Natural frequencies of elastically supported orthotropic reactangular plates

1977 ◽  
Vol 61 (1) ◽  
pp. 79-83 ◽  
Author(s):  
Edward B. Magrab
Keyword(s):  
Natural Frequencies ◽  
Elastically Supported

Vibration Suppression of an Elastically Supported Beam With Closely Spaced Natural Frequencies

2020 ◽  
Author(s):  
Haizhou Liu ◽  
Hao Gao
Keyword(s):  
Natural Frequencies ◽  
Vibration Suppression ◽  
Fixed Point Theory ◽  
Dynamic Performance ◽  
Point Theory ◽  
Primary System ◽  
Computationally Efficient ◽  
Wide Range ◽  
Univariate Optimization ◽  
Elastically Supported

Abstract Vibration suppression of distributed parameter systems is of great interest and has a wide range of applications. The dynamic performance of a primary system can be improved by adding dynamic vibration absorbers (DVA). Although the relevant topics have been studied for decades, the trade-off between capability of suppressing multiple resonant peaks and complexity of absorbers has not been well addressed. In this paper, the vibration suppression problem of a uniform Euler-Bernoulli beam with closely spaced natural frequencies is investigated. To achieve desired vibration reduction, a two-DOF DVA is connected to the beam through a pair of a spring and a dashpot. By introducing a virtual ground spring, the parameters of the absorber are determined via extended fixed point theory. The proposed method only requires univariate optimization and is computationally efficient. Numerical examples conducted verify the viability of the proposed method and the effectiveness of a two-DOF DVA in suppressing double resonances.

Effects of Different Models on Natural Frequencies of Short Span Bridges Used in High Speed Rail

2015 ◽  
Author(s):  
Said I. Nour ◽  
Mohsen A. Issa
Keyword(s):  
Timoshenko Beam ◽  
High Speed ◽  
Natural Frequencies ◽  
Bernoulli Beam ◽  
High Speed Rail ◽  
Vertical Stiffness ◽  
Short Span ◽  
Elastically Supported ◽  
Euler Bernoulli Beam ◽  
Track Modulus

The natural frequencies of vibration of short span bridges used in high-speed rail were investigated. Three different models of increasing complexity were evaluated and their effects on the vibration frequency were compared to the first basic model of simply supported Euler-Bernoulli beam. In the second and third cases, the bridge was modeled as an Euler-Bernoulli and Timoshenko beam supported at its two ends by identical spring elements with an equivalent vertical stiffness to simulate elastomeric bearings and soil foundation. The boundary value problem was solved numerically to extract the bridge eigenfrequencies. In the case of Euler-Bernoulli beam, curve fitting techniques were used to deduce accurate simple empirical formulae to calculate the first six natural frequencies of an elastically supported bridge. In the case of a Timoshenko beam, graphical solutions were proposed to compute the fundamental frequency. Results confirmed that the use of Timoshenko beam theory reduces the natural frequency and the consideration of flexible supports further decreases the natural frequency. In the fourth model, the interaction of the track and the bridge was included. The bridge was modeled as an elastically supported beam and the track was modeled as a spring-damper element with an equivalent vertical stiffness resulting from track components like rail pads, cross-ties and ballast. A parametric study was performed to analyze the effects of the track stiffness on the natural frequencies of the bridge. Graphical solutions were presented to quantify the change of the normalized natural frequencies of the system with the increase in the track modulus. Results indicated that the changes in the track modulus have no significant effects in models with rigid supports. A decrease in the fundamental frequency was noticeable with softer track modulus as the support flexibility increased.

Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry

2011 ◽  
Vol 226 (5) ◽  
pp. 1254-1262 ◽  
Author(s):  
S-J Jang ◽  
J W Kim ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Geometrical Properties ◽  
Plane Vibration ◽  
Numerical Example ◽  
Mass Centre ◽  
Out Of Plane ◽  
Triangular Relationship ◽  
Elastically Supported

The geometrical properties of vibration modes of a single rigid body with one plane of symmetry are presented. When in-plane vibration modes are represented by the axes normal to the plane of symmetry, three intersecting points of those axes and the plane of symmetry constitute two triangles whose orthocentres are coincident with the mass centre and planar couple point, while the induced wrenches of three out-of-plane modes are found to form two triangles whose orthocentres are lying on the mass centre and the perpendicular translation point. Examining these triangles reveals that the triangular areas are proportional to the distributions of the mass and stiffness in the vibrating system and the shapes of the triangles are related to the natural frequencies. A numerical example is provided to verify the proposed findings.

Free Out-of-Plane Vibration of a Ring Elastically Supported at Several Points

1982 ◽  
Vol 49 (4) ◽  
pp. 854-860 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
H. Okada
Keyword(s):  
Differential Equation ◽  
Infinite Series ◽  
Natural Frequencies ◽  
Circular Ring ◽  
Mode Shapes ◽  
Matrix Differential Equation ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Matrix Differential ◽  
Elastically Supported

An analysis is presented for the free out-of-plane vibration of a circular ring elastically supported against deflection, rotation, and torsion at several points located at equal angular intervals. The equations of out-of-plane vibration of the ring is expressed as a matrix differential equation by using the transfer matrix, the solution to which is conveniently given by infinite series. The vibrations arising in the ring are classified into several types, for each of which the natural frequencies and the mode shapes are calculated numerically up to higher modes.

Numerical Investigation on Lock-In Condition and Convective Heat Transfer From an Elastically Supported Cylinder in a Cross Flow

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
F. Baratchi ◽  
M. Saghafian ◽  
B. Baratchi
Keyword(s):  
Nusselt Number ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Cross Flow ◽  
Elastic Cylinder ◽  
Overset Grids ◽  
Wide Range ◽  
Flow Induced Vibrations ◽  
Lock In ◽  
Elastically Supported

In this numerical study, flow-induced vibrations of a heated elastically supported cylinder in a laminar flow with Re = 200 and Pr = 0.7 are simulated using the moving overset grids method. This work is carried out for a wide range of natural frequencies of the cylinder, while for all cases mass ratio and reduced damping coefficient, respectively, are set to 1 and 0.01. Here we study lock-in condition and its effects on force coefficients, the amplitude of oscillations, vortex shedding pattern, and Nusselt number and simultaneously investigate the effect of in-line oscillations of the cylinder on these parameters. Results show that for this cylinder, soft lock-in occurs for a range of natural frequencies and parameters like Nusselt number, and the amplitude of oscillation reach their maximum values in this range. In addition, this study shows that in-line oscillations of the cylinder have an important effect on its dynamic and thermal behavior, and one-degree-of-freedom simulation, for an elastic cylinder, which can vibrate freely in a flow field, is only valid for cases far from soft lock-in range.

scholarly journals Optical Characterization of a Bimorph Deformable Mirror

2005 ◽  
Author(s):  
David A. Horsley ◽  
Hyunkyu Park ◽  
Chih-Wei Chuang ◽  
Sophie P. Laut ◽  
John S. Werner
Keyword(s):  
Adaptive Optics ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Laser Doppler Vibrometer ◽  
Surface Profile ◽  
Mode Shapes ◽  
Deformable Mirror ◽  
Classical Plate Theory ◽  
Elastically Supported

This paper reports the results of interferometric characterization of a bimorph deformable mirror (DM) designed for use in an adaptive optics (AO) system. The natural frequencies of this DM were measured up to 20 kHz using both a custom stroboscopic phase-shifting interferometer as well as a commercial Laser Doppler Vibrometer (LDV). Interferometric measurements of the DM surface profile were analyzed by fitting the surface with mode-shapes predicted using classical plate theory for an elastically-supported disk. The measured natural frequencies were found to be in good agreement with the predictions of the theoretical model.

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