• Structural Engineering and Mechanics
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• v.81 no.6
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• pp.705-714
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• 2022

The aim of this paper is to investigate nonlinear dynamic responses of functionally graded composite beam resting on the nonlinear viscoelastic foundation subjected to moving mass with temperature rising. The non-linear strain-displacement relationship is considered in the finite strain theory and the governing nonlinear dynamic equation is obtained by using the Hamilton's principle. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then the governing equation is solved by using of multiple time scale method. The influences of temperature rising, material distribution parameter, nonlinear viscoelastic foundation parameters, magnitude and velocity of the moving mass on the nonlinear dynamic responses are investigated. Also, the buckling temperatures of the functionally graded beams based on the finite strain theory are obtained.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.471-497
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• 2022

In this paper, we study a system of nonlinear wave equations associated with the helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.

• Steel and Composite Structures
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• v.46 no.5
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• pp.611-619
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• 2023

In the present work, the flutter characteristics of porous nanocomposite cylindrical shells, reinforced with graphene platelets (GPLs) in supersonic airflow, have been investigated. Different distributions for GPLs and porosities have been considered which are named uniform and non-uniform distributions thorough the shell's thickness. The effective material properties have been determined via Halpin-Tsai micromechanical model. The cylindrical shell formulation considering supersonic airflow has been developed in the context of first-order shell and first-order piston theories. The governing equations have been solved using Galerkin's method to find the frequency-pressure plots. It will be seen that the flutter points of the shell are dependent on the both amount and distribution of porosities and GPLs and also shell geometrical parameters.

• 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.

• Coupled systems mechanics
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• v.11 no.6
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• pp.485-504
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• 2022

This paper presents nonlinear oscillations of a carbon nanotube reinforced composite beam subjected to lateral harmonic load with damping effect based on the modified couple stress theory. As reinforcing phase, three different types of single walled carbon nanotubes distribution are considered through the thickness in polymeric matrix. The non-linear strain-displacement relationship is considered in the von Kármán nonlinearity. The governing nonlinear dynamic equation is derived with using of Hamilton's principle.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 frequency response equation and the forced vibration response of the system are obtained. Effects of patterns of reinforcement, volume fraction, excitation force and the length scale parameter on the nonlinear responses of the carbon nanotube reinforced composite beam are investigated.

• Advances in concrete construction
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• v.14 no.5
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• pp.309-315
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• 2022

This paper depicts the diagram of cylindrical shells as an essential idea. It centers around an outline of exploration and use of cylindrical shell in expansive current circumstance. In view of investigation of the current and prospect of model as a piece of present exploration work, a straightforward contextual analysis is examined with Love's shell theory based on Galerkin's method. The cylindrical shells are attached from one end of the cylindrical shells. The frequencies of ring support shells are investigated against the half axial wave mode. The frequencies increase on increasing the half axial wave mode. Also, the frequencies are downsized with ring supports. The software MATLAB is preferred to others because in this software computing coding is very easy to do. Just single command 'eig' furnishes shell frequencies and mode shapes by calculating eigenvalues and eigenvectors respectively. The shell vibration frequencies for cylindrical shells are compared with those results found in the open literature.

• Computers and Concrete
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• v.31 no.1
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• pp.1-7
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• 2023

In this paper, Timoshenko-beam model is developed for the vibration of double carbon nanotubes. The resulting frequencies are gained for axial wave mode and length-to-diameter ratios. The natural frequency becomes more prominent for lower length-to-diameter ratios and diminished for higher ratios. The converse behavior is observed for axial wave mode with clamped-clamped and clamped-free boundary conditions. The frequencies of clamped-free are lower than that of clamped-clamped boundary condition. The eigen solution is obtained to extract the frequencies of double walled carbon nanotubes using Galerkin's method through axial deformation function. Computer softer MATLAB is used for formation of frequency values. The frequency data is compared with available literature and found to be in agreement.

• 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.

• Advances in concrete construction
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• v.15 no.4
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• pp.287-301
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• 2023

Hockey games attracts many fans around the world. This game requires a specific type of ball and a stick for controlling the motion and trace of the ball. This control of motion involves hitting the ball which is a direct intensive dynamic loading. The impact load transferred directly to the hand of the player and in the professional player may cause long term medical problems. Therefore, dynamic motion of the stick should be understood. In the current study, we analyze the dynamic motion of a hockey stick under impact loading from a hockey ball. In doing so, the stick geometry is simplified as a beam structure and quasi-2D relations of displacement is applied along with classical linear elasticity theory for isotropic materials. The governing equations and natural boundary condition are extracted using Hamilton's principle. The final equations in terms of displacement components are solved using Galerkin's numerical method. The results are presented using indentation and contact force values for variations of different parameters.

• Steel and Composite Structures
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• v.48 no.2
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• pp.145-161
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• 2023

This study investigates the influences of porosity on the stability of the orthotropic laminated plates under uniaxial and biaxial loadings based on the hyperbolic shear deformation theory. Three different porosity distribution are considered with three specific functions through the plate thickness. The stability equations of porous orthotropic laminated plates are derived by the virtual work principle. Applying the Galerkin method to partial differential equations, the critical buckling load relation of porous orthotropic laminated plates is obtained. After validating the accuracy of the proposed formulation in accordance with the available literature, a parametric analysis is performed to observe the sensitivity of the critical buckling load to shear deformation, porosity, orthotropy, loading factor, and different geometric properties.