• Steel and Composite Structures
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• 제15권4호
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• pp.379-397
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• 2013

Conoidal shells are doubly curved stiff surfaces which are easy to cast and fabricate due to their singly ruled property. Application of laminated composites in fabrication of conoidal shells reduces gravity forces and mass induced forces compared to the isotropic constructions due to the high strength to weight ratio of the material. These light weight shells are preferred in the industry to cover large column free open spaces. To ensure design reliability under service conditions, detailed knowledge about different behavioral aspects of conoidal shell is necessary. Hence, in this paper, static bending, free and forced vibration responses of composite conoidal shells are studied. Lagrange's equation of motion is used in conjunction with Hamilton's principle to derive governing equations of the shell. A finite element code using eight noded curved quadratic isoparametric elements is developed to get the solutions. Uniformly distributed load for static bending analysis and three different load time histories for solution of forced vibration problems are considered. Eight different stacking sequences of graphite-epoxy composite and two different boundary conditions are taken up in the present study. The study shows that relative performances of different shell combinations in terms of static behaviour cannot provide an idea about how they will relatively behave under dynamic loads and also the fact that the points of occurrence of maximum static and dynamic displacement may not be same on a shell surface.

• Smart Structures and Systems
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• 제22권1호
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• Wind and Structures
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• 제24권5호
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• pp.481-500
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• 2017

A novel three-degree-of-freedom (DOF) forced vibration system has been developed for identification of aeroelastic (self-excited) load parameters used in time-domain response analysis of wind-excited flexible structures. This system is capable of forcing sinusoidal motions on a section model of a structure that is used in wind tunnel aeroelastic studies along all three degrees of freedom - along-wind, cross-wind, and torsional - simultaneously or in any combination thereof. It utilizes three linear actuators to force vibrations at a consistent frequency but varying amplitudes between the three. This system was designed to identify all the parameters, namely, aeroelastic- damping and stiffness that appear in self-excited (motion-dependent) load formulation either in time-domain (rational functions) or frequency-domain (flutter derivatives). Relatively large displacements (at low frequencies) can be generated by the system, if required. Results from three experiments, airfoil, streamlined bridge deck and a bluff-shaped bridge deck, are presented to demonstrate the functionality and robustness of the system and its applicability to multiple cross-section types. The system will allow routine identification of aeroelastic parameters through wind tunnel tests that can be used to predict response of flexible structures in extreme and transient wind conditions.

• 한국항공우주학회지
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• 제40권11호
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• pp.948-956
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• 2012

본 논문에서는 SDM 형상의 세로와 방향의 안정성 미계수를 예측하였다. 피치와 요 방향에 대한 강제조화 진동운동을 이용하여 정적 및 동적 미계수를 한 번에 계산하였다. 계산은 비정상 해석을 위한 이중시간 적분법을 적용한 3차원 Euler 해석자를 사용하여 수행하였다. 본 연구에서는 마하수뿐만 아니라 다양한 운동 변수에 따른 미계수를 예측하였다. 예측된 결과는 이전에 발표된 수치적, 실험적 연구 결과들과 비교하여 검증하였다.

• 한국추진공학회지
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• 제14권5호
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• pp.15-23
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• 2010

블레이드 디스크에는 진동 저감을 위해 종종 마찰 감쇠기가 같은 부가적인 감쇠 요소가 부착된다. 마찰 감쇠기가 있는 블레이드 디스크의 강제 진동 해석 시스템이 개발 및 검증되었다. 비선형 진동 해석 방법인 다중 조화 방법과 주기 구조물의 효율적인 해석을 위한 주기 경계 조건이 사용되었으며 집중된 구조 비선형성인 마찰 감쇠기가 있는 구조물의 거동을 모사하기 위하여 가상 질량법으로 얻어진 모드 형상이 사용되었다. 이러한 모드와 일반적인 고유 모드의 상대적인 수렴성이 비교되었다.

