• Steel and Composite Structures
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• v.43 no.2
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• pp.241-256
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• 2022

In this article, an analytical procedure is presented for static analysis of composite cylinders with the geometrically nonlinear behavior, and non-uniform thickness profiles under different loading conditions by considering moderately large deformation. The composite cylinder includes two inner and outer isotropic layers and one honeycomb core layer with adjustable Poisson's ratio. The Mirsky-Herman theory in conjunction with the von-Karman nonlinear theory is employed to extract the governing equations which are a system of nonlinear differential equations with variable coefficients. The governing equations are solved analytically using the matched asymptotic expansion (MAE) method of the perturbation technique and the effects of moderately large deformations are studied. The presented method obtains the results with fast convergence and high accuracy even in the regions near the boundaries. Highlights: • An analytical procedure based on the matched asymptotic expansion method is proposed for the static nonlinear analysis of composite cylindrical shells with a honeycomb core layer and non-uniform thickness. • The effect of moderately large deformation has been considered in the kinematic relations by assuming the nonlinear von Karman theory. • By conducting a parametric study, the effect of the honeycomb structure on the results is studied. • By adjusting the Poisson ratio, the effect of auxetic behavior on the nonlinear results is investigated.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.2
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• pp.212-218
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• 2008

A possible source of resonant problems in a harbor is long waves generated by incident wave groups. The analytical solutions of the governing equations of second-order long waves derived using a multiple-scale perturbation method consist of the locked and free long waves. The locked long waves propagate at some group velocity, whereas the free long waves propagate at the shallow-water speed. To study the resonance of free long waves, a trapezoidally varying topography is employed. With certain combinations of incident angle, water depth, and ambient current velocity, free long waves can be trapped and resonated.

• Advances in aircraft and spacecraft science
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• v.4 no.5
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• pp.585-611
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• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

• Smart Structures and Systems
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• v.7 no.2
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• pp.103-116
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• 2011

This paper is concerned with the trajectory tracking and vibration suppression of a single-link flexible arm by using piezoelectric materials. The dynamics of a single flexible arm with PZT patches as sensor and actuator is derived using extended Hamilton's principle. Resulting equations show that the coupled beam dynamics including beam vibration and its rigid in-plane rotation takes place in two different time scales. By using singular perturbation theory, the system dynamics is divided into two subsystems. Then, a composite control scheme is elaborated that makes the orientation of the arm track a desired trajectory while suppressing its vibration. The proposed controller has two parts: one is a tracking controller designed for the slow (rigid) subsystem, and the other one is a stabilizing controller for the fast (flexible) subsystem. The outputs considered for the system are angular position of the hub and voltage of the sensor mounted on the structure. To avoid requiring further measurements of beam vibration and also angular velocity of the hub for the fast and slow control laws, respectively, two sliding mode observers for estimating the unknown states are also designed.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.659-671
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• 1998

Exercise of complete control on all aspects of any manufacturing / fabrication process is very difficult, leading to uncertainties in the material properties and geometric dimensions of structural components. This is especially true for laminated composites because of the large number of parameters associated with its fabrication. When the basic parameters like elastic modulus, density and Poisson's ratio are random, the derived response characteristics such as deflections, natural frequencies, buckling loads, stresses and strains are also random, being functions of the basic random system parameters. In this study the basic elastic properties of a composite lamina are assumed to be independent random variables. Perturbation formulation is used to model the random parameters assuming the dispersions small compared to the mean values. The system equations are analyzed to obtain the mean and the variance of the plate natural frequencies. Several application problems of free vibration analysis of composite plates, employing the proposed method are discussed. The analysis indicates that, at times it may be important to include the effect of randomness in material properties of composite laminates.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.1
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• pp.21-28
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• 2002

This paper intends to investigate the effects of speed fluctuation caused by the cogging torque in permanent magnetic motors on the stability of the transverse vibration for a spinning disk. Based on the Kirchhoff\`s plate theory and the assumed mode methods, a set of discretized equations of motion were derived for an annular disk rotating with a harmonically varying speed. Then, a perturbation method using the multiple time scales was employed and stability boundaries were determined explicitly in terms of the magnitude and frequency of speed fluctuation, a nominal sped and the modal characteristics of the disk. It is found that parametric resonance occurs at several speed ranges and a single mode or a combination of two modes are involved to cause instability. It is also observed that unstable regions become broadened as the spinning speed increases or two modes are combined in parametric instability. As numerical simulations, stability analysis of a conventional CD-ROM drive was performed. Results of this work can e used as guidelines for motor design and operations with low vibration.

• Structural Engineering and Mechanics
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• v.42 no.5
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• pp.677-699
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• 2012

This article studies the secondary resonances of a clamped-clamped microresonator under combined electrostatic and piezoelectric actuations. The electrostatic actuation is induced by applying the AC-DC voltage between the microbeam and the electrode plate that lies at the opposite side of the microbeam. The piezoelectric actuation is induced by applying the DC voltage between upper and lower sides of piezoelectric layer. It is assumed that the neutral axis of bending is stretched when the microbeam is deflected. The drift effect of piezoelectric layer (the phenomenon where there is a slow increase of the free strain after the application of a DC field) is neglected. The equations of motion are solved by using the multiple scale perturbation method. The system possesses a subharmonic resonance of order one-half and a superharmonic resonance of order two. It is shown that using the DC piezoelectric actuation, the sensitivity of AC-DC electrostatically actuated microresonator under subharmonic and superharmonic resonances may be tuned. In addition, it is shown that the tuning domain of the microbeam under combined electrostatic and piezoelectric actuations at subharmonic and superharmonic conditions is larger than the tuning domain of microbeam under only the electrostatic actuation.

• Steel and Composite Structures
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• v.33 no.2
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• pp.261-275
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• 2019

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

• Steel and Composite Structures
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• v.44 no.3
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

• Smart Structures and Systems
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• v.29 no.5
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• pp.705-714
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• 2022

In this paper, the effect of magnetic field on the vibration behavior of a Magnetorheological elastomer (MRE) sandwich MEMS actuated by electrostatic actuation with conductive skins are examined within the multiple scales (MMS) perturbation method. Magnetorheological smart materials have been widely used in vibration control of various systems due to their mechanical properties change under the influence of different magnetic fields. To investigate the vibrational behavior of the movable electrode, the Euler-Bernoulli beam theory, as well as Hamilton's principle is used to derive the equations and the related boundary conditions governing the dynamic behavior of the system are applied. The results of this study show that by placing the Magnetorheological elastomer core in the movable electrode and applying different magnetic fields on it, its natural vibrational frequency can be affected so that by increasing the applied magnetic field, the system's natural frequency increases. Also, the effect of various factors such as the electric potential difference between two electrodes, changes in the thickness of the core and the skins, electrode length, the distance between two electrodes and also change in vibration modes of the system on natural frequencies have been investigated.