• Advances in nano research
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• v.6 no.4
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• pp.323-337
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• 2018

The nonlinear free vibration of a nanorod subjected to finite strain is investigated. The governing equation of motion in material configuration in terms of displacement is determined. By means of Galerkin method, the Fourier series solutions satisfying some typical boundary conditions are determined. The amplitude-frequency relationship and interaction between the modes are studied. The effects of nonlocal elasticity are shown for different length of nanotubes and nonlocal parameter. The results show that nonlocal effects lead to additional internal modal interaction for nanorod vibrations.

• Steel and Composite Structures
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• v.44 no.4
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• pp.557-567
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• 2022

Nonlinear free vibration analysis of a functionally graded beam resting on the nonlinear viscoelastic foundation is studied with uniform temperature rising. The non-linear strain-displacement relationship is considered in the finite strain theory. The governing nonlinear dynamic equation is derived based on the finite strain theory 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 influences of temperature rising, material distribution parameter, nonlinear viscoelastic foundation parameters on the nonlinear free response and phase trajectory are investigated. In this paper, it is aimed that a contribution to the literature for nonlinear thermal vibration solutions of a functionally graded beam resting on the nonlinear viscoelastic foundation by using of multiple time scale method.

• 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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.43 no.5
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• pp.396-404
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• 2015

The UAV's wing has high aspect ratio that is suitable for the high altitude and long endurance. Knowing the real-time deformation of wing structure in flight, it can be utilized in structural health and loading status monitoring, improvement of control effectiveness and extraordinary vibration phenomena using displacement-strain relationship. In this paper, nonlinear displacement prediction algorithm was developed for prediction of large structural deflection in flight. The algorithm was validated through the comparison with finite element analysis results and also experimental results for several large tip displacements of cantilever beam. The predicted displacements using strains are agreed well with the measured values from laser displacement sensor.

• 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.

• Tunnel and Underground Space
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• v.19 no.6
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• pp.558-566
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• 2009

Time-dependent behavior is a basic mechanical property of rocks. Predicting the failure time of rock structures by analyzing the time-dependent characteristic is important and problematic. It is tried to predict the failure time of tunnel, slope & laboratory creep test specimen from measured displacement(or strain) and rate with relationship suggested by Voight($\ddot{\Omega}=A\dot{\Omega}^\alpha$, where $\Omega$ is a measurable quantity such as strain & displacement and A & $\alpha$ are constants). A & $\alpha$ are estimated through applying the nonlinear least square method to the single and double integrated Voight's equations and utilized to predict the failure time. Predicted failure time is in accordance with real one except minor error. Linear inverse rate method applied to creep strain and rate yields a poor linear correlation of data and precision of predicted failure time is not better than methods using strain and rate.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2492-2502
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• 2002

A rubber-like material model is generally characterized by hyperelasticity and formulated by a total stress-total strain relationship because the material shows nonlinear elastic behaviour under large deformation. In this study, a pressure potential obtained by a separately interpolated pressure is introduced to the non-linear finite element formulation incorporating with incompressible or almost incompressible condition of the material. The present formulation is somewhat different from the general formulation using the pressure computed in the displacement field. A non-linear finite element analysis program is developed for the plane strain and the axisymmetric contact problems of a rubber-like material. Various examples with rubber material are analyzed for its verification. The results about deformed shapes and stress distributions thought to be meaningful in comparison with a commercial program, MARC.

• Journal of the Korea Concrete Institute
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• v.15 no.3
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• pp.454-461
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• 2003

This study addressed a procedure to carry out an experimental study on a behavior of simple and continuous concrete beams. For this purpose, sample concrete beams were fabricated and sensors for the measurement of strains and deflections were attached both on the surface of the beams and inside them. Two types of sensors were used to measure strains associated with loading: electric resistance strain sensors and fiber optic sensors. Displacement gauges were also attached on the bottoms of beams to investigate the behavior of beams more rationally. The behavior of the beams was then evaluated throughout the results measured from different sensors while they were subject to steady loading up to failure. From results of this study, it was found that concurrent use of sensors and displacement gauges is helpful in investigating the behavior of concrete beams more effectively. Especially, combined-type strain sensors specifically fabricated in this experiment were found not to be affected by the occurrence of cracks so significantly and to be very effective in monitoring strains of concrete structure. It was also observed that beams show nonlinear force-displacement relationship and reinforcing bars take charge of resisting the external force once cracks occur in concrete beams.

• Steel and Composite Structures
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• v.17 no.6
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• pp.867-890
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• 2014

This paper deals with the geometric nonlinear bending analysis of laminated composite stiffened plates subjected to uniform transverse loading. The eight-noded degenerated shell element and three-noded degenerated curved beam element with five degrees of freedom per node are adopted in the present analysis to model the plate and stiffeners respectively. The Green-Lagrange strain displacement relationship is adopted and the total Lagrangian approach is taken in the formulation. The convergence study of the present formulation is carried out first and the results are compared with the results published in the literature. The stiffener element is reformulated taking the torsional rigidity in an efficient manner. The effects of lamination angle, depth of stiffener and number of layers, on the bending response of the composite stiffened plates are considered and the results are discussed.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.1
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• pp.1-11
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• 2016

The information about the deformations of high-aspect-ratio wings is needed for the real-time monitoring of structural responses. Wing deformation in flight can be predicted by using relationship between the curvatures and the strains on the wing skin. It is also necessary to consider geometric nonlinearity when the large deformation of wing is occurred. The strain distribution on fixed-end is complex in the chordwise direction because of the geometric shape of fixed-wings on fuselages. Hence, the wing displacement can be diversely predicted by the location of the strain sensing lines in the chordwise direction. We conducted a study about prediction method of displacements regardless of the chordwise strain sensing locations. To correct spanwise strains, the ratio of spanwise strain to chordwise strain, Poisson's ratio, and the ratio of the plate strain to the beam strain were used. The predicted displacements using the strain correction were consistent with those calculated by the FEA and verified through the bending testing.