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Keywords: differential equations
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Journal Articles
Article Type: Research Papers
J. Appl. Mech. July 2011, 78(4): 041002.
Published Online: April 12, 2011
... 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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. May 2011, 78(3): 031021.
Published Online: February 17, 2011
... 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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. March 2011, 78(2): 021019.
Published Online: December 20, 2010
... stress acting on the beam cross section. 3 The sixth-order differential equations in the present beam theory can be solved analytically. The presented three examples show that the resulting analytical solutions are more accurate than those given by the fourth-order differential equations of TBT...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. November 2010, 77(6): 061017.
Published Online: September 1, 2010
... with results of large impact. These shortcomings can become irrelevant when working with partial differential equations, especially the nonlinear type, for which there is no proof of existence and unicity regardless of the solution method employed. Self-consistency and its potential pitfalls were studied...
Journal Articles
Article Type: Errata
J. Appl. Mech. November 2010, 77(6): 067001.
Published Online: August 17, 2010
...Kees Wapenaar; Jacob Fokkema 07 07 2010 17 08 2010 differential equations diffusion flow matrix algebra vectors waves Matrix C defined in Appendices C and D is singular and hence expressions containing the inverse of C cannot be used as such. The singularity...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. March 2010, 77(2): 021015.
Published Online: December 14, 2009
... (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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. March 2010, 77(2): 021003.
Published Online: December 9, 2009
...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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. March 2010, 77(2): 021004.
Published Online: December 9, 2009
... 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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. November 2009, 76(6): 061006.
Published Online: July 23, 2009
... 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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. September 2009, 76(5): 051001.
Published Online: June 16, 2009
...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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. May 2009, 76(3): 031009.
Published Online: March 10, 2009
... 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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. November 2008, 75(6): 061018.
Published Online: August 21, 2008
...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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. March 2008, 75(2): 021012.
Published Online: February 25, 2008
... 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...
Journal Articles
Article Type: Technical Briefs
J. Appl. Mech. March 2008, 75(2): 024502.
Published Online: February 25, 2008
...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...
Journal Articles
Article Type: Technical Briefs
J. Appl. Mech. January 2008, 75(1): 014502.
Published Online: January 14, 2008
... 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...
Journal Articles
Article Type: Research Papers
J. Appl. Mech. January 2008, 75(1): 011012.
Published Online: January 14, 2008
.... 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...
Journal Articles
Article Type: Technical Briefs
J. Appl. Mech. September 2007, 74(5): 1031–1036.
Published Online: July 17, 2006
...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...
Journal Articles
Article Type: Technical Papers
J. Appl. Mech. July 2006, 73(4): 580–589.
Published Online: November 4, 2005
... 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...
Journal Articles
Article Type: Technical Papers
J. Appl. Mech. January 2007, 74(1): 41–46.
Published Online: April 26, 2005
... 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...
Journal Articles
Article Type: Technical Papers
J. Appl. Mech. November 2007, 74(6): 1247–1251.
Published Online: April 23, 2005
... 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...