A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack
| Autor: | Ankur Gupta, Shashank Soni, N.K. Jain |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Length scale
Materials science Applied Mathematics Mechanical Engineering Mathematical analysis Isotropy 02 engineering and technology Fundamental frequency Bending Condensed Matter Physics 01 natural sciences Vibration 020303 mechanical engineering & transports 0203 mechanical engineering 0103 physical sciences Plate theory Boundary value problem Galerkin method 010301 acoustics |
| Zdroj: | Journal of Mechanics. 36:465-484 |
| ISSN: | 1811-8216 1727-7191 |
| DOI: | 10.1017/jmech.2020.13 |
| Popis: | A non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|