• Structural Engineering and Mechanics
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• 제88권5호
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• pp.405-417
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• 2023

This paper reveals theoretical research to the nonlinear dynamic response and initial geometric imperfections sensitivity of the spinning graphene platelets reinforced metal foams (GPLRMF) cylindrical shell under different boundary conditions in thermal environment. For the theoretical research, with the framework of von-Karman geometric nonlinearity, the GPLRMF cylindrical shell model which involves Coriolis acceleration and centrifugal acceleration caused by spinning motion is assumed to undergo large deformations. The coupled governing equations of motion are deduced using Euler-Lagrange principle and then solved by a combination of Galerkin's technique and modified Lindstedt Poincare (MLP) model. Furthermore, the impacts of a set of parameters including spinning velocity, initial geometric imperfections, temperature variation, weight fraction of GPLs, GPLs distribution pattern, porosity distribution pattern, porosity coefficient and external excitation amplitude on the nonlinear harmonic resonances of the spinning GPLRMF cylindrical shells are presented.

• 대한기계학회논문집A
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• 제24권10호
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• pp.2413-2419
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• 2000

Harmonic resonances in a continuous rotating shaft with distributed mass are discussed. The restoring force of the shaft has geometric stiffening nonlinearity due to the extension of the shaft centerline. The effect of a distributed lateral force, such as the gravity, is assumed. The possibility of the occurrences of harmonic resonances, the shapes of resonance curves, and internal resonance phenomena are investigated.

• Advances in nano research
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• 제12권4호
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• pp.353-363
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• 2022

This paper presents an investigation about superharmonic and subharmonic resonances 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 (CNTs) distribution are considered through the thickness in polymeric matrix. The governing nonlinear dynamic equation is derived based on the von Kármán nonlinearity 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. Effects of different patterns of reinforcement, volume fraction, excitation force and the length scale parameter on the frequency-response curves of the carbon nanotube reinforced composite beam are investigated. The results show that volume fraction and the distribution of CNTs play an important role on superharmonic and subharmonic resonances of the carbon nanotube reinforced composite beams.

• Structural Engineering and Mechanics
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• 제70권5호
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• pp.623-637
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• 2019

This paper analyzes the non-stationary vibration and super-harmonic resonances in nonlinear dynamic motion of viscoelastic nano-resonators. For this purpose, a new coupled size-dependent model is developed for a plate-shape nano-resonator made of nonlinear viscoelastic material based on modified coupled stress theory. The virtual work induced by viscous forces obtained in the framework of the Leaderman integral for the size-independent and size-dependent stress tensors. With incorporating the size-dependent potential energy, kinetic energy, and an external excitation force work based on Hamilton's principle, the viscous work equation is balanced. The resulting size-dependent viscoelastically coupled equations are solved using the expansion theory, Galerkin method and the fourth-order Runge-Kutta technique. The Hilbert-Huang transform is performed to examine the effects of the viscoelastic parameter and initial excitation values on the nanosystem free vibration. Furthermore, the secondary resonance due to the super-harmonic motions are examined in the form of frequency response, force response, Poincare map, phase portrait and fast Fourier transforms. The results show that the vibration of viscoelastic nanosystem is non-stationary at higher excitation values unlike the elastic ones. In addition, ignoring the small-size effects shifts the secondary resonance, significantly.

• 한국소음진동공학회논문집
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• 제15권6호
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• pp.706-711
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• 2005

Torsional oscillations of a system incorporating a Hooke's joint are investigated by studying a simple similar nonlinear 2-degree-of-freedom model, which has linear and quadratic nonlinear parametric excitations. The simple system is identified to have the possibilities of primary, sub harmonic and combination resonances. The case of simultaneous primary and combination resonances is selected for perturbation analysis to have the reduced amplitude-equations of motion. The same procedure is applied to the system incorporating a Hooke's joint.

• Steel and Composite Structures
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• 제52권5호
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• pp.557-569
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• 2024

Nonlinear internal modals interactions analysis of axially functionally graded nanorods is evaluated on the basis of nonlocal elasticity theory and Rayleigh beam model for the first time. Functionally graded materials can be determined as nonhomogeneous composites which are obtained by combining of two various materials in order to get a new ideal material. In this research, material properties of nanorods are supposed to be calmly varied along the axial direction. Hamilton's principle is used to derive the equations with consideration of Von-Kármán's geometrically nonlinearity. Harmonic Differential Quadrature (HDQ) and Multiple Scale (MS) solution techniques are used to derive an approximate-analytic solution to the linear and nonlinear free axial vibration problem of non-classical nanorods for clamped-clamped and clamped-free boundary conditions. A parametric study is carried out to indicate the effects of index of AFG, aspect ratio, mode number, internal resonances and nonlinear amplitude on nonlinear nonlocal frequencies of axially functionally graded nanorods. Also, the effects of nonlocal and nonlinear coefficients and AFG index on relationships of internal resonances have been investigated. The presented theatrical-semi analytical model has the ability to predict very suitable results for extracting the internal modal interactions in the AFG nanorod.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.767-782
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• 2022

