• Journal of KSNVE
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• v.10 no.1
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• pp.64-73
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• 2000

We present finite element equations in the Laplace-domain for linear viscoelastic and viscoelstically damped structures governed by a constitutive equation involving factional order derivative opeartors. These equations yield a nonstandard eigenproblem consisted of frequency dependent stiffness matrix. To solve this nonstandard eigenproblem we suggest an eigenvalue iteration procedure in the Laplace-domain. Improved Zenor and GHM material function type constitutive equations in the Laplace-domain are also available for this procedure. From above equations, complex eigenvalues and complex eigenvectors are obtained. Using obtained eigenvalues and eigenvectors, time domain analysis is performed by means of mode superposition. Finally, finite element solutions of viscoelastic and viscoeleastically damped sandwich beam are presented as an example.

• Wind and Structures
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• v.28 no.2
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• pp.89-97
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• 2019

The non-linear equations governing wind-induced internal pressures for a two-compartment building with background leakage are linearized based on some reasonable assumptions. The explicit admittance functions for both building compartments are derived, and the equivalent damping coefficients of the coupling internal pressure system are iteratively obtained. The RMS values of the internal pressure coefficients calculated from the non-linear equations and linearized equations are compared. Results indicate that the linearized equations generally have good calculation precision when the porosity ratio is less than 20%. Parameters are analyzed on the explicit admittance functions. Results show that the peaks of the internal pressure in the compartment without an external opening (Compartment 2) are higher than that in the compartment with an external opening (Compartment 1) at lower Helmholtz frequency. By contrast, the resonance peak of the internal pressure in compartment 2 is lower than that in compartment 1 at higher Helmholtz frequencies.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.319-330
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• 2020

This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke's Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener's models based on Hamilton's principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.4
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• pp.274-280
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• 2003

If a sinusoidal excitation force moves back and forth along a structure with a certain frequency, the structure will be excited with the difference frequency of these two frequencies. A low frequency vibration shaker has been developed using this force frequency shifting without actually moving a shaker The shaker consists of an ordinary eccentric mass shaker, a plate, constant springs, and time varying dampers. The dampers are turned on and off in a sequential manner to simulate a traveling slide of an excitation force. The operation of the shaker is simulated by solving the equations of motion of the shaker. Characteristics of the shaker have been found and they can be utilized to design efficient low frequency shakers.

• Journal of the Korean Society for Nondestructive Testing
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• v.15 no.2
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• pp.386-394
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• 1995

The fringes developed by misalignment, an application of Moire method measuring small deformation of specimen, was transformed to frequency function. After that, theory of normalization was applied to derive the equations explaining the relation of the deformation and Moire fringes. Above all, the equations were produced to explain the rotation and increasing of fringes. In addition to that, the relation of fringe number and strain was illustated with the equations deduced from frequency function and geometrical method respectively. These two expressions were more effective than the used ones owing to the one can accommodate the other.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.12 s.243
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• pp.1586-1596
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• 2005

In this paper, a structural damage identification method (SDIM) is developed to identify the line crack-like directional damages generated within a cylindrical shell. First, the equations of motion for a damaged cylindrical shell are derived. Based on a theory of continuum damage mechanics, a small material volume containing a directional damage is represented by the effective orthotropic elastic stiffness, which is dependent of the size and the orientation of the damage with respect to the global coordinates. The present SDIM is then derived from the frequency response function (FRF) directly solved from the equations of motion of a damaged shell. In contrast with most existing SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM may require only the FRF-data measured at damaged state. By virtue of utilizing FRF-data, one may choose as many sets of excitation frequency and FRF measurement point as needed to acquire a sufficient number of equations for damage identification analysis. The numerically simulated damage identification tests are conducted to study the feasibility of the present SDIM.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.491-505
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• 2010

A computational analysis of the nonlinear free vibration of corrugated annular plates with shallow sinusoidal corrugations under uniformly static ambient temperature is examined. The governing equations based on Hamilton's principle and nonlinear bending theory of thin shallow shell are established for a corrugated plate with a concentric rigid mass at the center and rotational springs at the outer edges. A simple harmonic function in time is assumed and the time variable is eliminated from partial differential governing equations using the Kantorovich averaging procedure. The resulting ordinary equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the temperature-dependent characteristic relations of frequency vs. amplitude for nonlinear vibration of heated corrugated annular plates are obtained. Several numerical results are presented in both tabular and graphical forms, which demonstrate the accuracy of present method and illustrate the amplitude frequency dependence for the plate under such parameters as ambient temperature, plate geometry, rigid mass and elastic constrain.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1043-1052
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• 2014

This paper deals with in-plane free vibrations of the horseshoe circular arch. Simultaneous ordinary differential equations governing free vibration of the arch are derived with respect to the radial and tangential deformations. Particularly, differential equations are obtained under the arc length coordinate rather than the angular one in order to extend the horseshoe arch whose subtended angle is greater than ${\pi}$ radians. The differential equations are numerically solved for calculating the natural frequencies accompanying with the corresponding mode shapes. In parametric studies, effects of the rotatory inertia, slenderness ratio and circumferential arc length ratio on frequency parameters are extensively discussed.