scholarly journals The Vibration of Simply Supported Non-Uniform Cross Sectional Pipe Conveying Fluid Resting on Viscoelastic Foundation

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Natural Frequencies ◽  
Flexural Vibration ◽  
Bernoulli Model ◽  
Viscoelastic Foundation ◽  
Cross Sectional ◽  
Flowing Fluid ◽  
Simply Supported ◽  
Critical Velocities ◽  
Stiffness And Damping ◽  
The Mathematical Model

The induced flexural vibration of slender pipe systems with continuous non uniform cross sectional area containing laminar flowing fluid lying on extended Winkler viscoelastic foundation is considered. The Euler Bernoulli model of the pipe has hinged ends. The inlet flow is considered constant steady that interacts with the wall of the pipe. The mathematical model is developed and its corresponding solution is obtained. The influence of the combination of variation of cross section, foundation stiffness and damping on the critical velocities, complex natural frequencies and stabilization of the system is presented.

The Natural Frequency Calculation Method of Simply-Supported Beam in the Sunshine Temperature Field

2013 ◽  
Vol 394 ◽  
pp. 364-367
Author(s):  
Yong Chun Cheng ◽  
Yu Ping Shi ◽  
Guo Jin Tan
Keyword(s):  
Temperature Field ◽  
Calculation Method ◽  
Natural Frequencies ◽  
Bernoulli Model ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Frequency Calculation ◽  
Natural Frequency Calculation ◽  
Beam Bridge ◽  
T Beam

The related researches show that , the sunshine temperature field can cause the changes of the natural frequencies of the simply-supported beam. In order to recover the influence law of the temperature field on the natural frequencies, the calculation method of the natural frequencies of the simply-supported beam bridge is formed. First, according to the principles of stress equivalence, transform the sunshine temperature field to the partiality axis forces. Based on the Bernoulli model, the calculation method of the natural frequencies of the simply-supported beam under the partiality axis forces at both ends is formed. At last, take one simply-supported T beam as the object of numerical modeling and verify the validity and the reliability of this method.

The NAVMI Factor and Natural Frequency of a Circular Plate Exposed to Water in Flexural Vibration

2011 ◽  
Vol 199-200 ◽  
pp. 1445-1450
Author(s):  
Hui Juan Ren ◽  
Mei Ping Sheng
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Integration Method ◽  
Flexural Vibration ◽  
The Other ◽  
Additional Mass ◽  
Simply Supported ◽  
Higher Order Modes

The expression of NAVMI factor and the natural frequency of a circular plate, which is placed in a hole of an infinite grid wall with one side exposed to water, are derived from the viewpoint of the additional mass. 10 Nodes Gauss-Legender integration method and the iteration method are employed to obtain the numerical results of the NAVMI factors, AVMI factors and the natural frequencies. It can be found from the results that NAVMI factors of the first two order modes are far bigger than those of the other modes when the boundary condition of a circular plate is certain. The first two order modal NAVMI factors of the circular plate with clamped and simply supported boundary conditions are far bigger than those of the circular plate with free-edged boundary condition, and the NAVMI factors are almost the same for the three order or much higher order modes regardless of the boundary condition. It is also observed that the natural frequencies of the circular plate exposed to water are smaller than those exposed to air, and the natural frequencies of the circular plate exposed to water with both sides are smaller than those of the circular plate exposed to water with one side.

Vibration of Centrally Stiffened Rectangular Plate

1961 ◽  
Vol 65 (610) ◽  
pp. 695-697 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Orthotropic Plate ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Empirical Method ◽  
Rectangular Plates ◽  
Stiffened Plate ◽  
Simply Supported ◽  
Stiffening Ribs ◽  
Square Plate ◽  
Semi Empirical

Natural frequencies of free flexural vibration of rectangular plates may, in many cases, be considerably increased by attaching to the plate one or more elastic stiffening ribs parallel to one edge, or by casting or machining the plate and stiffeners integrally.Hoppmann has determined by a semi-empirical method the natural frequencies of an integrally stiffened simply-supported square plate, using the concept of a homogeneous orthotropic plate of uniform thickness having elastic compliances which are equivalent to those of the stiffened plate. Filippov has obtained the exact solution for the fundamental frequency of a simply-supported square plate having a number of equally spaced stiffeners and has considered the effect of point loads applied to the stiffeners in a direction perpendicular to the plane of the plate.

