• Structural Engineering and Mechanics
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• v.41 no.6
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• pp.711-734
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• 2012

The foundation of a tall building frame resting on settable soil mass undergoes differential settlements which alter the forces in the structural members significantly. For tall buildings it is essential to consider seismic forces in analysis. The building frame, foundation and soil mass are considered to act as single integral compatible structural unit. The stress-strain characteristics of the supporting soil play a vital role in the interaction analysis. The resulting differential settlements of the soil mass are responsible for the redistribution of forces in the superstructure. In the present work, the nonlinear interaction analysis of a two-bay ten-storey plane building frame- layered soil system under seismic loading has been carried out using the coupled finite-infinite elements. The frame has been considered to act in linear elastic manner while the soil mass to act as nonlinear elastic manner. The subsoil in reality exists in layered formation and consists of various soil layers having different properties. Each individual soil layer in reality can be considered to behave in nonlinear manner. The nonlinear layered system as a whole will undergo differential settlements. Thus, it becomes essential to study the structural behaviour of a structure resting on such nonlinear composite layered soil system. The nonlinear constitutive hyperbolic soil model available in the literature is adopted to model the nonlinear behaviour of the soil mass. The structural behaviour of the interaction system is investigated as the shear forces and bending moments in superstructure get significantly altered due to differential settlements of the soil mass.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.623-631
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• 2005

The approximate controllability for the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator is studied. The existence, uniqueness and a variation of solutions of the system are also given.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.687-697
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• 2015

This paper shows that the solutions to the perturbed nonlinear functional differential system

• Geomechanics and Engineering
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• v.32 no.2
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• pp.125-135
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• 2023

Nonlinear vibration analysis of composite beam reinforced by carbon nanotubes resting on the nonlinear viscoelastic foundation is investigated in this study. The material properties of the composite beam is considered as a polymeric matrix by reinforced carbon nanotubes according to different distributions. With using Hamilton's principle, the governing nonlinear partial differential equations are derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained. In addition, the effects of different patterns of reinforcement, linear and nonlinear damping coefficients of the viscoelastic foundation on the nonlinear vibration responses and phase trajectory of the carbon nanotube reinforced composite beam are investigated.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.1227-1233
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• 1993

In this paper we present the differential geometric approach for the analysis and design of sliding modes in nonlinear variable structure feedback systems. We also design the robust controller for the nonlinear system using variable structure control theory on the basis of differential geometric methods and feedback linearization applying Min-Max control based on the Lyapunov second method. The robustness against parameter uncertainties for robot manipulators with flexible joint is considered. Simulation results are presented and show the advantage of the proposed nonlinear control method.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.879-890
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• 2020

In this paper we study the stability properties of solutions of nonlinear impulsive integro-differential systems by using an integral inequality under the stability of the corresponding variational impulsive integro-differential systems. Also, we give examples to illustrate our results.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• Steel and Composite Structures
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• v.46 no.5
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• pp.637-647
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• 2023

Nonlinear free vibration and stability responses of a carbon nanotube reinforced composite beam under temperature rising are investigated in this paper. The material of the beam is considered as a polymeric matrix by reinforced the single-walled carbon nanotubes according to different distributions with temperature-dependent physical properties. With using the Hamilton's principle, the governing nonlinear partial differential equation is derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The critical buckling temperatures, the nonlinear natural frequencies and the nonlinear free response of the system is obtained. The effect of different patterns of reinforcement on the critical buckling temperature, nonlinear natural frequency, nonlinear free response and phase plane trajectory of the carbon nanotube reinforced composite beam investigated with temperature-dependent physical property.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.247-254
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• 2014

In this paper, we investigate bounds for solutions of nonlinear perturbed differential systems.