• Structural Engineering and Mechanics
• /
• v.33 no.6
• /
• pp.747-763
• /
• 2009

In this work, the linear vibration characteristics of $90^{\circ}$ pipe bends and their cylindrical and toroidal shell components are studied. The finite element method, based on shear-deformation shell elements, is used to carry out a vibration analysis of metallic multiple $90^{\circ}$ mitred pipe bends. Single, double, and triple mitred bends are considered, as well as a smooth bend. Sample natural frequencies and mode shapes are given. To validate the procedure, comparison of the natural frequencies is made with existing results for cylindrical and toroidal shells. The influence of the multiplicity of the bend, the boundary conditions, and the various geometric parameters on the natural frequency is described. The differential quadrature method, based on classical shell theory, is used to study the vibration of components of these bends. Regression formulas are derived for cylindrical shells (straight pipes) with one or two oblique edges, and for sectorial toroidal shells (curved pipes, pipe elbows). Two types of support are considered for each case. The results given provide information about the vibration characteristics of pipe bends over a wide range of the geometric parameters.

• Structural Engineering and Mechanics
• /
• v.29 no.5
• /
• pp.531-550
• /
• 2008

This paper adopts the numerical assembly method (NAM) to determine the exact solutions of natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and springmass systems. First, the coefficient matrix for an intermediate station with various concentrated elements, cross-section change and/or pinned support and the ones for the left-end and right-end supports of a beam are derived. Next, the overall coefficient matrix for the entire beam is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact solutions for the natural frequencies of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and the associated mode shapes are obtained by substituting the corresponding values of integration constants into the associated eigenfunctions.

• Structural Monitoring and Maintenance
• /
• v.6 no.2
• /
• pp.85-101
• /
• 2019

The effects of foundation scour depth and riverbed condition on the natural frequencies of a typical cross-river integral abutment bridge have been studied. The conventional operational modal analysis technique has been employed in order to extract the modal properties of the bridge and the results have been used in the Finite Element (FE) model updating procedure. Two tests have been carried out in two different levels of water and wet condition of the riverbed. In the first test, the riverbed was in dry condition for two subsequent years and the level of water was 10 meter lower than the natural riverbed. In the second test, the river was opened to water flow from the upstream dam and the level of water was 2 meter higher than the natural riverbed. The results of these two tests have also been used in order to find to what extend the presence of water flow in the river and saturation of the surrounding soil affect the bridge natural frequencies. Finally, the updated FE model of the bridge has been applied in a series of parametric analyses incorporating the effect of piles' relative scour depth on the bridge natural frequency of the first four vibration modes.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.10a
• /
• pp.267-274
• /
• 1999

An understanding of the natural frequencies of a beam is virtually a prerequisite to the understanding of its response in forced vibration due to shock, ground acceleration or moving loads. Contrary to the frequencies of the prismatic bars with arbitrary boundary conditions, those of a tapered bar are hard to determine when one employs convevtional neutral equilibrium or energy method. In this paper, finite element method is adopted to determine the fundamental frequencies of the non-symmetrically tapered bars. The bars assume the shapes of straight lines along the axis. The parameters considered in this study are sectional parameter, m,n and taper parameter, $\alpha$ For the structural engineer's convenience, the results by finite element method are expressed by simple algebraic equations, by which first mode frequencies are easily estimated. And they agree fairy well with those by F.E.M in most cases.

• Computers and Concrete
• /
• v.32 no.4
• /
• pp.365-371
• /
• 2023

On the basis of Flügge shell theory, the vibrations of single walled carbon nanotubes (SWCNTs) are investigated. The structure of armchair single walled carbon nanotubes are used here. Influences of length-to-diameter ratios and the two boundary conditions on the natural frequencies of armchair SWCNTs are examined. The Rayleigh-Ritz method is employed to determine eigen frequencies for single walled carbon nanotubes. The solution is obtained using the geometric characteristics and boundary conditions for natural frequencies of SWCNTs. The natural frequencies decrease as ratio of length to diameter increase and the effect of frequencies is less significant and more prominent for long tube. To assess the frequency confirmation carried out in this paper are compared with the earlier computations.

