... instability associated to a surfacelike oscillation. The system of dynamic differential equations and boundary conditions that governs the small plane oscillations of the half-space about the steady sliding state is established. The general form of the surface solutions to the plane strain case is given...

... and solutions are derived, which consist of three parts: the biharmonic part, the shear part, and the transcendental part. For a nonhomogeneous plate, the exact governing differential equations and solutions under pure normal loadings and pure shear loadings, respectively, are obtained directly from the refined...

... 2 w ̂ Therefore, the solution w for the second-order differential equation above is composed of a general solution w g and a particular solution w p as 33 w = w g + w p The general solution w g is given by the homogeneous part of Eq...

.../ie020779g Sides , P. J. , 2002 , “ Scaling of Differential Equations. Analysis of the Fourth Kind ,” Chem. Eng. Educ. 0009-2479 , 36 ( 3 ), pp. 232 – 235 . Deen , W. M. , 1998 , Analysis of Transport Phenomena , Oxford University Press , New York . Astarita , G...

...Kees Wapenaar; Jacob Fokkema We thank Stefan Stijlen for bringing the singularity of matrix C to our attention. 07 07 2010 17 08 2010 differential equations diffusion flow matrix algebra vectors waves Matrix C defined in Appendices C and D is singular...

... (multiwave) mode. The sandwich section is symmetric, and all constituent phases, i.e., the facings and the core, are assumed to be orthotropic. The buckling problem is formulated as an eigenboundary-value problem for differential equations, with the axial load being the eigenvalue. The complication...

...I. H. Stampouloglou; E. E. Theotokoglou From the biharmonic equation of the plane problem in the polar coordinate system and taking into account the variable-separable form of the partial solutions, a homogeneous ordinary differential equation (ODE) of the fourth order is deduced. Our study...

... of motion and heat conduction for the considered thermoelastic sphere are uncoupled and simplified by using Helmholtz decomposition theorem. By using a spherical wave solution, a system of governing partial differential equations is further reduced to a coupled system of three ordinary differential...

... variables, the problem is reduced to solving a coupled nonlinear system of ordinary differential equations subject to a set of boundary conditions. The problem is solved by developing a suitable numerical technique based on finite difference approach. Computational results concerning the variation...

...F. G. O’Neill; D. Priour The predictions of two numerical models of the deformation of fishing netting are compared. Analytical solutions are found to the differential equations that govern one of these models, and these solutions are used to evaluate the accuracy of both. There is very good...

... by constructing an appropriate set of multipole functions. These functions are singular on the axis of the cavity, they satisfy the governing differential equation in each half-space, and they satisfy the continuity conditions across the interface between the two half-spaces. Seven recent publications...

...Zhong-min Wang; Yan Wang; Yin-feng Zhou Based on the thin plate theory and the two-dimensional viscoelastic differential type constitutive relation, the differential equation of motion of a viscoelastic plate containing an all-over part-through crack and subjected to uniformly distributed...

... of stochastic axial compressive load. The method of averaging, both first order and second order, is applied. The averaged Itô differential equation governing the p th norm is established and the p th moment Lyapunov exponent is then obtained. White noise and real noise are considered as models of wideband...

...Jagadish Babu Gunda; Ranjan Ganguli A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation...

... rods (structures) mechanical stability viscoelasticity damping deformation bifurcation differential equations damping fractional calculus stability viscoelasticity In many recent studies of the viscoelastic deformation processes, it was shown that the behavior of the material can...

.... The resulting fractional-order differential equation is more complex (i.e., it involves higher derivatives) than the constitutive equation governing the material per se. Also, the use of a fractional-order model results in more complexity of the helix’ effective viscoelastic response than does an integer-order...

...L. Noels; R. Radovitzky Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element interfaces of the discretization. In order to ensure consistency...

... justified and demonstrative. Being described by the system of ordinary differential equations, they allow one to employ powerful tools of the theoretical mechanics and oscillation theory. The method is applied to the case of the plane model of the rotor system partly filled with incompressible liquid. Both...

... to a new coordinate system having its origin at the vertex of the corner. An asymptotic analysis in the vicinity of the sharp corner reduces the equations to a set of coupled, ordinary differential equations with variable coefficients. By a suitable transformation of variables the equations are simplified...

... and the other two edges clamped. Because Bessel functions satisfy the biharmonic differential equation of solid thin plate, the basic idea of the method is to superpose different Bessel functions to satisfy the edge conditions such that the governing differential equation and the boundary conditions of the thin...