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An extension of line spring model for vibration analysis of thin isotropic plate containing multiple part-through cracks: an analytical approach

Jain N. K., Gupta A., Salhotra R., Rawani A. M., Soni S., Mishra A., Joshi P. V.

Vibrations in Physical Systems

2018

Vol. 29

art. no. 2018022

In the present study, the effect of multiple part-through cracks on the vibration characteristics of thin isotropic rectangular plate is presented. The proposed analytical model is developed using Kirchhoff’s classical plate theory and the crack terms are formulated using the simplified Line Spring Model (LSM). The application of Berger's formulation helps to transform the derived governing equation in the form of well known Duffing equation with cubic nonlinearities and then the solution for final governing equation is obtained using Galerkin's method for two different boundary conditions. The fundamental frequency of the plate as affected by the number of cracks, cracks length, cracks orientation, and plate aspect ratio for different boundary condition is presented. It is found that the results obtained for natural frequencies are maximally affected by number of cracks, crack length and orientations.

Optimization of an M/M/1/N feedback queue with retention of reneged customers

Kumar R., Jain N. K., Som B. K.

Operations Research and Decisions

2014

Vol. 24, No. 3

45--58

Customer impatience has become a threat to the business world. Firms employ various customer retention strategies to retain their impatient (or reneged) customers. Customer retention mechanisms may help to retain some or all impatient customers. Further, due to unsatisfactory service, customers may rejoin a queue immediately after departure. Such cases are referred to as feedback customers. Kumar and Sharma take this situation into account and study an M/M/1/N feedback queuing system with retention of reneged customers. They obtain only a steady-state solution for this model. In this paper, we extend the work of Kumar and Sharma by performing an economic analysis of the model. We develop a model for the costs incurred and perform the appropriate optimization. The optimum system capacity and optimum service rate are obtained.