Vibration of cracked structures: A state of the art review

A new approach for free vibration of axially functionally graded beams with non-uniform cross-section

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1936&context=lkcsb_research

The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution

Discrete singular convolution for beam analysis

Natural frequencies of cracked functionally graded material plates by the extended finite element method

Vibration and stability of cracked rectangular plates

The vibration and stability of plates with mixed edge conditions are considered in this paper. A simply supported rectangular plate which is clamped along the central portion on two opposite edges and a plate with partial clamping along one edge are analyzed. The problems are formulated as dual series equations and reduced to homogeneous Fredholm integral equations of the second kind. Comparisons with numerical results obtained by other investigators are made. Vibration and buckling mode shapes are illustrated. A vibration analysis of a plate simply supported adjacent to the corners is also made. This case is formulated as a coupled system of dual series equations which is reduced to a system of homogeneous integral equations. In all of the solutions given, the singularity is isolated and treated analytically.

Eigenvalue Problems of Rectangular Plates With Mixed Edge Conditions

Vibration and buckling of a rectangular plate with an internal support

This paper treats the bending of a uniformly loaded circular plate with mixed conditions on the boundary. Two cases are considered: 1) clamped—simply supported and 2) simply supported—free. Deflections and bending moments are calculated at the center of the plate and compared to results obtained by other investigators. Excellent agreement is found except when the clamped segment or support segment is short compared with the circumference. An auxiliary function, which permits the stress intensity factor to be determined, is also tabulated for each case.

Bernhard Stahl

Papers

Vibration and stability of cracked rectangular plates

Eigenvalue Problems of Rectangular Plates With Mixed Edge Conditions

Vibration and buckling of a rectangular plate with an internal support

Bending of a Uniformly Loaded Circular Plate with Mixed Boundary Conditions