• Journal of Theoretical and Applied Mechanics
• /
• 제1권1호
• /
• pp.89-96
• /
• 1995

An analytical method is presented for predicting the effect of a local deviation in the form of a concentrated mass along a radial line on the free bending vibration characteristics of a nearly axisymmetric circular plate. The approach is based on the Rayleigh-Ritz method and the expression of local deviation of the concentrated radial mass as the variation of heaviside unit step function. The effects of the concentrated mass on the natural frequencies and mode shapes of the plate are predicted with a proposed nondimensional mass parameter.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2000년도 춘계학술대회논문집A
• /
• pp.602-607
• /
• 2000

Fuel-storage tank is a representative example of liquid-structure interaction systems. In order to prevent the undesired structural failure by a variety of external loads, the reliable analysis of the dynamic response of such structural system is of a great importance. In this paper, we address the analytical study on free vibration of axisymmetric cylindrical fuel-storage tanks together with the parametric investigation of eigen-characteristics with respect to the relative fuel fill-height and the relative tank height. Numerical results illustrating theoretical results are also included.

• Structural Engineering and Mechanics
• /
• 제28권6호
• /
• pp.749-765
• /
• 2008

Free axisymmetric vibrations of layered cylindrical shells of variable thickness are studied using spline function approximation techniques. Three different types of thickness variations are considered namely linear, exponential and sinusoidal. The equations of axisymmetric motion of layered cylindrical shells, on the longitudinal and transverse displacement components are obtained using Love's first approximation theory. A system of coupled differential equations on displacement functions are obtained by assuming the displacements in a separable form. Then the displacements are approximated using Bickley-spline approximation. The vibrations of two-layered cylindrical shells, made up of several types of layered materials and different boundary conditions are considered. Parametric studies have been made on the variation of frequency parameter with respect to the relative layer thickness, length ratio and type of thickness variation parameter.

• Structural Engineering and Mechanics
• /
• 제29권4호
• /
• pp.411-422
• /
• 2008

In the present study, free vibration analysis of thick annular plates is analyzed by discrete singular convolution method. The Mindlin plate theory is employed. The material is isotropic, homogeneous and obeys Hook's law. In this paper, discrete singular convolution method is used for discretization of equations of motion. Axisymmetric frequency values are presented illustrating the effect of radius ratio and thickness to radius ratio of the annular plate. The influence of boundary conditions on the frequency characteristics is also discussed. Comparing results with those in the literature validates the present analysis. It is shown that the obtained results are very accurate by this approach.

• Advances in nano research
• /
• 제15권2호
• /
• pp.141-153
• /
• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Coupled systems mechanics
• /
• 제12권2호
• /
• pp.127-149
• /
• 2023

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

• Structural Engineering and Mechanics
• /
• 제24권4호
• /
• pp.447-461
• /
• 2006

Here, the axisymmetric free flexural vibrations and thermal stability behaviors of functionally graded spherical caps are investigated employing a three-noded axisymmetric curved shell element based on field consistency approach. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The effective material properties are evaluated using homogenization method. A detailed numerical study is carried out to bring out the effects of shell geometries, power law index of functionally graded material and base radius-to-thickness on the vibrations and buckling characteristics of spherical shells.

• 한국소음진동공학회논문집
• /
• 제12권4호
• /
• pp.280-286
• /
• 2002

It has been long suspected that the transition region may give rise to local pressure fluctuations and radiated sound that are different from those created by the fully-developed turbulent boundary layer at equivalent Reynolds number. Experimental investigation described in this paper concerns the characteristics of pressure fluctuations at the transition. Flush-mounted microphones and hot wires are used to measure the pressure fluctuations and local flow velocities within the boundary layer in the low noise wind tunnel. From this experiment we could observe the spatial and temporal development process of T-S wave using Wigner-Ville method and find the relations between the characteristic frequency of T-S wave and free stream velocity and the boundary layer thickness based on nondimensional pressure spectra scaled on outer variables.

• Steel and Composite Structures
• /
• 제43권5호
• /
• pp.581-601
• /
• 2022

The main objective of this research work is to investigate the free vibration behavior of annular sandwich plates resting on the Kerr foundation at thermal conditions. This sandwich configuration is composed of two FGM face sheets as coating layer and a porous GPLRC (GPL reinforced composite) core. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the core thickness direction. To model closed-cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme is used, while the Poisson's ratio and density are computed by the rule of mixtures. Besides, the material properties of two FGM face sheets change continuously through the thickness according to the power-law distribution. To capture fundamental frequencies of the annular sandwich plate resting on the Kerr foundation in a thermal environment, the analysis procedure is with the aid of Reddy's shear-deformation plate theory based high-order shear deformation plate theory (HSDT) to derive and solve the equations of motion and boundary conditions. The governing equations together with related boundary conditions are discretized using the generalized differential quadrature (GDQ) method in the spatial domain. Numerical results are compared with those published in the literature to examine the accuracy and validity of the present approach. A parametric solution for temperature variation across the thickness of the sandwich plate is employed taking into account the thermal conductivity, the inhomogeneity parameter, and the sandwich schemes. The numerical results indicate the influence of volume fraction index, GPLs volume fraction, porosity coefficient, three independent coefficients of Kerr elastic foundation, and temperature difference on the free vibration behavior of annular sandwich plate. This study provides essential information to engineers seeking innovative ways to promote composite structures in a practical way.

• Structural Engineering and Mechanics
• /
• 제62권1호
• /
• pp.113-123
• /
• 2017

The bi-material elastic system consisting of the circular hollow cylinder and the infinite elastic medium surrounding this cylinder is considered and it is assumed that on the inner free face of the cylinder a point-located axisymmetric time harmonic force, with respect to the cylinder's axis and which is uniformly distributed in the circumferential direction, acts. The shear-spring type imperfect contact conditions on the interface between the constituents are satisfied. The mathematical formulation of the problem is made within the scope of the exact equations of linear elastodynamics. The focus is on the frequency-response of the interface normal and shear stresses and the influence of the problem parameters, such as the ratio of modulus of elasticity, the ratio of the cylinder thickness to the cylinder radius, and the shear-spring type parameter which characterizes the degree of the contact imperfectness, on these responses. Corresponding numerical results are presented and discussed. In particular, it is established that the character of the influence of the contact imperfection on the frequency response of the interface stresses depends on the values of the vibration frequency of the external forces.