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In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force. Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.

A modified system of nonlinear fractional-order differential equations become used to classify humans of various personalities and different Impact Factors of Memory (IFM); with unique set of model parameters. The model was used to interpret and predict the functions of the union of various people with external circumstance(s) and adapted to neighborhood environment in which the statistics collections were achieved to analyze numerous measures affecting marriages, unique challenges in marriage and associated occasions were investigated through the use of questionnaire. Data had been analyzed and the outcomes have been carried out as parameters to validate the model. Adams Predictor-Corrector Method was used to test the chaoticity of the system and it was confirmed via numerical simulations. Numerical simulation outcomes had been presented to reveal the effectiveness of the model and the accuracy of the statements established. The mathematical information implied by the model unveil an underlying mechanism which can give an explanation for couple disruption in relationships that were initially deliberated to remain all the time. Despite the terrible aspects of relationships, some human beings were still satisfied in their intimate members of the family. The study was addressed on a field survey (use of questionnaires) and with the aid of interrogating the members one on one. A feasible path for future work is the choice to attain balance through modelling and to validate the results with the aid of numerical simulations.