scholarly journals Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 567
Author(s):  
Łukasz Żmuda-Trzebiatowski ◽  
Piotr Iwicki
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Correlation Technique ◽  
Limit Loads ◽  
Linear Buckling ◽  
Geometrical Imperfections ◽  
Linear Problems ◽  
Formed Channel ◽  
Corrugated Wall

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

scholarly journals Investigation of natural frequencies of axially loaded thin-walled columns

2018 ◽  
Vol 219 ◽  
pp. 02018
Author(s):  
Łukasz Żmuda-Trzebiatowski
Keyword(s):  
Applied Load ◽  
Natural Frequencies ◽  
Elastic Buckling ◽  
Correlation Technique ◽  
Buckling Loads ◽  
Perfectly Plastic ◽  
Linear Buckling ◽  
Thin Walled ◽  
Elastic Perfectly Plastic ◽  
Flexural Torsional Buckling

The paper deals with correlation between natural frequencies of two steel thin-walled columns and the corresponding applied load. The structures are made of cold-formed lipped channel sections. The columns lengths were assumed to follow two buckling patterns – global flexural and flexural-torsional buckling. In the thicker structure two material models were considered – linearly-elastic and elastic-perfectly plastic. Numerical computations cover dynamic eigenvalue problem, linear buckling and geometrically (and materially) non-linear analysis. The correlation between squares of natural frequencies and the applied load is linear in both columns. The first natural frequencies drop to zero due to structural buckling. This method, called the Vibration Correlation Technique, allows to predict buckling loads on the basis of measured vibration frequencies of the structures. Plasticity does not affect the corresponding curves – the use of the presented technique is limited to the structures exhibiting elastic buckling behaviour.

Vibrations of Twisted Cantilevered Plates—Experimental Investigation

1985 ◽  
Vol 107 (1) ◽  
pp. 187-196 ◽  
Author(s):  
J. C. MacBain ◽  
R. E. Kielb ◽  
A. W. Leissa
Keyword(s):  
Research Study ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Turbine Engine ◽  
Aspect Ratios ◽  
Engine Blade ◽  
Vibrational Characteristics ◽  
Cantilevered Plates ◽  
Effect Of Support

The experimental portion of a joint government/industry/university research study on the vibrational characteristics of twisted cantilevered plates is presented. The overall purpose of the research study was to assess the capabilities and limitations of existing analytical methods in predicting the vibratory characteristics of twisted plates. Thirty cantilevered plates were precision machined at the Air Force’s Aero Propulsion Laboratory. These plates, having five different degrees of twist, two thicknesses, and three aspect ratios representative of turbine engine blade geometries, were tested for their vibration mode shapes and frequencies. The resulting nondimensional frequencies and selected mode shapes are presented as a function of plate tip twist. The trends of the plate natural frequencies as a function of the governing geometric parameters are discussed. The effect of support compliance on the plate natural frequency and its impact on numerically modeling twisted plates is also presented.

Vibration and Modal Analysis of Induction Motor

2012 ◽  
Vol 226-228 ◽  
pp. 92-97 ◽  
Author(s):  
Rui Li ◽  
Qi Fen Jia ◽  
Shun Zhong
Keyword(s):  
Induction Motor ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Acoustic Noise ◽  
Mode Shapes ◽  
Electrical Machine ◽  
3D Finite Element ◽  
Motor Mode ◽  
Element Technique ◽  
Motor Vibration

Calculation of the induction motor machine modal frequencies of an electrical machine accurately is the base of reducing acoustic noise and vibration. This paper presents a detailed research on the induction motor mode shapes and natural frequencies of induction motor by using 3D finite element technique, based on simplified modal, The influence of and mounting feet and rotor on mode shapes and natural frequencies are investigated systematically. Mounting feet and rotor have a great effect on natural frequencies, the mounting feet and rotor will result in the number of the motor low-vibration mode increases\the frequencies rise obviously, the mounting feet result in motor vibration mode becomes more complicated, rotor modals become an important part of motor mode shapes, the number of the motor low-vibration mode increases. Predictions are validated against experimental results.

