Localization is one of the oldest mathematical and technical problems that have been at the forefront of research and development for decades. In a wireless sensor network (WSN), nodes are not able to recognize their position. To solve this problem, studies have been done on algorithms to achieve accurate estimation of nodes in WSNs. In this paper, we present an improvement of a localization algorithm namely Gaussian mixture semi-definite programming (GM-SDP-2). GMSDP is based on the received signal strength (RSS) to achieve a maximum likelihood location estimator. The improvement lies in the placement of anchors through the Fuzzy C-Means clustering method where the cluster centers represent the anchors’ positions. The simulation of the algorithm is done in Matlab and is based on two evaluation metrics, namely normalized root-mean-squared error (RMSE) and cumulative distribution function (CDF). Simulation results show that our improved algorithm achieves better performance compared to those using a predetermined placement of anchors.

The authors developed a simple and efficient method, called the Coupled Displacement method, to study the linear free vibration behavior of the moderately thick rectangular plates in which a single-term trigonometric/algebraic admissible displacement, such as total rotations, are assumed for one of the variables (in both X,Y directions), and the other displacement field, such as transverse displacement, is derived by making use of the coupling equations. The coupled displacement method makes the energy formulation to contain half the number of unknown independent coefficients in the case of a moderately thick plate, contrary to the conventional Rayleigh-Ritz method. The smaller number of undetermined coefficients significantly simplifies the vibration problem. The closed form expression in the form of fundamental frequency parameter is derived for all edges of simply supported moderately thick rectangular plate resting on Pasternak foundation. The results obtained by the present coupled displacement method are compared with existing open literature values wherever possible for various plate boundary conditions such as all edges simply supported, clamped and two opposite edges simply supported and clamped and the agreement found is good.