• Steel and Composite Structures
• /
• v.35 no.5
• /
• pp.659-670
• /
• 2020

This paper proposes the use of a porous core between layers of laminated composite plates to examine its effect on the natural frequencies of the resulted porous laminated composite sandwich plate (PLCSP) resting on a two-parameter elastic foundation. Moreover, it has been suggested that the dispersion of porosity has two different functionally graded (FG) patterns which are compared with a uniformly dispersed (UD) profile to find their best vibrational efficiency in the proposed PLCSPs. In FG patterns, two types of dispersions, including symmetric (FG-S) and asymmetric (FG-A) patterns have been considered. To derive the governing Eigen value equation of such structures, the first order shear deformation theory (FSDT) of plates has been employed. Accordingly, a finite element method (FEM) is developed to solve the derived Eigen value equation. Using the mentioned theory and method, the effects of porosity parameters, fiber orientation of laminated composite, geometrical dimensions, boundary conditions and elastic foundation on the natural frequencies of the proposed PLCSPs have been studied. It is observed that embedding porosity in core layer leads to a significant improvement in the natural frequencies of PLCSPs. Moreover, the natural frequencies of PLCSPs with FG porous core are higher than those with UD porous core.

• Structural Engineering and Mechanics
• /
• v.62 no.1
• /
• pp.65-77
• /
• 2017

The free vibration analysis of fluid conveying Timoshenko pipeline with different boundary conditions using Differential Transform Method (DTM) and Adomian Decomposition Method (ADM) has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical fluid velocity of the pipelines on different supports are analyzed based on Timoshenko model by using DTM and ADM in this study. At first, the governing differential equations of motion of fluid conveying Timoshenko pipeline in free vibration are derived. Parameter for the nondimensionalized multiplication factor for the fluid velocity is incorporated into the equations of motion in order to investigate its effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, the efficient and easy mathematical techniques called DTM and ADM are used to solve the governing differential equations of the motion, respectively. The calculated natural frequencies of fluid conveying Timoshenko pipelines with various combinations of boundary conditions using DTM and ADM are tabulated in several tables and figures and are compared with the results of Analytical Method (ANM) where a very good agreement is observed. Finally, the critical fluid velocities are calculated for different boundary conditions and the first five mode shapes are presented in graphs.

• Journal of Electrical Engineering and Technology
• /
• v.12 no.5
• /
• pp.1842-1850
• /
• 2017

Reducing the noise and vibration of the BLDC motors is very essential for some special applications. In this paper, a new structural design is introduced to increase the natural frequencies of the stator in BLDC motors as increasing the natural frequencies can reduce the severe effects of the structural resonances, including high levels of noise and vibration. The design is based on placing a single hole on definite regions at the stator cross sectional area (each region contains one tooth and its upper parts in the stator yoke) in an optimum way by which the natural frequencies at different modes are shifted to the higher values. The optimum diameter and locations for the holes are extracted by the Response Surface Methodology (RSM) and the modal analyses in the iterative process are done by Finite Element Method (FEM). Moreover, the motor performance by the optimum stator structure is analyzed by FEM and compared with the prototype motor. Preventing the stator magnetic saturation and the motor cogging torque enhancement are the two constraints of the optimization problem. The optimal structural design method is applied experimentally and the validity of the design method is confirmed by the simulated and experimental results.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.14 no.6
• /
• pp.1281-1288
• /
• 1994

Beams curved in plan are often designed with the circular curved member system including warping effects. In this study, the curved bridges are idealized as the circular curved member system with singly symmetric cross sections and simply supported ends. Displacement fields of them to satisfy the boundary conditions are expanded by Fourier series and the governing equation of natural frequencies of them is derived. The distributions of the characteristics of natural frequencies of them are shown according to the variations of relevant parameters-angle of intersection, curvature, and parameter of symmetry of cross section which can represent the properties of the curved bridges. A parametric study is conducted to investigate the effect of relevant parameters on natural frequencies.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.15 no.5 s.98
• /
• pp.604-611
• /
• 2005

The relationship between floor impact sound and vibration has been studied by field measurements, and the vibration modal characteristics have been analyzed. Vibration levels impacted by a standard heavy-weight impact source have been predicted according to the main design parameters using finite element method. Experimental results show that the dominant frequencies of the heavy impact sounds range below 100 Hz and that they are coincident with natural frequencies of the concrete slab. In addition, simple 2-dimensional finite element models are proposed to substitute 2 types of 3-dimensional models of complicated floor structural slabs those by The analytical result shows that the natural frequencies from first to fifth mode well correspond to those by experiments with an error of less than $12\%$, and acceleration peak value iscoincident with an error of less than $2\%$. Using the finite element model. vibration levels areestimated according to the design Parameters, slab thickness, compressive strength, and as a result, the thickness is revealed as effective to increase natural frequencies by $20\~30\%$ and to reduce the vibration level by 3$\~$4 dB per 30 mm of extra thickness.