Flexural Vibration of Rectangular Plates with Stiffeners Parallel to the Edges

1963 ◽  
Vol 67 (634) ◽  
pp. 664-668 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Natural Frequencies ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Equivalent System ◽  
Simply Supported ◽  
Finite Difference Equations ◽  
Four Corners

SummaryThe basis of the procedure described in the paper is the replacement of the stiffeners by an approximately equivalent system of line springs. One of two methods may then be used to determine the natural frequencies. A rectangular plate with edge stiffeners, point-supported at the four corners, is used to demonstrate the application of the Rayleigh-Ritz method. Numerical results obtained are compared with known approximate solutions based on finite difference equations. A Holzer-type iteration is employed in the case of a plate with parallel stiffeners, where the two edges perpendicular to the stiffeners are simply supported, the other two edges having any combination of conditions.

scholarly journals Effect of Prestress Force on Natural Bending Frequency of External Prestressed Steel Beams

2018 ◽  
Vol 12 (1) ◽  
pp. 62-70 ◽  
Author(s):  
Tang Bai-jian ◽  
Wang Fei ◽  
Chen Song
Keyword(s):  
Natural Frequencies ◽  
Cross Sectional Area ◽  
Steel Beams ◽  
Steel Beam ◽  
Sectional Area ◽  
View Point ◽  
The Finite Element Method ◽  
Cross Sectional ◽  
Simply Supported ◽  
Odd Order

Introduction: Natural bending frequencies of externally prestressed steel beam have certain sensitivity to prestress force, so they can be used to find the magnitude of prestress force. Methods: To answer the question if the existence of externally prestressed tendons increases or decreases the natural bending frequencies of a simply supported steel beam, the calculating formula for natural frequencies is deduced by using the energy method from the view point of prestress mechanism and further verified by the finite element method. Using this formula of universal property, the influence of prestress force, eccentricity and cross-sectional area of tendons on natural bending frequencies of prestressed steel beam is clearly revealed. Results and Conclusion: For external prestressed steel beams with straight tendons, their natural frequencies increase with the eccentricity and cross-sectional area of the prestressed tendon, and the eccentricity has a much larger effect on natural frequencies than the cross-sectional area does. The prestress force has no influence on the oven-order frequencies but decreases the odd-order frequencies. With the increasing order number, the prestress effect is much weaker than the effects caused by the eccentricity and cross-sectional area of the tendon.

scholarly journals Flow Induced Vibration of Cantilever Tapered Pipes Transporting Fluid

2021 ◽  
Vol 16 ◽  
pp. 8-13
Author(s):  
Mohamed Gaith
Keyword(s):  
Cross Section ◽  
Mass Fraction ◽  
Natural Frequencies ◽  
Fluid Velocity ◽  
Inviscid Fluid ◽  
Sectional Area ◽  
Flow Induced Vibration ◽  
Cross Sectional ◽  
Uniform Cross Section ◽  
The Mathematical Model

A cantilevered tapered slender pipe conveying an incompressible, inviscid fluid of one material is not a conserved system. For certain large fluid velocity, the pipe with uniform cross section would go unstable via flutter Hopf bifurcation. In this paper, the flow induced vibration for cantilever tapering pipe transporting a fluid is presented. Euler Bernoulli and Hamilton’s theories are applied to develop the mathematical model which will be solved using well known Galerkan’s procedure. The effect of smooth tapering of the circular cross sectional area, flow velocity and pipe to fluid mass fraction on the complex natural frequencies and stability will be investigated.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

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.

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