• Advances in nano research
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• v.9 no.3
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• pp.157-172
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• 2020

The aim of this present research is the effect of the higher-order terms of the governing equation on the forced longitudinal vibration of a nanorod model and making comparisons of the results with classical nonlocal elasticity theory. For this purpose, the free axial vibration along with forced one under the two various linear and harmonic axial concentrated forces in zigzag Single-Walled Carbon Nanotube (SWCNT) are analyzed dynamically. Three various theories containing the classical theory, which is called Eringen's nonlocal elasticity, along with Rayleigh and Bishop theories (higher-order theories) are established to justify the nonlocal behavior of constitutive relations. The governing equation and the related boundary conditions are derived from Hamilton's principle. The assumed modes method is adopted to solve the equation of motion. For the free axial vibration, the natural frequencies are calculated for the various values of the nonlocal parameter only based on Eringen's theory. The effects of the nonlocal parameter, thickness, length, and ratio of the excitation frequency to the natural frequency over time in dimensional and non-dimensional axial displacements are investigated for the first time.

• Smart Structures and Systems
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• v.18 no.6
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• pp.1125-1143
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• 2016

Forced vibration analysis of a simple supported viscoelastic nanobeam is studied based on modified couple stress theory (MCST). The nanobeam is excited by a transverse triangular force impulse modulated by a harmonic motion. The elastic medium is considered as Winkler-Pasternak elastic foundation.The damping effect is considered by using the Kelvin-Voigt viscoelastic model. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Timoshenko beam theory by using finite element method. The effects of the transverse shear deformation and rotary inertia are included according to the Timoshenko beam theory. The obtained system of differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. Numerical results are presented to investigate the influences the material length scale parameter, the parameter of the elastic medium and aspect ratio on the dynamic response of the nanobeam. Also, the difference between the classical beam theory (CBT) and modified couple stress theory is investigated for forced vibration responses of nanobeams.

• Smart Structures and Systems
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• v.22 no.5
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• pp.527-546
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• 2018

This article presents an analysis into the nonlinear forced vibration of a micro cylindrical shell reinforced by carbon nanotubes (CNTs) with considering agglomeration effects. The structure is subjected to magnetic field and transverse harmonic mechanical load. Mindlin theory is employed to model the structure and the strain gradient theory (SGT) is also used to capture the size effect. Mori-Tanaka approach is used to estimate the equivalent material properties of the nanocomposite cylindrical shell and consider the CNTs agglomeration effect. The motion equations are derived using Hamilton's principle and the differential quadrature method (DQM) is employed to solve them for obtaining nonlinear frequency response of the cylindrical shells. The effect of different parameters including magnetic field, CNTs volume percent and agglomeration effect, boundary conditions, size effect and length to thickness ratio on the nonlinear forced vibrational characteristic of the of the system is studied. Numerical results indicate that by enhancing the CNTs volume percent, the amplitude of system decreases while considering the CNTs agglomeration effect has an inverse effect.

• Journal of Ship and Ocean Technology
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• v.3 no.2
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• pp.17-26
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• 1999

An experimental investigation on hydrodynamic forces acting on a porpoising craft at high advanced speeds up to Froude numbers Fn=6.0(Fn=U\ulcorner:Lo\ulcorner denote overall length of ship) in calm water is performed. Captive model tests and forced motion tests are carried out to measure the hydrodynamic forces. The results show that significant nonlinear effects for motion amplitudes appear in the restoring, the added mass and the damping coefficients. The experimental results are compared with the results of a prediction method of the hydrodynamic forces include the nonlinear effects, and show a good agreement with them. A simulation using the predicted hydrodynamic forces in a nonlinear motion equation is carried out to obtain the porpoising motion of a craft in calm water. The calculated results are in fairly good agreement with experimental ones.

• Journal of KSNVE
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• v.11 no.1
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.4
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• pp.315-324
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• 2011

This paper presents a historical study on the derivation of the differential equation of motion for the single-degree-of-freedom m-k system with the harmonic excitation. It was Euler for the first time in the history of vibration theory who tackled the equation of motion for that system analytically, then gave the solution of the free vibration and described the resonance phenomena of the forced vibration in his famous paper E126 of 1739. As a result of the chronological progress in mechanics like pendulum condition from Galileo to Euler, the author asserts two conjectures that Euler could apply to obtain the equation of motion at that time.

