• Journal of KSNVE
• /
• v.4 no.2
• /
• pp.137-146
• /
• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2009.09a
• /
• pp.377-384
• /
• 2009

Noise & vibration-free screw pile method is being developed for solution of noise and vibration problem in existing pile method. In this paper, prior to pilot test construction, conditions which a PHC pile and a screw PHC pile were constructed into ground were modeled by finite element code and through the parametric study in cohesive soils, the behaviors of two kinds of pile according to soil characteristics were compared.

• Computers and Concrete
• /
• v.3 no.5
• /
• pp.285-299
• /
• 2006

The free vibration of stiffened and damaged coupled shear walls is investigated using the mixed finite element method. The anisotropic damage model is adopted to describe the damage extent of the reinforced concrete shear wall element. The internal energy of a locally damaged shear wall element is derived. Polynomial shape functions established by Kwan are used to present the component of displacements vector on each point within the wall element. The principle of virtual work is employed to deduce the stiffness matrix of a damaged shear wall element. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls and the lateral deflection, and increases the natural frequencies. The effects of the damage extent and the stiffening beam on the free vibration characteristics of the structure are studied. The optimal location of the stiffening beam for increasing as far as possible the first natural frequency of vibration is presented.

• Wind and Structures
• /
• v.23 no.1
• /
• pp.59-73
• /
• 2016

In this paper, a hyperbolic shear deformation beam theory is developed for free vibration analysis of functionally graded (FG) sandwich beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded sandwich beam are assumed to vary according to power law distribution of the volume fraction of the constituents. The core layer is still homogeneous and made of an isotropic material. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Illustrative examples are given to show the effects of varying gradients and thickness to length ratios on free vibration of functionally graded sandwich beams.

• Wind and Structures
• /
• v.21 no.3
• /
• pp.273-287
• /
• 2015

In this paper, a free vibration analysis of functionally graded beam made of porous material is presented. The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Geomechanics and Engineering
• /
• v.9 no.3
• /
• pp.361-372
• /
• 2015

In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Advances in nano research
• /
• v.8 no.2
• /
• pp.103-114
• /
• 2020

In this research, buckling and free vibration of rectangular polymeric laminate reinforced by graphene sheets are investigated. Various patterns are considered for augmentation of each laminate. Critical buckling load is evaluated for different parameters, including boundary conditions, reinforcement pattern, loading regime, and laminate geometric states. Furthermore, vibration analysis is investigated for square laminate. Elastic properties of the composite are calculated using a combination of both molecular dynamics (MD) and the rule of mixture (MR). Kinematics of the plate is approximated based on the first shear deformation theory (FSDT). The current analysis is performed based on the energy method. For the numerical investigation, Ritz method is applied, and for shape functions, Chebyshev polynomials are utilized. It is found that the number of layers is effective on the buckling load and natural frequency of laminates which made from non-uniform layers.

• Structural Engineering and Mechanics
• /
• v.8 no.3
• /
• pp.243-256
• /
• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• Structural Engineering and Mechanics
• /
• v.45 no.2
• /
• pp.259-275
• /
• 2013

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.23 no.7
• /
• pp.654-661
• /
• 2013

The dynamic characteristics of a free-piston stirling engine(FPSE) with regard to the working frequency is investigated from theoretical and experimental studies. The FPSE is modeled as a two degree-of-freedom linear vibration system. A theoretical expression on the working frequency is derived from the instability condition for self-excitation based on the linear vibration model. A ${\gamma}$-type free-piston stirling engine is fabricated for experimental studies, and its working frequency is measured on various heater temperatures. Comparisons between the theoretical and experimental results reveal that the working frequency of the test FPSE depends on both the temperature of the compression space and the temperature difference between the expansion and compression spaces.