• Structural Engineering and Mechanics
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• v.81 no.2
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• pp.179-194
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• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.1
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• pp.1-9
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• 1976

Using the computer programs for calculation of natural vibrations of ship's hull developed by the authors et al., an investigation into influences of various parameters on the accuracy of calculation was done through example calculations of a 30,000 DWT petroleum products carrier M/S Sweet Brier built by Korea Shipbuilding and Engineering Corporation. The methodical principles employed for the computer program development are as follows; (a) the ship system is reduced to an equivalent discrete elements system conforming to Myklestad-Prohl model, (b) the problem formulation is of transfer matrix method, and (c) to obtain solutions an extended $G\ddot{u}mbel's$ initial value method is introduced. The scope of the investigation is influences of number of discrete elements, choice of significant system parameters such as rotary inertia, bending stiffness and shear stiffness, and simplification of distributions of added mass and stiffness as trapezoidal ones referred to those of midship section on the calculation accuracy. From the investigation the followings are found out; (1) To obtain good results for the modes up to the seven-noded thirty or more divisions of the hull is desirable. For fundamental mode fifteen divisions may give fairly good results. (2) The influence of rotary inertia is negligibly small at least for the modes up to the 5- or 6- noded. (3) In the case of assuming either bending modes or shear modes the calculation results in considerably higher frequencies as compared with those based on Timoshenko beam theory. However, the calculation base on the slender beam theory surprisingly gives frequencies within 10% error for fundamental modes. (4) It is proved that to simplify distributions of added mass and stiffness as trapezoidal ones referred to those of midship section is a promising approach for the prediction of natural frequencies at preliminary design stage; provided good accumulation of data from similar type ships, we may expect to obtain natural frequencies within 5% error.

• Steel and Composite Structures
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• v.29 no.3
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• pp.319-332
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• 2018

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.471-502
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• 2016

This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).

• Steel and Composite Structures
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• v.14 no.2
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• pp.105-120
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• 2013

Flexural behavior of thin walled steel-concrete composite sections as cross sections for beams is investigated by conducting an experimental study supported by applicable analytical predictions. The experimental study consists of testing up to failure, simply supported beams of effective span 1440 mm under two point loading. The test specimens consisted of composite box and channel (with lip placed on tension side and compression side) sections, the behavior of which was compared with companion empty sections. To understand the role of shear connectors in developing the composite action, some of the composite sections were provided with novel simple bar type and conventional bolt type shear connectors in the shear zone of beams. Two RCC beams having equivalent ultimate moment carrying capacities as that of composite channel and box sections were also considered in the study. The study showed that the strength to weight ratio of composite beams is much higher than RCC beams and ductility index is also more than RCC and empty beams. The analytical predictions were found to compare fairly well with the experimental results, thereby validating the applicability of rigid plastic theory to cold-formed steel concrete composite beams.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.729-736
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• 2018

This paper studies thermal buckling and post-buckling behaviors of functionally graded materials (FGM) tubes subjected to a uniform temperature rise and resting on elastic foundations via a refined beam model. Compared to the Timoshenko beam theory, the number of unknowns of this model are the same and no correction factors are required. The material properties of the FGM tube vary continuously in the radial direction according to a power function. Two ends of the tube are assumed to be simply supported and in-plane boundary conditions are immovable. Energy variation principle is employed to establish the governing equations. A two-step perturbation method is adopted to determine the critical thermal buckling loads and post-buckling paths of the tubes with arbitrary radial non-homogeneity. Through detailed parametric studies, it can be found that the tube has much higher buckling temperature and post-buckling strength when it is supported by an elastic foundation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.7
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• pp.562-569
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion Is derived by using Lagrange’s equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results In higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally. as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid Is Increased. The time which produce the maximum dynamic deflection of the simply supported pipe Is delayed according to the increment of the crack severity.

• Current Optics and Photonics
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• v.4 no.4
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• pp.293-301
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• 2020

In this paper we propose and theoretically analyze a monolithic multiparametric sensor consisting of a superstructure of surface-relief waveguide Bragg gratings (WBGs), a micro-machined diaphragm, and a cantilever beam. Diaphragms of two different configurations, namely circular and square, are designed and analyzed separately for pressure measurement. The square diaphragm is then selected for further study, since it shows relatively higher sensitivity compared to the circular one, as it incurs more induced stress when any pressure is applied. The cantilever beam with a proof mass is designed to enhance the sensitivity for acceleration measurement. A unique mathematical method using coupled-mode theory and the transfer-matrix method is developed to design and analyze the shift in the Bragg wavelength of the superstructure configuration of the gratings, due to simultaneously applied pressure and acceleration. The effect of temperature on the wavelength shift is compensated by introducing another Bragg grating in the superstructure configuration. The measured sensitivities for pressure and acceleration are found to be 0.21 pm/Pa and 6.49 nm/g respectively.

• Structural Engineering and Mechanics
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• v.91 no.4
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• pp.417-426
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• 2024

Nanotechnology has emerged as a promising avenue for enhancing musical structures. In this study, we analyze the static behavior of laser harp (i.e., electronic musical instrument) reinforced with Zinc Oxide (ZnO) nanoparticles. Leveraging the piezoelectric properties of ZnO nanoparticles, the structure is subjected to an electric field for intelligent control. The electronic musical structure is situated in a foundation with vertical springs and shear modulus constants. We employ the exponential Shear Deformation Beam Theory (ESDBT) to mathematically model the structure. A micro-electro-mechanical model is employed to determine the equivalent properties of the system. By utilizing nonlinear stress-strain relations, energy methods, and Hamilton's principle, we derive the motion equations. The buckling load of the electronic musical beam is calculated using the Difference Quadrature Method (DQM). The primary objective of this study is to present a mathematical model for electronic musical beams and determining the buckling load of the structure and to investigate the influence of nanotechnology and electric fields on its buckling behavior. The buckling is the case when the structure becomes deforms and unstable. Our findings reveal that the application of negative external voltage to the electronic musical structure increases both the stiffness and the buckling load of the musical system. Furthermore, reinforcing the electronic musical structure with ZnO nanoparticles results in an increased buckling load. Notably, the maximum enhancement in the 28-day compressive and tensile strengths of samples containing zinc oxide nanoparticles compared to the control sample resulting in increases of 18.70% and 3.77%, respectively.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.94-98
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• 1999

Optical scanning systems use glavanometers to point the laser beam to the desired position on the workpiece. The angular speed of a galvanometer is typically controlled using Proportional+Integral+Derivative(PID) control algorithms. However, natural variations in the dynamics of different galvanometers due to manufacturing, aging, and environmental factors(i.e., process uncertainty) impose a hard limit on the bandwidth of the galvanometer control system. In general, the control bandwidth translates directly into efficiency of the system response. Since the optical scanning system must have rapid response, the higher control bandwidth is required. Auto-tuning PID algorithms have been accepted in this area since they could overcome some of the problems related to process uncertainty. However, when the galvanometer is attached to a larger mechanical system, the combined dynamics often exhibit resonances. It is well understood that PId algorithms may not have the capacity to increase the control bandwidth in the face of such resonances. This paper compares the achieable performance and robustness of a galvanometer control system using a PID controller tuned by the Ziegler-Nichols method and a controller designed by the Quantitative Feedback Theory(QFT) method. The results clearly indicate that-in contrast to PID designs-QFT can deliver a single, fixed controller which will supply high bandwidth design even when the dynamics is uncertain and includes mechanical resonances.