This results in variationally consistent partial differential plate equations of motion and pertinent boundary conditions.
The governing equations, coupled with pertinent boundary conditions, are solved by employing a conservative control volume formulation, in the environment of a three-dimensional unstructured mesh.
The nature of the boundary conditions in strain-gradient elasticity is highlighted through the solution of the pertinent boundary value problems.
An eigenvalue problem is formulated for a two-dimensional flexible duct by satisfying pertinent boundary conditions across the fluid-plate interfaces.
In order to arrive at nonlinear ordinary differential equations, similarity transformations are defined differently compared to the steady case and these nonlinear differential equations along with pertinent boundary condition are solved numerically by Runge Kutta Fehlberg 45 method.
The Havriliak Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of an infinite series.
The translational addition theorem for cylindrical wave functions in conjunction with the appropriate orthogonal series expansions and the pertinent boundary conditions are employed to develop an exact 3D elasticity solution for free vibrations of a simply (shear diaphragm) supported elastic circular cylinder of finite length with an eccentrically located inner circular cavity.
Adopting these in the boundary conditions on the plate surfaces and along the edges, a set of dynamic equations with pertinent edge boundary conditions are derived on implicit form.
The methods presented are general, new in the context of geotechnical and geomechanical engineering, and can assist in the modelling of spatial variability and quantification of uncertainty linked to geotechnical rock properties and pertinent lithological boundaries.
This seemed particularly pertinent because disciplinary boundaries change with time and what may currently be perceived as complementary medicine could later become conventional medicine.
This made it possible to reduce three differential equations, hitherto treated as governing equations that characterize the vibrated particle bed, to a single partial differential equation with pertinent initial and boundary conditions.
