Analytical and Experimental Modal Characteristics of Cylindrical Shells

2005 ◽  
Author(s):  
Basem Alzahabi
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Offshore Structures ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Design Stage ◽  
Scaled Model ◽  
Modal Characteristics ◽  
Acoustic Signature

Cylindrical Shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. The acoustic signature of submarines is very critical in such high performance structure. Submarines are not only required to sustain very high dynamic loadings at all time, but also being able maneuver and perform their functions under sea without being detected by sonar systems. Reduction of sound radiation is most efficiently achieved at the design stage, and the acoustic signatures may be determined by considering operational scenarios, and modal characteristics. The acoustic signature of submarines is generally of two categories; broadband which has a continuous spectrum; and a tonal noise which has discrete frequencies. Therefore, investigating the dynamic characteristics of cylindrical shells is very critical first step in developing a strategy for modal vibration control for specific operating conditions. Unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. Mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then experimental modal analysis of the scaled model utilizing a fixed response approach was performed to obtain the modal characteristics of the cylindrical shell between 0 and 800 Hz. The cylinder was excited at predetermined points with an impact hammer, while the response was measured using an accelerometer at specified fixed point. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. A total of ten natural frequencies were found within that range with their corresponding mode shapes. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.

Membrane and Bending Strain in Cylindrical Shell Vibrations

2009 ◽  
Author(s):  
Basem Alzahabi ◽  
Henry Kowalski
Keyword(s):  
Natural Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Operating Conditions ◽  
Total Strain ◽  
Design Stage ◽  
Total Strain Energy ◽  
Scaled Model ◽  
Membrane Strain

Cylindrical Shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. Therefore, investigating the dynamic characteristics of cylindrical shells is very critical in developing a strategy for modal vibration control for specific operating conditions. Reduction of vibration amplitudes and in sound radiation is most efficiently achieved at the design stage, and the acoustic signatures may be determined by considering operational scenarios, and modal characteristics. In cylindrical shells, mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes, and unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. The ratio of membrane strain energy to total strain energy is high for modes with simple modal patterns and decrease toward zero as the number of nodal (n) lines increase, while the ratio of bending energy to total strain energy is small for simple nodal patterns and increase with increase in complexity of it. Modes associated with membrane deformation require a lot of strain energy while modes associated with bending deformation require less strain energy. The lowest natural frequency occurs where the sum of the two energies are at minimum. Moreover, the natural frequencies that are controlled by membrane strain energy are approximately independent of the shell thickness change. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then the experimental modal analysis of the scaled model utilizing strain gauges was performed to decouple the strain components. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

PNEUMATIC VIBROISOLATION SYSTEM OF THE BASE DESK WITH NATURAL FREQUENCY REGULATION

2021 ◽  
Vol 113 ◽  
pp. 91-100
Author(s):  
Radka JÍROVÁ ◽  
Lubomír PEŠÍK
Keyword(s):  
Natural Frequency ◽  
Automotive Industry ◽  
Natural Frequencies ◽  
Dynamical Behaviour ◽  
Operating Conditions ◽  
Frequency Regulation ◽  
The Stability ◽  
Short Time

Vibroisolation systems of base desks for machine and testing facilities usually cannot effect efficient changing of their own frequencies according to operating conditions. Especially in the case of the automotive industry, the possibility of changing natural frequencies is very desirable. During varying operating conditions, the vibroisolation system needs to be regulated easily and quickly regarding the minimisation of dynamical forces transmitted to the ground and to ensure the stability of the testing process. This paper describes one of the options of tuning the base desk at a relatively short time and by sufficient change of own frequencies, which decides the dynamical behaviour of the whole system.

