• Advances in nano research
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• v.6 no.3
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• pp.279-298
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• 2018

Present investigation deals with the free vibration characteristics of nanoscale-beams resting on elastic Pasternak's foundation based on nonlocal strain-gradient theory and a higher order hyperbolic beam model which captures shear deformation effect without using any shear correction factor. The nanobeam is lying on two-parameters elastic foundation consist of lower spring layers as well as a shear layer. Nonlocal strain gradient theory takes into account two scale parameters for modeling the small size effects of nanostructures more accurately. Hamilton's principal is utilized to derive the governing equations of embedded strain gradient nanobeam and, after that, analytical solutions are provided for simply supported conditions to solve the governing equations. The obtained results are compared with those predicted by the previous articles available in literature. Finally, the impacts of nonlocal parameter, length scale parameter, slenderness ratio, elastic medium, on vibration frequencies of nanosize beams are all evaluated.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.121-133
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• 2017

This paper proposes an analytical solution method for free vibration of curved functionally graded (FG) nonlocal beam supposed to different thermal loadings, by considering porosity distribution via nonlocal elasticity theory for the first time. Material properties of curved FG beam are assumed to be temperature-dependent. Thermo-mechanical properties of porous FG curved beam are supposed to vary through the thickness direction of beam and are assumed to be temperature-dependent. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG structures. The rule of power-law is modified to consider influence of porosity according to even distribution. The governing equations of curved FG porous nanobeam under temperature field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is used to achieve the natural frequencies of porous FG curved nanobeam supposed to thermal loadings with simply supported boundary condition. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality, porosity volume fractions, type of temperature rising, gradient index, opening angle and aspect ratio of curved FG porous nanobeam on the natural frequency are successfully discussed. It is concluded that these parameters play key roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Ocean Systems Engineering
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• v.8 no.1
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• pp.57-77
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• 2018

The present paper deals with the finite element analysis of water tanks with rigid baffle. Fluid is discretized by two dimensional eight-node isoparametric elements and the governing equation is simulated by pressure based formulation to reduce the degrees of freedom in the domain. Both free vibration and force vibration analysis are carried out for different sizes and positions of block at tank bottom. The fundamental frequency depends on block height and it reduces with the increase of block height. The variation of hydrodynamic pressure on tank walls not only depends of the exciting frequency but also on the size and position of rigid block at tank bottom. The hydrodynamic pressure has higher value when the exciting frequency is equal and lower than the fundamental frequency of the water in the tank. Similarly, the hydrodynamic pressure increases with the increase of width of the block for all exciting frequencies when the block is at the centre of tank. The left and right walls of tank have experienced different hydrodynamic pressure when the block is placed at off-centre. However, the increase in hydrodynamic pressure on nearest tank wall becomes insignificant after a certain value of the distance between the wall and the rigid block.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.2
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• pp.45-53
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• 2004

In this paper, the stiffness and damping matrix are experimentally constructed using the structural modal information on frequencies, damping ratio and modal vectors, which are obtained by shaking table tests. Free vibration, harmonic and white noise vibration tests are performed. The acceleration of the shaking table was used as the input signal, and the corresponding accelerations of each floor were measured as output signals. The characteristics and limitations of modal information from each test are compared. The results of this study would be a basic resource of the analytical and experimental studies on the system identification of structures.

• Journal of the Korea institute for structural maintenance and inspection
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• v.20 no.5
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• pp.93-101
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• 2016

In this study, the governing equations of motion for multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium were derived. DTM(differential transformation method) was applied to vibration analysis of multi-cracked nonuniform nanobeam based on nonlocal elasticity theory and embedded in an elastic medium. The non-dimensional natural frequencies of this nanobeam were obtained for eoe, crack stiffness and elastic medium stiffness with various boundary conditions. The results obtained by this method was compared with previous works and showed the close agreement between two methods. The important conclusions obtained by this study are as follows : 1. As the length of nanobeam is shorter, the effect of scale coefficient is greater. 2. The locations of crack change non-dimensional natural frequency, In the case of fixed-fixed ends, the non-dimensional natural frequency is the biggest in the first crack location of 0.6L of nanobeam length, and the smallest in both ends. In the case of fixed-free ends, the closer the location of first crack go tho the free end, the bigger the non-dimensional natural frequency. 3. As the stiffness of crack is greater, the non-dimensional natural frequency is smaller, And the effect of crack stiffness is similar on both fixed-free ends and fixed-fixed ends. 4. The bigger the stiffness of elastic medium, the greater the non - dimensional natural frequency.

