... for the obtained approximate solutions. Liao and other authors applied this method in a successful manner for various strong nonlinear applications in science and engineering. See, e.g., Refs. [ 14 15 16 17 18 19 20 21 22 ]. partial differential equations boundary layers MHD flow over a rotating...

... methods many-particle systems Schrödinger equation interaction functional dynamical functional particle method DFPM partial differential equations The numerical treatment through the application of particle methods has been a very active research area in recent years but these methods have...

... problem. In this study, we propose a method to simulate the two-phase flows in 1, 2 or 3 dimensions with the same system of partial differential equations. A one-pressure, conditionally hyperbolic model [1] was used and solved by a nonconservative finite volume scheme associated to a fractional step...

... and computational fluid dynamics technology. The mathematical model for the two-phase gas-dynamical processes consists of a system of first-order, nonlinear coupled partial differential equations. An adaptive grid generation algorithm is developed to account for the expansion of the computational domain due...

... elastic materials, the dynamic equations from the rod theory reduce to 12 first-order nonlinear partial differential equations (PDEs), which can also be derived using the Newton–Euler method . Goyal and Goyal et al. used the finite difference method to solve the 12 first-order PDEs in their studies...

... of external pressure and axial load are taken into account. A nonlinear hypothesis of deformation of a plane cross section is formulated. The system of partial differential equations of motion for a shell is derived on the basis of Hamilton’s principle. The system of equations is analytically solved...

... and elucidating pathways for their application to more general problems. 12 10 2010 08 12 2010 13 12 2010 15 02 2011 15 02 2011 beams (structures) partial differential equations Beams are structural members with one dimension much larger than the other two. Examples...

... and solve partial differential equations and the complexity therein. The elastodynamic responses of several general geometries and loading cases (interior, Neumann, and Dirichlet) are computed with the method and then compared with results generated using the earlier rectangular CA and finite element...

...Xiao-Dong Yang; Li-Qun Chen; Jean W. Zu The vibrations and stability are investigated for an axially moving rectangular antisymmetric cross-ply composite plate supported on simple supports. The partial differential equations governing the in-plane and out-of-plane displacements are derived...

...A. A. Jafari; S. A. Eftekhari In this paper, a new version of mixed finite element–differential quadrature formulation is presented for solving time-dependent problems. The governing partial differential equation of motion of the structure is first reduced to a set of ordinary differential...

...Lixiang Yang; Yung-Yu Chen; S.-T. John Yu This paper reports the eigenstructure of a set of first-order hyperbolic partial differential equations for modeling waves in solids with a trigonal 32 symmetry. The governing equations include the equation of motion and partial differentiation...

... of first-order, nonlinear coupled partial differential equations with inhomogeneous terms. The model poses an initial value problem with discontinuous initial and boundary conditions that arise due to the design complexity and nonuniformity of granular propellant distribution in the mortar tube...

... by a set of nonlinear coupled partial differential equations (PDEs), which is obtained by using the modified Ginzburg–Landau theory. The Chebyshev collocation method is employed for the numerical analysis of the PDE model. An extended proper orthogonal decomposition is then carried out to construct a set...

...-infinite stretching flat sheet are transformed into a partial differential equation with variable coefficients. An analytic technique for highly nonlinear problems, namely, the homotopy analysis method, is applied to give convergent analytical approximations, which agree well with the numerical results...

... 2009 damping eigenvalues and eigenfunctions Lyapunov methods method of moments noise partial differential equations resonance stability stochastic processes parametric resonance moment Lyapunov exponents bounded noise The equations of motion for many engineering problems...

... processes. The system is assumed to operate beyond its stochastic instability threshold—although only slightly—and its nonlinear model is used accordingly. The analysis is based on the solution of the Fokker–Planck–Kolmogorov partial differential equation for the relevant stationary PDF of the response...

... component of a complex combination of the midsurface normal displacement and its static-geometric dual, a stress function. However, an attempt to formally replace the Fourier index n by a partial derivative in the circumferential angle θ results in a partial differential equation, which is eighth order in θ...

... theory, includes geometric imperfection and von Kármán-type geometric nonlinearity. The solutions to the governing nonlinear partial differential equations are sought using the multiterm Galerkin technique. The nonlinear equilibrium paths through limit points and bifurcation points are traced using...

...Mira Mitra; S. Gopalakrishnan In this paper, a 2D wavelet-based spectral finite element (WSFE) is developed for a anisotropic laminated composite plate to study wave propagation. Spectral element model captures the exact inertial distribution as the governing partial differential equations (PDEs...

...F. G. O’Neill; R. D. Neilson A dynamic model of a diamond mesh cod-end subject to harmonic forcing is developed. The partial differential equations governing the displacements of the cod-end and the tension in the twine are first derived and then analyzed using the harmonic balance method...