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.

scholarly journals Vibrational Analysis on Hemp and Okra Fibres Mixed Glass Fiber Polyester Composite

2021 ◽  
Vol 8 (11) ◽  
pp. 55-62
Author(s):  
Putti Venkata Siva Teja ◽  
Badatala Ooha ◽  
Kondeti Sravanth
Keyword(s):  
Glass Fiber ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Fiber Composite ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Machine Component ◽  
Free System ◽  
Glass Fiber Composite

In transverse vibrations the element moves to and fro in a direction perpendicular to the direction of the advance of the wave. To determine the vibration characteristics i.e., natural frequencies and mode shapes, modal analysis is a process for a structure or a machine component while is being designed. In real life, aero planes, missiles, rockets, space vehicles, satellites, sub marines etc are modeled as free-free mechanical systems. In this paper an attempt was made to compare natural frequency for two composite materials- ladies finger with Glass fiber composite and Hemp with Glass fiber composite by taking as cantilever beams. The cantilever beam which is fixed at one end is vibrated to obtain the natural frequency, mode shapes at four different modes. A simple low cost demonstration experiment is performed in this paper by using common apparatus in order to compare theoretical, numerical (FEM analysis) profiles of two free-free thin two rectangular composite beams of dimensions 305*49.5* 7 in mm. Keywords: Natural frequencies, Mode shapes, Vibration characteristics, Ladies finger fiber, Hemp fiber, Glass fiber, FEM analysis, Free-Free system.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Investigation of stiffness of small wind turbine blade based on vibration analysis technique

2019 ◽  
Vol 44 (1) ◽  
pp. 49-59
Author(s):  
Nilesh Chandgude ◽  
Nitin Gadhave ◽  
Ganesh Taware ◽  
Nitin Patil
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Element Analysis ◽  
Finite Element Software ◽  
Small Wind Turbine

In this article, three small wind turbine blades of different materials were manufactured. Finite element analysis was carried out using finite element software ANSYS 14.5 on modeled blades of National Advisory Committee for Aeronautics 4412 airfoil profile. From finite element analysis, first, two flap-wise natural frequencies and mode shapes of three different blades are obtained. Experimental vibration analysis of manufactured blades was carried out using fast Fourier transform analyzer to find the first two flap-wise natural frequencies. Finally, the results obtained from the finite element analysis and experimental test of three blades are compared. Based on vibration analysis, we found that the natural frequency of glass fiber reinforced plastic blade reinforced with aluminum sheet metal (small) strips increases compared with the remaining blades. An increase in the natural frequency indicates an increase in the stiffness of blade.

Managing Vortex Induced Vibration in Well Jumper Systems

2008 ◽  
Author(s):  
Kenneth Bhalla ◽  
Lixin Gong
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Cross Flow ◽  
Mitigation Measures ◽  
Mode Shapes ◽  
Bottom Current ◽  
Vortex Induced Vibration ◽  
Flow Response ◽  
Out Of Plane ◽  
Lock In

The purpose of this paper is to present a method that has been developed to identify if vortex induced vibration (VIV) occurs in well jumper systems. Moreover, a method has been developed to determine when VIV mitigation measures such as strakes are required. The method involves determining the in-plane and out-of-plane natural frequencies and mode shapes. The natural frequencies are then used, in conjunction with the maximum bottom current expected at a given location to determine if suppression is required. The natural frequency of a jumper system is a function of many variables, e.g. span length, leg height, pipe diameter and thickness, buoyancy placement, buoyancy uplift, buoyancy OD, insulation thickness, and contents of the jumper. The suppression requirement is based upon calculating a lower bound lock-in current speed based upon an assumed velocity bandwidth centered about the lock-in current. The out-of-plane VIV cross-flow response is produced by a current in the plane of the jumper; whereas the in-plane VIV cross-flow response is produced by the out-of-plane current. Typically, the out-of-plane natural frequency is smaller than the in-plane natural frequency. Jumpers with small spans have higher natural frequencies; thus small span jumpers may require no suppression or suppression on the vertical legs. Whereas, larger span jumpers may require no suppression, suppression on the vertical legs or suppression on all the legs. The span of jumper systems (i.e. production, water injection, gas lift/injection ...) may vary in one given field; it has become apparent that not all jumper systems require suppression. This technique has allowed us to recognize when certain legs of a given jumper system may require suppression, thus leading to a jumper design whose safety is not compromised while in the production mode, as well as minimizing downtime and identifying potential savings from probable fatigue failures.

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