• Steel and Composite Structures
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• v.24 no.2
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• pp.151-176
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• 2017

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element ($1{\pm}z/R$) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.399-416
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• 2010

The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-step beam carrying multiple rigid bars, with each of the rigid bars possessing its own mass and rotary inertia, fixed to the beam at one point and supported by a translational spring and/or a rotational spring at another point. Where the fixed point of each rigid bar with the beam does not coincide with the center of gravity the rigid bar or the supporting point of the springs. The effects of the distance between the "fixed point" of each rigid bar and its center of gravity (i.e., eccentricity), and the distance between the "fixed point" and each linear spring (i.e., offset) are studied. For a beam carrying multiple various concentrated elements, the magnitude of each lumped mass and stiffness of each linear spring are the well-known key parameters affecting the free vibration characteristics of the (loaded) beam in the existing literature, however, the numerical results of this paper reveal that the eccentricity of each rigid bar and the offset of each linear spring are also the predominant parameters.

• Smart Structures and Systems
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• v.21 no.1
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• pp.65-74
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• 2018

In this article, an analytic non-classical model for the free vibrations of nanobeams accounting for surface stress effects is developed. The classical continuum mechanics fails to capture the surface energy effects and hence is not directly applicable at nanoscale. A general beam model based on Gurtin-Murdoch continuum surface elasticity theory is developed for the analysis of thin and thick beams. Thus, surface energy has a significant effect on the response of nanoscale structures, and is associated with their size-dependent behavior. To check the validity of the present analytic solution, the numerical results are compared with those obtained in the scientific literature. The influences of beam thickness, surface density, surface residual stress and surface elastic constants on the natural frequencies of nanobeams are also investigated. It is indicated that the effect of surface stress on the vibrational response of a nanobeam is dependent on its aspect ratio and thickness.

• International Journal of Fluid Machinery and Systems
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• v.2 no.3
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• pp.197-205
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• 2009

Since large-scale commercial wind turbine generator systems such as MW-class wind turbines are becoming widely operated, the vibration and distortion of the blade are becoming larger and larger. Therefore the soft structure design instead of the solid-design is one of the important concepts to reduce the structural load and the cost of the wind turbine rotors. The objectives of the study are development of the fluid-structure coupled analysis code and evaluation of soft rotor-blade design to reduce the unsteady structural blade load. In this paper, fluid-structure coupled analysis for the HAWT rotor blade is performed by free wake panel method coupled with hinge-spring blade model for the flapwise blade motion. In the model, the continuous deflection of the rotor blade is represented by flapping angle of the hinge with one degree of freedom. The calculation results are evaluated by comparison with the database of the NREL unsteady aerodynamic experiment. In the analysis the unsteady flapwise moments in yawed inflow conditions are compared for the blades with different flapwise eigen frequencies.

• Advances in concrete construction
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• v.8 no.1
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• pp.9-19
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• 2019

This paper describes an experimental investigation on hybrid fiber reinforced concrete (HYFRC) beams. And the main aim of this present paper is to examine the dynamic characteristics and damage evaluation of undamaged and damaged HYFRC beams under free-free constraints. In this experimental work, totally four RC beams were cast and analyzed in order to evaluate the dynamic behavior as well as static load behavior of HYFRCs. Hybrid fiber reinforced concrete beams have been cast by incorporating two different fibers such as steel and polypropylene (PP). Damage of HYFRC beams was obtained by cracking of concrete for one of the beams in each set under four-point bending tests with different percentage variation of damage levels as 50%, 70% and 90% of maximum ultimate load. And the main dynamic characteristics such as damping, fundamental natural frequencies, mode shapes and frequency response function at each and every damage level has been assessed by means of non-destructive technique (NDT) with hammer excitation. The fundamental natural frequency and damping values obtained through dynamic tests for HYFRC beams were compared with control (reference) RC beam at each level of damage which has been acquired through static tests. The static experimental test results emphasize that the HYFRC beam has attained higher ultimate load as compared with control reinforced concrete beam.