Flexural Vibration of Cylindrical Shells Partially Coupled With External and Internal Fluids

1997 ◽  
Vol 119 (3) ◽  
pp. 476-484 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Good Accuracy ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Flexural Vibration ◽  
Rayleigh Quotient ◽  
Mode Shapes ◽  
Virtual Mass ◽  
Coupled Vibration ◽  
Theory Of Shells ◽  
Shell Axis

In this paper, the free flexural vibrations of a partially fluid-loaded simply supported circular cylindrical shell are studied; the fluid is assumed to be inviscid and to present a free-surface parallel to the shell axis. The presence of external and internal fluids are both studied and the problem for incompressible and compressible fluid are both discussed by using the added virtual mass approach. Circumferential dependence of displacement is extended in a Fourier series. The maximum potential energy of the cylinder is evaluated using a sum of reference kinetic energies of the shell vibrating in vacuum; this fact allows the proposed method to be independent from the theory of shells used. Then, the Rayleigh quotient for fluid-shell coupled vibration is formulated and minimized to obtain the Galerkin equation whose solution gives the natural frequencies and mode shapes. Numerical computations are performed to obtain the modal characteristics as functions of the level of water in contact with the shell in the range of good accuracy of the theory, that is around the half-wet shell level. Results for both a shell partially surrounded and filled with water are obtained and compared.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

scholarly journals UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

2016 ◽  
Vol 54 (6) ◽  
pp. 785 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Ngoc Huyen
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Material Parameters ◽  
Flexural Vibrations ◽  
Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

Free Vibrations of Composite Shallow Circular Cylindrical Shell Panels With a Bonded Central Stiffening Shell Strip

2001 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Shallow Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Adhesive Layer ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Order System ◽  
Theoretical Formulation ◽  
First Order ◽  
Stress Resultant

Abstract This study is concerned with the “Free Vibrations of Composite Shallow Circular Cylindrical Shells or Shell Panels with a Central Stiffening Shell Strip”. The upper and lower shell elements of the stiffened composite system are considered as dissimilar, orthotropic shallow shells. The upper relatively narrow stiffening shell strip is centrally located and adhesively bonded to the lower main shell element In the theoretical formulation, a “First Order Shear Deformation Shell Theory (FSDST)” is employed. The complete set of the shallow shell dynamic equations (including the stress resultant-displacement and the constitutive equations) and the equations of the thin flexible, adhesive layer are first reduced to a set of first order system of ordinary differential equations. This final set forms the governing equations of the problem. Then, they are integrated by means of the “Modified Transfer Matrix Method”. In the adhesive layer, the “hard” and the “soft” adhesive effects are considered. It was found that the material characteristics of the adhesive layer influence the mode shapes and the corresponding natural frequencies of the composite shallow shell panel system. Additionally, some parametric studies on the natural frequencies are presented.

Diagnosis of Type, Location and Size of Cracks by Using Generalized Differential Quadrature and Rayleigh Quotient Methods

2013 ◽  
Vol 43 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Majid Akbarzadeh Khorshidi ◽  
Delara Soltani
Keyword(s):  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Rayleigh Quotient ◽  
Differential Quadrature ◽  
Mode Shapes ◽  
Quadrature Method ◽  
Torsion Spring ◽  
Free Boundary Conditions ◽  
Generalized Differential ◽  
The Relationship

Abstract In this paper, an appropriate and accurate algorithm is pro- posed to diagnosis of lateral or vertical cracks on beam, based on beam natural frequencies. Clamped-free boundary conditions are assumed for the beam. The crack in beam is modelled by without mass torsion spring. Then, the relationship between the beam natural frequencies, location and stiffness of the crack is presented by using the Rayleigh quotient and the governing equation is solved by using generalized differential quadrature method (GDQM). If there is only one crack in the beam, then three natural frequencies are used as inputs to the algorithm and mode shapes corresponding to each the natural frequencies are calculated. Finally, type, location and severity of cracks in beam, are diagnosed.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1996 ◽  
Vol 118 (1) ◽  
pp. 28-35 ◽  
Author(s):  
K. M. Gorrepati ◽  
M. D. Rao
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

This paper presents the analysis of modal parameters (natural frequencies, damping and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joints with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

Vibration Analysis of a Railway Carbody Model as a Non-Circular Cylindrical Shell

2007 ◽  
Author(s):  
Yukinori Kobayashi ◽  
Kotaro Ishiguri ◽  
Takahiro Tomioka ◽  
Yohei Hoshino
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Elastic Vibration ◽  
Mode Shapes ◽  
Simply Supported ◽  
Vibration Problems ◽  
Good Agreement

Railway carbody is modeled as a non-circular cylindrical shell with simply-supported ends in this paper. The shell model doesn’t have end plates of the carbody and other equipments attached to actual carbody are neglected. We have applied the transfer matrix method (TMM) to the analysis of three-dimensional elastic vibration problems on the carbody. We also made a 1/12 size carbody model for experimental studies to verify the validity of the numerical simulation. The model has end plates and was placed on soft sponge at both ends of the model to emulate the freely-support. The modal analysis was applied to the experimental model, and natural frequencies and mode shapes of vibration were measured. Comparing the results by TMM and the experiment, natural frequencies and mode shapes of vibration for lower modes show good agreement each other in spite of differences of boundary conditions.

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