available for the purpose. We have accordingly to make some simplifying assumptions, not strictly true, in order to obtain an approximate solution. In many cases, results are thus obtained which give a very close agreement with observation, and this is so far gratifying. But modern experimental work in radiation makes it clear that the phenomena have not yet been co-ordinated with the electrodynamical theory of electrons. It is reasonable to enquire if this is due to the failure of mathematicians to provide an explanation, whether because the approximations used are not accurate enough, or because the conception of the electronic systems considered is not sufficiently general ?

Exact Relationships between Eigenvalues of FGM Circular Plates Based on RPT and those of Isotropic Homogeneous Circular Plates Based on CPT

2007 ◽  
Vol 353-358 ◽  
pp. 3002-3005
Author(s):  
Lian Sheng Ma ◽  
Lei Wu
Keyword(s):  
Eigenvalue Problem ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Transverse Shear Deformation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Third Order ◽  
Classical Plate Theory ◽  
Graded Material

Based on the mathematical similarity of the eigenvalue problem of the Reddy’s third-order plate theory (RPT) and the classical plate theory (CPT), relationships between the solutions of axisymmetric vibration or buckling of functionally graded material (FGM) circular plates based on RPT and those of isotropic homogeneous circular plates based on CPT are presented, from which one can easily obtain the RPT solutions of axisymmetric vibration or buckling of FGM circular plates expressed in terms of the well-known CPT solutions of isotropic circular plates without much tedious mathematics. Effects of rotary inertia are not considered in the present analysis. The relationships obtained from the present analysis may be used to check the validity, convergence and accuracy of numerical results of FGM plates based on RPT, and also show clearly the intrinsic features of the effect of transverse shear deformation on the classical solutions.

scholarly journals Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Alvaro H. Salas S ◽  
Cesar A. Gómez S
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Third Order ◽  
Forcing Term ◽  
Projective Riccati Equation Method

The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term.

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