• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.928-933
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• 2004

The vibration characteristic is a primary design factor. The cylindrical shells are used as a primary components of complex structure. also, The cylindrical shells have oblique angle. In this study, The vibrational characteristics of steel and plain wave GFRP cylindrical shell with an oblique end are given by experimental and finite element method. To be find characteristic of the oblique end, the mass of the cylindrical shell is maintained. Natural frequency and mode shapes of isotropic and plain weave composite shells are obtained by modal test. The results are compared with those of the finite element method. The simply supported boundary conditions with bolts along the circumferential direction of the GFRP shell are well achieved. Also, The clamped boundary conditions is applied to the steel specimen. Those are shown to agree well with the analytical results and finite element analysis results.

• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.525-544
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• 2019

In the present study, buckling and free vibration analyses of annular thin sector plate made of functionally graded materials (FGMs) resting on visco-elastic Pasternak foundation, subjected to external radial, circumferential and shear in-plane loads is investigated. Material properties are assumed to vary along the thickness according to an power law with Poisson's ratio held constant. First, based on the classical plate theory (CPT), the governing equation of motion is derived using Hamilton's principle and then is solved using the generalized differential quadrature method (GDQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. Finally, the effects of power-law exponent, ratio of radii, thickness of the plate, sector angle, and coefficients of foundation on the fundamental and higher natural frequencies of transverse vibration and critical buckling loads are considered for various boundary conditions. Also, vibration and buckling mode shapes of functionally graded (FG) sector plate have been shown in this research. One of the important obtained results from this work show that ratio of the frequency of FG annular sector plate to the corresponding values of homogeneous plate are independent from boundary conditions and frequency number.

• Advances in nano research
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• v.14 no.2
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• pp.141-154
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• 2023

Effects of viscoelastic foundation on vibration of curved-beam structure with clamped and simply-supported boundary conditions is investigated in this study. In doing so, a micro-scale laminate composite beam with two piezoelectric face layer with a carbon nanotube reinforces composite core is considered. The whole beam structure is laid on a viscoelastic substrate which normally occurred in actual conditions. Due to small scale of the structure non-classical elasticity theory provided more accurate results. Therefore, nonlocal strain gradient theory is employed here to capture both nano-scale effects on carbon nanotubes and microscale effects because of overall scale of the structure. Equivalent homogenous properties of the composite core is obtained using Halpin-Tsai equation. The equations of motion is derived considering energy terms of the beam and variational principle in minimizing total energy. The boundary condition is assumed to be clamped at one end and simply supported at the other end. Due to nonlinear terms in the equations of motion, semi-analytical method of general differential quadrature method is engaged to solve the equations. In addition, due to complexity in developing and solving equations of motion of arches, an artificial neural network is design and implemented to capture effects of different parameters on the inplane vibration of sandwich arches. At the end, effects of several parameters including nonlocal and gradient parameters, geometrical aspect ratios and substrate constants of the structure on the natural frequency and amplitude is derived. It is observed that increasing nonlocal and gradient parameters have contradictory effects of the amplitude and frequency of vibration of the laminate beam.

• Advances in nano research
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• v.14 no.2
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• pp.127-139
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• 2023

This paper studies the free vibration behavior of bi-dimensional functionally graded (BFG) nanobeams subjected to arbitrary boundary conditions. According to Eringen's nonlocal theory and Hamilton's principle, the underlying equations of motion have been obtained for BFG nanobeams. Moreover, the variable substitution method is utilized to establish the structure's state-space differential equations, followed by forming the dynamic stiffness matrix based on state-space differential equations. In order to compute the natural frequencies, the current study utilizes the Wittrick-Williams algorithm as a solution technique. Moreover, the nonlinear vibration frequencies calculated by employing the proposed method are compared to the frequencies obtained in previous studies to evaluate the proposed method's performance. Some illustrative numerical examples are also given in order to study the impacts of the nonlocal parameters, material property gradient indices, nanobeam length, and boundary conditions on the BFG nanobeam's frequency. It is found that reducing the nonlocal parameter will usually result in increased vibration frequencies.

• Advances in nano research
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• v.15 no.6
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• pp.551-565
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• 2023

Coupled porous curved beams, due to their low weight and high flexibility, have many applications in engineering. This study investigates the vibration behavior of coupled porous curved beams in different boundary conditions. The system consists of two curved beams connected by a mid-layer of elastic springs. These beams are made of various materials, such as homogenous steel foam, and composite materials with PMMA (polymethyl methacrylate) and SWCNT (single-walled carbon nanotube) used as the matrix and nanofillers, respectively. To obtain equivalent material properties, the role of mixture (RoM) was employed, followed by the implementation of the porosity function. The system's governing equations were obtained by employing FSDT and Hamilton's law. To investigate thermal vibration, temperature was implemented as a load in the governing equations. The GDQ method was used to solve these equations. To demonstrate the applicability of the GDQ method in calculating the frequencies of the system and the correctness of the developed program, a validation study was conducted. After validation, numerous examples were presented to investigate the behavior of single and coupled curved beams in various material properties and boundary conditions. The results indicate that the frequencies of the curved beams and the system depend highly on the amount of porosity (n) and the distribution pattern. The system frequencies decreased with an increase in the porosity coefficient. The stiffness of the springs had no effect on the first mode frequency but increased frequencies of other modes in a specific range. The frequencies of the system decreased with an increase in environmental temperature.