In this paper, the nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells exposed to the thermal environment and a uniformly distributed harmonic loading using a semi-analytical method is investigated. The cylindrical shell is surrounded by a nonlinear viscoelastic foundation consisting of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The distribution of temperature and material constitutive of the stiffeners are continuously changed through the thickness direction. The cylindrical shell has three layers consisting of metal, FGM, and ceramic. The interior layer of the cylindrical shell is rich in metal, while the exterior layer is rich in ceramic, and the FG material is located between two layers. The nonlinear vibration problem utilizing the smeared stiffeners technique, the von Kármán equations, and the Galerkin method has been solved. The multiple scales method is utilized to examine the nonlinear vibration behavior of SSMFG cylindrical shells. The considered resonant case is 1:3:9 internal resonance and subharmonic resonance of order 1/3. The influences of different material and geometrical parameters on the vibration behavior of SSMFG cylindrical shells are examined. The results show that the angles of stiffeners, temperature, and elastic foundation parameters have a strong effect on the vibration behaviors of the SSMFG cylindrical shells.

• Advances in nano research
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• 제16권2호
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• pp.111-125
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• 2024

Recently, a lot of research has been done on the analysis of axial vibrations of homogeneous and FG nanotubes (nanorods) with various aspects of vibrations that have been fully mentioned in history. However, there is a lack of investigation of the dynamic internal resonances of FG nanotubes (nanorods) between them. This is one of the essential or substantial characteristics of nonlinear vibration systems that have many applications in various fields of engineering (making actuators, sensors, etc.) and medicine (improving the course of diseases such as cancers, etc.). For this reason, in this study, for the first time, the dynamic internal resonances of FG nanorods in the simultaneous presence of large-amplitude size dependent behaviour, inertial and shear effects are investigated for general state in detail. Such theoretical patterns permit as to carry out various numerical experiments, which is the key point in the expansion of advanced nano-devices in different sciences. This research presents an AFG novel nano resonator model based on the axial vibration of the elastic nanorod system in terms of derivation from large-amplitude size dependent internal modals interactions. The Hamilton's Principle is applied to achieve the basic equations in movement and boundary conditions, and a harmonic deferential quadrature method, and a multiple scale solution technique are employed to determine a semi-analytical solution. The interest of the current solution is seen in its specific procedure that useful for deriving general relationships of internal resonances of FG nanorods. The numerical results predicted by the presented formulation are compared with results already published in the literature to indicate the precision and efficiency of the used theory and method. The influences of gradient index, aspect ratio of FG nanorod, mode number, nonlinear effects, and nonlocal effects variations on the mechanical behavior of FG nanorods are examined and discussed in detail. Also, the inertial and shear traces on the formations of internal resonances of FG nanorods are studied, simultaneously. The obtained valid results of this research can be useful and practical as input data of experimental works and construction of devices related to axial vibrations of FG nanorods.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1994년도 추계학술대회논문집; 한국종합전시장, 18 Nov. 1994
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• pp.35-39
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• 1994

One of the important characteristics of the response of nonlinear systems is the existence of subharmonic resonances. When some conditions in parameter space are satisfied. It is possible even in the presence of damping for a periodically excited nonlinear system to possess a response which is the combination of a contribution at the excitation frequency and a component at the system natural frequency. The system natural frequency being a submultiple of the excitation frequency implies that the resulting response is a subharmonic oscillation. In general, there also co-exists, for the system, a response at the excitation frequency, and initial conditions determine which of the steady-state responses is achieved in an experiment or a numerical simulation. In single-degree-of-freedom systems with harmonic excitation, depending on the type of the nonlinearity, e.g., cubic or quadratic the frequency of subharmonic response is respectively, one-third or one-half of that of the excitation frequency. Although subharmonic resonance is one of the principal characteristics of a nonlinear system the subharmonic responses of structures in the presence of internal resonances have been studied very rarely. In this work, we consider subharmonic responses in the two-mode approximation of the plate equations. It is assumed that the two modes are in one-to-one internal resonance. Constant and periodic steady-state solutions of the averaged equations are studied. Finally, the results of direct time integration of the original equations of motion are presented and compared with those obtained from the averaged equations.

• 대한기계학회논문집A
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• 제25권12호
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• pp.2002-2008
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• 2001

Nonlinear vibration characteristics of a piezoelectric-type micro actuator used for hard disk drives are experimentally studied. The nonlinear characterisitics include hysteresis, superharmonic resonance, jump phenomenon, and shifting of natural frequencies. The vibration modes and frequencies of the commercial actuator of the Hutchinson's Magnum series are measured using a laser vibrometer. From harmonic excitation to the PZT acturator, we observe interesting hysteresis patterns with 3 times input frequency. It is shown that the micro actuator has the typical 3 times superhamonic resonances coupled to the first torsional and sway modes of the suspension.