• Journal of the Korea Institute of Military Science and Technology
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• v.23 no.4
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• pp.363-370
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• 2020

In this study, pitching stability derivatives of the conical shell configuration is predicted using commercial CFD code. Unsteady flow analysis with forced harmonic motion of the model is performed using overset mesh. The test is conducted about Basic finner missile configuration. The static and dynamic stability derivatives are good agreement with available experimental data. As the same way, a conical shell is analyzed in Mach number 1.6 and various reduced frequency. The static and dynamic derivatives are obtained from the time-pitching moment coefficient histories in each of four cases of mean angle of attack. The variation of reduced frequency is not affected static and dynamic derivatives. Increasing the mean angle of attack, static derivatives are increased slowly. Comparison of the Cm curves at the steady and unsteady state results shows that the Cm curve including the damping effect is lower than otherwise case, approximately 9-18 %.

• The Journal of Korean Physical Therapy
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• v.23 no.5
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• pp.15-21
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• 2011

Purpose: The purpose of this study was to describe the influence of respiration on the segmental motion of the lumbar spine in the lying position. Methods: Twelve healthy females without a history of low back pain participated. Lumbosacral lordosis, intervertebral body angles, intervertebral body displacements, and anterior heights of the intervertebral disc of the lumbar spine were measured at inspiration, expiration and forced expiration in the supine and prone positions via fluoroscopy. Results: The results of lumbar kinematic analysis in the supine position according to respiration pattern were as follows. The L4/5 intervertebral body angle was significantly higher at forced expiration than at expiration (p<0.05). The L3/4 anterior height of the intervertebral disc was significantly higher at expiration than at forced inspiration and the L5/S1 anterior height of the intervertebral disc was significantly higher at inspiration than at forced expiration (p<0.05). There were no significant differences in the intervertebral body displacements and lumbosacral lordosis in the supine position (p>0.05). The results of lumbar kinematic analysis in the prone position according to respiration pattern were as follows. The L5/S1 anterior height of the intervertebral disc was significantly higher at inspiration than at forced expiration (p<0.05). However, there was no significant difference in the intervertebral body angle, the intervertebral body displacements, and the lumbosacral lordosis (p>0.05). Conclusion: These findings suggested that respiration can affect the intervertebral body angle and anterior height of the intervertebral disc in some segments. The results from this study serve as a step in the development of guidelines for lumbar kinematic analysis for lumbar breathing training.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.12-23
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• 2021

In the conventional experiment to assess the towing operations, the towing stability of the towed vessel has been evaluated under the condition without lateral motion of the tug-boat. However, the tug-boats may have a lateral force to change the direction of the towed vessel. In this study, experiments have been conducted considering unsteady conditions in the towing system. First, a towing test system in a Circular Water Channel (CWC) using the conventional experimental method is built. Second, the towing characteristics of the towed vessel are investigated using the conventional method, and they are compared with other research results and stability discriminant criteria. Third, the lateral motion of the tug-boat was modeled as a sinusoidal motion using a forced oscillation device changing frequency and amplitude. Finally, the discussion is given in terms of both towing- and course-stability of the towed vessel according to the lateral motion of the tug-boat.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.256-263
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• 2008

The assumed modes method is developed to derive a set of linear differential equations describing the motion of a flexible wind turbine blade and to propose an approach to investigate the forced responses result from various wind excitations. In this work, we have adopted Euler beam theory and considered that the root of the blade is clamped at the rigid hub. And the aerodynamic parameters and forces are determined based on Blade Element Momentum (BEM) theory and quasi-steady airfoil aerodynamics. Numerical calculations show that this method gives good results and it can be used fur modeling and the forced vibration analysis including the coupling effect of wind-turbine blades, as well as turbo-machinery blades, aircraft propellers or helicopter rotor blades which may be considered as straight non-uniform beams with built-in pre-twist.