• Advances in aircraft and spacecraft science
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• v.10 no.3
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• pp.257-279
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• 2023

This manuscript is dedicated to deriving the closed form solutions of free vibration of viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory that not considered before. The kinematic displacements of Euler-Bernoulli and Timoshenko theories are developed to consider the thin nanobeam structure (i.e., zero shear strain/stress) and moderated thick nanobeam (with constant shear strain/stress). To consider the internal damping viscoelastic effect of the structure, Kelvin/Voigt constitutive relation is proposed. The perforation geometry is intended by uniform symmetric squared holes arranged array with equal space. The partial differential equations of motion and boundary conditions of viscoelastic perforated nonlocal nanobeam with elastic foundation are derived by Hamilton principle. Closed form solutions of damped and natural frequencies are evaluated explicitly and verified with prestigious studies. Parametric studies are performed to signify the impact of elastic foundation parameters, viscoelastic coefficients, nanoscale, supporting boundary conditions, and perforation geometry on the dynamic behavior. The closed form solutions can be implemented in the analysis of viscoelastic NEMS/MEMS with perforations and embedded in elastic medium.

• Steel and Composite Structures
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• v.50 no.1
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• pp.25-43
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• 2024

In this article, a mathematical model is developed to predict the dynamic behavior of bio-inspired composite beam with helicoidal orientation scheme under variable axial load using a unified higher order shear deformation beam theory. The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory. Constitutive equation of composite beam is proposed based on plane stress problem. The variable axial load is distributed through the axial direction by constant, linear, and parabolic functions. The equations of motion and associated boundary conditions are derived in detail by Hamilton's principle. Using the differential quadrature method (DQM), the governing equations, which are integro-differential equations are discretized in spatial direction, then they are transformed into linear eigenvalue problems. The proposed model is verified with previous works available in literatures. Parametric analyses are developed to present the influence of axial load type, orthotropic ratio, slenderness ratio, lamination scheme, and boundary conditions on the natural frequencies of composite beam structures. The present enhanced model can be used especially in designing spacecrafts, naval, automotive, helicopter, the wind turbine, musical instruments, and civil structures subjected to the variable axial loads.

• Nuclear Engineering and Technology
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• v.44 no.3
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• pp.283-296
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• 2012

The natural convection in a horizontal enclosure heated from the bottom wall, cooled at the top wall, and having a square adiabatic body in the center is studied. Three different Prandtl numbers (0.01, 0.7 and 7) are considered for the investigation of the effect of the Prandtl number on natural convection. Adiabatic boundary conditions are employed for the side walls. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral methodology for different Rayleigh numbers varying over the range of $10_3$ to $10_6$. It had been experimentally reported that the heat transfer mode becomes oscillatory when Pr is out of a specific Pr band beyond the critical Ra. In this study, we reproduced this phenomenon numerically. It was found that when Ra=$10_6$, only the case for intermediate Pr (=0.7) reached a non-changing steady state and the low and high Pr number cases (Pr=0.01 and 7) showed a periodically oscillatory fashion hydrodynamically and thermally. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls for different Rayleigh numbers and Prandtl numbers are presented to show the overall heat transfer characteristics in the system. Further, the isotherms and streamline distributions are presented in detail to compare the physics related to their thermal behavior.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.202-213
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• 1999

Effects of the rotary inertia of concentrated masses on the natural vibrations of fluid conveying pipes have been studied by theoretical modeling and computer simulation. For analysis, two boundary conditions for pipe ends, simply supported and clamped-clamped, are assumed and Galerkin's method is used for transformation of the governing equation to the eigenvalues problem and the natural frequencies and mode shapes for the system have been calculated by using the newly developed computer code. Moreover, the critical velocities related to a system instability have been investigated. The main conclusions for the present study are (1) Rotary inertia gives much change on the higher natural frequencies and mode shapes and its effect is visible when it has small value, (2) The number and location of nodes can be changed by rotary inertia, (3) By introducing rotary inertia, the second natural frequency approaches to the first as the location of the concentrated mass approaches to the midspan of the pipe, and (4) The critical fluid velocities to initiate the system unstable are unchanged by introduction of rotary inertia and the first three velocities are $\pi$, 2$\pi$, and 3$\pi$ for the simply supported pipe and 2$\pi$, 8.99, and 12.57 for the clamped-clamped pipe.

• Structural Engineering and Mechanics
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• v.9 no.3
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• pp.269-288
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• 2000

The governing differential equations for free vibration of multi-step orthotropic shear plates with variably distributed mass, stiffness and viscous damping are established. It is shown that a shear plate can be divided into two independent shear bars to determine the natural frequencies and mode shapes of the plate. The jk-th natural frequency of a shear plate is equal to the square root of the square sum of the j-th natural frequency of a shear bar and the k-th natural frequency of another shear bar. The jk-th mode shape of the shear plate is the product of the j-th mode shape of a shear bar and the k-th mode shape of another shear bar. The general solutions of the governing equations of the orthotropic shear plates with various boundary conditions are derived by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. A numerical example demonstrates that the present methods are easy to implement and efficient. It is also shown through the numerical example that the selected expressions are suitable for describing the distributions of stiffness and mass of typical multi-storey buildings.