| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 799215 | Mechanics Research Communications | 2011 | 8 Pages |
A general formulation termed the ‘Unified Framework’ is presented in this paper, which yields nth-order expressions governing mode shapes and natural frequencies for damaged elastic structures such as rods, beams, plates and shells of any shape. The formulation is applicable to damaged elastic, self-adjoint systems for arbitrary boundary conditions and applies to structures with any damage profile or those having more than one area of damage. The formulation considers the geometric discontinuity at the damage location and perturbation to modes and natural frequencies. It makes no ad hoc assumptions regarding the physical behavior at the damage location such as added springs or changes in Young’s modulus. The geometric discontinuity manifests itself in terms of discontinuities in cross-sectional properties, such as depth, area or area moment of inertia. Considering the geometric discontinuity along with the perturbation of modes and natural frequencies, the initial homogenous differential equation with non-constant coefficients is changed to a series of non-homogeneous differential equations with constant coefficients. Solutions of this series of differential equations is obtained in this paper. The theory incorporates the change in mass due to damage, where applicable.
Research Highlights► A general formulation ‘Unified Framework’ which yields nth-order expressions governing mode shapes and natural frequencies for damaged elastic structures. ► The formulation is applicable to self-adjoint systems with arbitrary boundary conditions and with any damage profile and to structures with multiple damages. ► It makes no ad hoc assumptions regarding the physical behavior at the damage location. ► The formulation includes energy equivalent inertia effects along with energy equivalent stiffness effects of damage.
