Investigation of Rocking Semicircular and Parabolic Disk Equilibria, Stability, and Natural Frequencies

2014 ◽  
Author(s):  
Michael J. Mazzoleni ◽  
Michael B. Krone ◽  
Brian P. Mann
Keyword(s):  
Natural Frequency ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Stable Equilibrium ◽  
Pitchfork Bifurcation ◽  
Equation Of Motion ◽  
Bistable Behavior ◽  
Wide Range ◽  
Stable Equilibrium Position ◽  
Good Agreement

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular and parabolic disks. Horace Lamb’s method for deriving the natural frequency of an arbitrary rocking disk is applied to two shapes with semicircular and parabolic cross sections, respectively. For the case of the semicircular disk, the system’s equation of motion is derived to verify Lamb’s method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the case of the parabolic disk, this investigation unveils a super-critical pitchfork bifurcation for changes in a single geometric parameter which reveals that the system can exhibit bistable behavior. Rapid prototyping technology was used to manufacture sample disks across a wide range of parameters, and a laser tachometer was used to experimentally determine the natural frequency of each disk. Comparisons between experiment and theory show good agreement.

Dynamics of Rocking Semicircular, Parabolic, and Semi-Elliptical Disks: Equilibria, Stability, and Natural Frequencies

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Michael J. Mazzoleni ◽  
Michael B. Krone ◽  
Brian P. Mann
Keyword(s):  
Natural Frequency ◽  
Cross Sections ◽  
Experimental Validation ◽  
Natural Frequencies ◽  
Stable Equilibrium ◽  
Pitchfork Bifurcation ◽  
Bistable Behavior ◽  
Elliptical Cross ◽  
Stable Equilibrium Position ◽  
Good Agreement

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular, parabolic, and semi-elliptical disks. Horace Lamb's method for deriving the natural frequency of an arbitrary rocking disk is applied to three shapes with semicircular, parabolic, and semi-elliptical cross sections, respectively. For the case of the semicircular disk, the system's equation of motion is derived to verify Lamb's method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the cases of the parabolic and semi-elliptical disks, this investigation reveals a supercritical pitchfork bifurcation for changes in a single geometric parameter which indicates that the systems can exhibit bistable behavior. Comparisons between experimental validation and theory show good agreement.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

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.

scholarly journals Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

2020 ◽  
Vol 10 (15) ◽  
pp. 5245
Author(s):  
Chunfeng Wan ◽  
Huachen Jiang ◽  
Liyu Xie ◽  
Caiqian Yang ◽  
Youliang Ding ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Timoshenko Beam Theory ◽  
Rotary Inertia ◽  
Cross Sectional

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.

Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Xiaolei Song ◽  
Haijun Liu
Keyword(s):  
Analytical Model ◽  
Natural Frequencies ◽  
Classical Problem ◽  
Mode Shapes ◽  
Wide Range ◽  
Fundamental Understanding ◽  
Clamped Beams ◽  
Transverse Deflection ◽  
Symmetric And Antisymmetric Modes ◽  
Good Agreement

Abstract Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.

Natural Frequency and Vibration Modal Analysis of Composite Laminated Plate

2013 ◽  
Vol 711 ◽  
pp. 396-400
Author(s):  
Long Sheng Zhao ◽  
Jin Wu Wu
Keyword(s):  
Natural Frequency ◽  
Good Accuracy ◽  
Natural Frequencies ◽  
Equation Of Motion ◽  
Theory Method ◽  
Laminated Plate ◽  
Simply Supported ◽  
Composite Laminated Plate ◽  
Experiment Method ◽  
Vibration Modal

In this paper,a layer-wise theory is used to analyze the natural frequency and vibration modal of the composite laminated plate. Layer-wise theory assumes that displacement is continue through thickness direction and has good accuracy to analyze free vibration. The frequency and vibration modal are acquired while building the equation of motion according to layer-wise theory. Through comparing layer-wise theory and other theories, numerical results show that layer-wise theory is credible to analyze composite laminated plate. At the same time, experiment is used in this paper to acquire the natural frequencies and vibration modal of a simply supported composite laminated plate. Lastly, combination of the theory method and experiment method canprobably predict the natural frequencies and vibration modal.

scholarly journals Coupled Dynamic Analysis for the Riser-Conductor of Deepwater Surface BOP Drilling System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Kanhua Su ◽  
Stephen Butt ◽  
Jianming Yang ◽  
Hongyuan Qiu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Cross Sections ◽  
Lateral Displacement ◽  
Bending Moment ◽  
Equation Of Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Drilling System ◽  
Natural Frequency Analysis

