Vibration of an axially loaded heterogeneous pinned-pinned beam with an intermediate roller support

The present paper is devoted to the issue of what effect the axial load (compressive or tensile) has on the eigenfrequencies of a heterogeneous pinned-pinned beam with an intermediate roller support (called a PrsP beam). This problem is a three point boundary value problem (eigenvalue problem) associated with homogeneous boundary conditions. If the Green functions of the three point boundary value problem (BVP) are known the eigenvalue problem that provide the eigenfrequencies for the beam loaded axially can be transformed into an eigenvalue problem governed by a homogeneous Fredholm integral equation. The later eigenvalue problems can be reduced to an algebraic eigenvalue problem which then can be solved numerically by using an effective solution algorithm which is based on the boundary element method.

Asymmetric compressive stability of rotating annular plates

In the present research, buckling behaviour of an isotropic homogeneous rotating annular plate subjected to uniform compression on both inner and outer edges is analysed. It is further assumed that the plate is rotatingwith a constant angular speed. Formulation is based on the first order shear deformation plate theory, which is valid for thin and moderately thick plates. The complete set of equilibrium quations and the associated boundary conditions are obtained for the plate. Prebuckling loads of the plate are obtained under flatness and axisymmetric deformations. Using the adjacent equilibrium riterion, the linearised stability equations are extracted. An asymmetric stability analysis is performed to obtain the critical buckling loads of the plate and the buckled configurations of the rotating plate. To this end, trigonometric functions through the circumferential direction and the generalised differential quadrature discretization across the radial direction are used which result in an algebraic eigenvalue problem. Benchmark results are given in graphical presentations for combinations of free, simply-supported, sliding supported, and clamped types of boundary conditions. It is shown that rotation enhances the buckling loads of the plate for all types of boundary conditions and alters the buckled shape of the plate.

On the equivalence of discrete Sturm–Liouville problem with nonlocal boundary conditions to the algebraic eigenvalue problem

We consider the finite difference approximation of the second order Sturm–Liouville equation with nonlocal boundary conditions (NBC). We investigate the condition when the discrete Sturm–Liouville problem can be transformed to an algebraic eigenvalue problem and denote this condition as solvability condition. The examples of the solvability for the most popular NBCs are provided. The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/ 2014).