• Coupled systems mechanics
• /
• v.9 no.3
• /
• pp.265-280
• /
• 2020

In this paper, a new refined hyperbolic shear deformation beam theory for the free vibration analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equations of motion are derived from the Hamilton's principle. Navier type solution method was used to obtain frequencies, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the free vibration response of a simply supported FG beams.

• Journal of KSNVE
• /
• v.9 no.2
• /
• pp.273-284
• /
• 1999

The cylindrical shells are used as primary components of complex structures such as airplane fuselages and nuclear pressure vessels. Recently the free vibration analysis of these structures are investigated by many researchers. The engineering informations on experimental validation of the free vibration behavior on the simply supported cylindrical shells are very few. The experimental methods for realizing the physical boundary condition of simply supported edges are examined. Natural frequencies and mode shapes of the isotropic and plain weave composite simply supported shells are obtained by modal tests. A theoretical and finite element analysis are also performed in order to validate the experimental results. The experimental results indicate that the simply supported boundary conditions with bolts along the circumferential direction of shell in both ends are well achieved. Those are shown to agree with the analytical results and with the finite element analysis results. These methods can be used to realize other experimental simple support boundary conditions.

• Steel and Composite Structures
• /
• v.32 no.5
• /
• pp.643-655
• /
• 2019

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.740-745
• /
• 2003

The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method is based on the collocation method, no integration procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is required. A special coordinate transformation has been devised to consider the complicated free boundary conditions at boundary nodes. By the use of the special coordinate transformation, the radius of curvature involved in the free boundary conditions can be successfully dealt with. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by exact method and other analytical methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.965-970
• /
• 2002

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass with translational elastic support at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a wide range of section ratio, dimensionless spring constant and mass ratio.

• Advances in concrete construction
• /
• v.10 no.6
• /
• pp.499-507
• /
• 2020

In current study, utilizing the Kelvin's theory with polynomial, exponential and trigonometric volume fraction laws for functionally graded cylindrical shell vibrations. Effects of different parameters for ratios of length- and height-to-radius and angular speed versus fundamental natural frequencies been determined for two categories of cylindrical shells with clamped-free edge condition. By increasing different value of height-to-radius ratio, the resulting backward and forward frequencies increase and frequencies decrease on increasing length-to-radius ratio. Moreover, on increasing the rotating speed, the backward frequencies increases and forward frequencies decreases. The frequencies are same when the cylinder is stationary. The frequencies increases and decreases on changing the constituent materials. The frequency results are verified with the earlier literature for the applicability of present model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.955-962
• /
• 2002

According to the trends of construction of large size vessel with high power, the natural frequencies of the bending modes of propeller blades have been lower than the past. Therefore, it is expected that the noise and vibration problems of the marine propeller are frequently occurred. As main issue of the propeller noise and vibration problem, the cavitation noise and singing noise due to the flow induced excitation of the bending modes of propeller blade in the high frequency range has been studied by the hydrodynamic researchers in the view point of the excitation force reduction. In this paper, the vibration mode characteristics of propeller with a large diameter in very large vessel are investigated by the vibration analysis of the finite element method using MSC/Nastran and the vibration measurement by the impact test on the propeller blade. According to the results, the natural frequencies of various blade bending modes in water entrained condition could be estimated from the natural frequencies taken by the measurement and free vibration analysis in the dry condition, and it could be estimated how the high frequency noise such as singing is generated from the blade bending modes.

• Structural Engineering and Mechanics
• /
• v.77 no.5
• /
• pp.587-599
• /
• 2021

Based on Euler-Bernoulli beam theory and continuous element method, the free vibration of bi-dimensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams.

• Computers and Concrete
• /
• v.33 no.1
• /
• pp.27-39
• /
• 2024

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.12
• /
• pp.2008-2018
• /
• 1997

In this study, free vibration analysis of double through-the-width split beam is studied based on the author's earlier work. Each segment which constructs double through-the-width split beam is considered as Timoshenko beam. The effect of coupling between longitudinal and transverse vibration on the natural frequencies of split beams is considered. Data acquisition and modal test of double split beam for clamped-free boundary condition are carried out. Experimental and numerical results obtained by ANSYS were compared with the calculated data by present theory and their comparisons give good agreement with one another. The influences of the size and location of double split, shear deformation, and boundary conditions on the natural frequencies are demonstrated for illustrative purpose. Effects of double split on the dynamic characteristics of beams can be used to detect the size and the location of damages in structures.