Formulation of Problems for Stationary Dispersive Equations of Higher Orders on Bounded Intervals with General Boundary Conditions

Boundary value problems for linear stationary dispersive equations of order 2l + 1, l ∈ N with general linear boundary conditions have been considered on finite intervals (0, L). The existence and uniqueness of regular solutions have been established.

Asymmetric Conduction in an Infinite Functionally Graded Cylinder: Two-Dimensional Exact Analytical Solution Under General Boundary Conditions

This paper focuses on using an analytical method to obtain an exact solution for a long cylindrical vessel made of functionally graded materials (FGMs). Heat conduction equations are assumed to be in both radial and circumferential directions. The conduction coefficients are considered as different power-law functions of the radius. The general linear boundary conditions are adopted to make the solution applicable to the full range of problems. The obtained solution is successfully validated. Through solving illustrative test examples, the effects of material constants and boundary conditions on temperature distribution are studied. The obtained formulation can be utilized for tailoring of FGM based on the actual sophisticated thermal boundary conditions in the production process. The current analytical findings can help to manage the temperature distribution in FGMs which is an essential parameter in controlling the thermal stresses.

Free Response and Absolute Vibration Suppression of Second-Order Flexible Structures—The Traveling Wave Approach

The paper considers the problem of suppressing the free vibration, induced by nonzero initial conditions, in a flexible system governed by the wave equation. First an exact response of the system, with general linear boundary conditions, is derived in terms of propagating waves that are reflected from the boundaries. The solution is explicit and with clear physical interpretation. The general expressions for the response are then used to investigate the behavior of the system under control with the absolute vibration suppression controller, which was originally designed for tracking control. It is shown that the vibration suppression properties of this controller apply also to nonzero initial conditions. In cases where the load end is free or contains only damping, the vibration stops completely in finite time and if it contains only inertia and damping it decays exponentially without vibration.