• Advances in nano research
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• 제8권1호
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• pp.25-36
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• 2020

Rotating systems concern with torsional vibration, and it should be considered in vibration analysis. To do this, the time-dependent torsional vibrations in a single-walled carbon nanotube (SWCNT) under the linear and harmonic external torque, are investigated in this paper. Eringen's nonlocal elasticity theory is considered to demonstrate the nonlocality and constitutive relations. Hamilton's principle is established to derive the governing equation of motion and consequently related boundary conditions. An analytical method, called the Galerkin method, is utilized to discretize the driven differential equations. Linear and harmonic torsional loads, along with determined amplitude, are applied to the SWCNT as the external torques. SWCNT is considered under the clamped-clamped end supports. In free vibration, analysis of small scale effect reveals the capability of natural frequencies in different modes, and this results desirably are in coincidence with another study. The forced torsional vibration in the time domain, especially for carbon nanotubes, has not been done before in the previous works. The previous forced studies were devoted to the transverse vibrations. It should be emphasized that the dynamical analysis of torsion is novel, workable, and at the beginning of the path. The variations of nonlocal parameter, CNT's thickness, and the influence of excitation frequency on time-dependent angular displacement and nondimensional angular displacement are investigated in the context.

• Advances in nano research
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• 제8권1호
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• pp.69-82
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• 2020

In this study, the free and forced vibration analysis of micro sandwich plate with porous core layer and magneto-electric face sheets based on modified couple stress theory and first order shear deformation theory under simply supported boundary conditions is illustrated. It is noted that the core layer is composed from balsa wood and also piezo magneto-electric facesheets are made of BiTiO₃-CoFe₂O₄. Using Hamilton's principle, the equations of motion for micro sandwich plate are obtained. Also, the Navier's method for simply support boundary condition is used to solve these equations. The effects of applied voltage, magnetic field, length to width ratio, thickness of porous to micro plate thickness ratio, type of porous, coefficient of porous on the frequency ratio are investigated. The numerical results indicate that with increasing of the porous coefficient, the non-dimensional frequency increases. Also, with an increase in the electric potential, the non-dimensional frequency decreases, while and with increasing of the magnetic potential is vice versa.

• Coupled systems mechanics
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• 제8권3호
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• pp.199-218
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• 2019

This paper studies the forced vibration of the hydro-elastic system consisting of the anisotropic (orthotropic) plate, compressible viscous fluid and rigid wall within the scope of the exact equations and relations of elastodynamics for anisotropic bodies for describing of the plate motion, and with utilizing the linearized exact Navier-Stokes equations for describing of the fluid flow. For solution of the corresponding boundary value problem it is employed time-harmonic presentation of the sought values with respect to time and the Fourier transform with respect to the space coordinate on the coordinate axis directed along the plate length. Numerical results on the pressure acting on the interface plane between the plate and fluid are presented and discussed. The main aim in this discussion is focused on the study of the influence of the plate material anisotropy on the frequency response of the mentioned pressure. In particular, it is established that under fixed values of the shear modulus of the plate material a decrease in the values of the modulus of elasticity of the plate material in the direction of plate length causes to increase of the absolute values of the interface pressure. The numerical results are presented not only for the viscous fluid case but also for the inviscid fluid case.

• Structural Engineering and Mechanics
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• 제83권4호
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• pp.451-463
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• 2022

The present study deals with forced vibrations of an elastic circular plate supported along its circular edge by unilateral elastic springs. The plate is assumed to be subjected to a uniformly distributed and a concentrated load. Under the combination of these loads, equations of motion are explicitly derived for static and dynamic response analyses by assuming a series of the displacement functions of time and other unknown parameters which are to be determined by employing Lagrangian functional. The approximate solution is sought by applying the Lagrange equations of motions by using the potential energy of the external forces that includes the contributions of the edge forces and the external moments, i.e., those of the effects of the boundary condition to the analysis. For the numerical treatment of the problem in the time domain, the linear acceleration procedure is adopted. The tensionless character of the support is taken into account by using an iterative process and, the coordinate functions for the displacement field are selected to partially fulfill the boundary conditions so that an acceptable approximation can be achieved faster. Numerical results are presented in the figures focusing on the nonlinearity of the problem due to the plate lift-off from the unilateral springs at the edge support.

• Advances in nano research
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• 제14권5호
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.