Deepwater surface BOP (surface blowout prevention, SBOP) drilling differs from conventional riser drilling system. To analyze the dynamic response of this system, the riser-conductor was considered as a beam with varied cross-sections subjected to loads throughout its length; then an equation of motion and free vibration of the riser-conductor string for SBOP was developed. The finite difference method was used to solve the equation of motion in time domain and a semianalytical approach based on the concept of section division and continuation was proposed to analyze free vibration. Case simulation results show that the method established for SBOP system natural frequency analysis is reasonable. The mode shapes of the riser-conductor are different between coupled and decoupled methods. The soil types surrounding the conductor under mudline have tiny effect on the natural frequency. Given that some papers have discussed the response of the SBOP riser, this work focused on the comparison of the dynamic responses on the wellhead and conductor with variable conditions. The dynamic lateral displacement, the bending moment, and the parameters’ sensitivity of the wellhead and the conductor were analyzed.

scholarly journals Binary-Encounter Model for Direct Ionization of Molecules by Positron-Impact

Atoms ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 99
Author(s):  
Małgorzata Franz ◽  
Katarzyna Wiciak-Pawłowska ◽  
Jan Franz
Keyword(s):  
Cross Sections ◽  
Positron Impact ◽  
Standard Quantum ◽  
Direct Ionization ◽  
Wide Range ◽  
Small Set ◽  
The Cross ◽  
Ionization Cross Sections ◽  
Binary Encounter ◽  
Good Agreement

We introduce two models for the computation of direct ionization cross sections by positron impact over a wide range of collision energies. The models are based on the binary-encounter-Bethe model and take into account an extension of the Wannier theory. The cross sections computed with these models show good agreement with experimental data. The extensions improve the agreement between theory and experiment for collision energies between the first ionization threshold and the peak of the cross section. The models are based on a small set of parameters, which can be computed with standard quantum chemistry program packages.

Natural Frequencies of Stator in Induction Motors

1997 ◽  
Author(s):  
Isao Suzuki ◽  
Shinichi Noda ◽  
Kazunobu Itomi ◽  
Fuminori Ishibashi
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Induction Motors ◽  
Fem Analysis ◽  
Stator Core ◽  
Second Stage ◽  
Contact Surfaces ◽  
Natural Frequency Analysis ◽  
Spring Constants ◽  
Good Agreement

Abstract Totally enclosed induction motors in which the stator core is pressed in the frame are in general used in industrial machines and manufactured with similar construction around the world. These motors produce a strong electromagnetic noise, which is caused by resonance between the natural frequencies of the stator core and the harmonics of electromagnetic forces. Therefore, it is very important to estimate its natural frequencies at the stage of design. As the first stage of research to estimate the natural frequencies of the stator core pressed into the motor frame, the dual rings were chosen as the object of studies. They are similar to the motor in construction and are easy to use to solve the problems. The purpose of this study is to investigate the effects of the tight fit to the natural frequencies and to find an analytical method by FEM. The authors have found that the introduction of spring elements with radial and circumferential spring constants at the contact surfaces provides accurate calculated results of the natural frequency by FEM. This paper describes about the spring constants obtained from experiments and analysis. As a result, when the spring constants in the radial direction are infinite and those in the circumferential direction are variable, it is clear that the spring constants for natural frequency analysis by FEM were expressed as a function of contact pressure on the contact surfaces. In the second stage, the measurement and calculation of natural frequency in the actual stator core with a frame was performed, and these results showed good agreement. These spring constants will be useful in FEM analysis of stator cores pressed into cylindrical induction motor frames.

Natural frequency response of laminated hybrid composite beams with and without cutouts

2014 ◽  
Vol 34 (9) ◽  
pp. 851-857 ◽  
Author(s):  
Ahmet Erkliğ ◽  
Mehmet Bulut ◽  
Eyüp Yeter
Keyword(s):  
Natural Frequency ◽  
Hybrid Composite ◽  
Fiber Orientation ◽  
Natural Frequencies ◽  
Hybrid Composites ◽  
Fiber Type ◽  
Glass Fibers ◽  
Composite Beams ◽  
Stacking Sequence ◽  
Good Agreement

Abstract This study deals with the effect of hybridization on the natural frequency of woven laminated hybrid composite beams with and without cutouts under the clamped-free boundary condition. Woven carbon, Kevlar and S-glass fibers with epoxy were used for the production of hybrid composites. Natural frequencies of the hybrid composite beams were experimentally determined for [(0/90)3]S stacking sequence. Numerical analyses were performed to investigate the influences of fiber orientation angles, circular and rectangular cutouts, cutout size ratios and positions on natural frequency. Good agreement between experimental and numerical results was found from a comparison of natural frequencies. The results shows that the fiber type used in the layers, cutout size and position on the beam strongly effects the natural frequency.

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