42 research outputs found
Uniqueness of analytic solutions for stationary plate oscillations in an annulus
AbstractThe equations governing the harmonic oscillations of a plate with transverse shear deformation are considered in an annular domain. It is shown that under nonstandard boundary conditions where both the displacements and tractions are zero on the internal boundary curve, the corresponding analytic solution is zero in the entire domain. This property is then used to prove that a boundary value problem with Dirichlet or Neumann conditions on the external boundary and Robin conditions on the internal boundary has at most one analytic solution
Solution techniques for elementary partial differential equations
After a brief review of elementary ODE techniques and discussions on Fourier series and Sturm-Liouville problems, the author introduces the heat, Laplace, and wave equations as mathematical models of physical phenomena. He then presents a number of solution techniques and applies them to specific initial/boundary value problems for these models. Discussion of the general second order linear equation in two independent variables follows, and finally, the method of characteristics and perturbation methods are presented
An initial-boundary value problem for elastic plates
In contrast to the classical linear theory of elasticity the solution of the initial boundary-value problem of elastic-plastic bodies genuinely depends on the history of loading. Incremental methods take this fact into account, in general, by replacing the highly non-linear problem by a sequence of linear problems. This change of the mathematical model may lead to mispredictions of the behaviour of the considered body like the missing out of bifurcations and drifting of the solution. Moreover, minimum properties of incremental variational principles have only reduced value because the basic assumption of the exact knowledge of the reference state holds exclusively for the natural state
An enhanced theory of bending of plates
Describes the construction and application of various analytic and numerical integration techniques. Problem solving in areas such as solid mechanics, fluid dynamics, thermoelasticity, plates and shells, liquid crystals, diffusion and diffraction theory, Hamiltonian systems, resonance, nonlinear waves, plasma, flight dynamics, and structural networks are presented in an accessible manner
Uniqueness of solution for the Robin problem in high-frequency vibrations of elastic plates
Dynamic transmission problems for plates
The existence of distributional solutions is investigated for the boundary intergral equations associated with the bending of a thin elastic plate in the dynamic contact problem