In vivo structural dynamic analysis of the dragonfly wing: the effect of stigma as its modulator

2019 ◽  
Vol 377 (2150) ◽  
pp. 20190132 ◽  
Author(s):  
Amit Kumar ◽  
Navin Kumar ◽  
Rakesh Das ◽  
Piyush Lakhani ◽  
Bharat Bhushan
Keyword(s):  
Drag Coefficient ◽  
Natural Frequencies ◽  
Leading Edge ◽  
Micro Air Vehicles ◽  
Active Role ◽  
Image Correlation ◽  
Mode Shapes ◽  
Correlation Technique ◽  
Structural Dynamic

The flapping of the dragonfly forewing under in vivo condition has been analysed by image correlation technique to get an insight of its structural dynamics. The modal parameters such as flapping frequency, natural frequencies, mode shapes and modal strain have been obtained that will facilitate the biomimetic design of wings for micro air vehicles. The stigma, which is a pigmented spot at the leading edge of the wing near the tip having heavier mass, takes an active role in the real-time flapping by shaping its trajectory as eight-shaped, which enhances the drag coefficient and stroke efficiency. The extra mass on it and its removal transformed the trajectory into two different elliptical and oval shapes, respectively, which reduced the drag coefficient and stroke efficiency of the flapping wing by altering the flapping kinematics. This article is part of the theme issue ‘Bioinspired materials and surfaces for green science and technology (part 2)’.

Explicit Vibration Solutions of a Cable Under Complicated Loads

1997 ◽  
Vol 64 (4) ◽  
pp. 957-964 ◽  
Author(s):  
P. Yu
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Free Vibration Analysis ◽  
Dynamical Analysis ◽  
Mode Shapes ◽  
Concentrated Loads ◽  
Closed Form Solutions ◽  
Independent Mode ◽  
Complex Arrangement

This paper is concerned with the dynamical analysis of a sagged cable having small equilibrium curvature and horizontal supports under both distributed and concentrated loads. The loads are applied in vertical as well as horizontal directions. Based on a free vibration analysis, a transfer matrix method is generalized for solving coupled, nonhomogeneous differential equations to obtain closed-form solutions for the natural frequencies and the associated vibration mode shapes in vertical, horizontal, and longitudinal directions. It is shown that two sets of independent mode shapes associated with two sets of independent frequencies always exist and can be obtained via an equation of one variable only. This method demonstrates its advantages in dealing with interactions of modes in different directions, complex arrangement of concentrated loads, and high-order modes oscillations.

Investigations of Natural Frequencies and Vibration Mode Shapes for a Post-Buckled Beam With Different Attached Masses

2010 ◽  
Author(s):  
Pascaline Cette ◽  
Adam J. Sneller ◽  
Brian P. Mann
Keyword(s):  
Axial Load ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Chaotic Behavior ◽  
Nonlinear Behavior ◽  
Mode Shapes ◽  
Large Displacements ◽  
Central Mass ◽  
Buckled Beam ◽  
Beam Motion

This paper considers the theoretical response of a base-excited post-buckled beam. A mass that can be varied was attached to the midspan of the clamped-clamped beam. The theoretical model for the post-buckled beam was first investigated by applying the extended Hamilton principle to obtain a partial differential equation for beam motion carrying a central mass. This equation was used to analyze the behavior of the pre- and post-buckled natural frequencies in terms of the axial load. The first three buckled configurations were then examined, and plots showing the pre- and post-buckled modal frequencies were constructed. It was found that the addition of a central mass to the beam significantly lowered its first natural frequency, while the second frequency was relatively unaffected. A set of experiments were performed and it was shown that adding a mass on the beam increased the occurrence of snap through behavior. This nonlinear behavior produced large displacements and chaotic behavior.

Buckling and Free Vibration of Nonuniformly Heated Functionally Graded Carbon Nanotube Reinforced Polymer Composite Plate

2017 ◽  
Vol 17 (06) ◽  
pp. 1750064 ◽  
Author(s):  
Nivish George ◽  
P. Jeyaraj ◽  
S. M. Murigendrappa
Keyword(s):  
Temperature Field ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Plate ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Mode Shapes ◽  
Reinforced Polymer

Buckling and free vibration behavior of functionally graded carbon nanotube reinforced polymer composite plate subjected to nonuniform temperature fields have been investigated using finite element approach. The effective material constants of the plate are obtained using the extended rule of mixture along with efficiency parameters of the carbon nanotube (to include geometry-dependent material properties). Influence of boundary conditions, aspect ratio, functional grading of the carbon nanotube, nonuniform thermal loading on thermal buckling and free vibration behavior of the heated plate are analyzed. It is observed that temperature fields and functional grading are influenced on the critical buckling temperature of the plates. Further, nature of functional grading showed significant change in buckling mode shapes irrespective of the boundary conditions. The first few natural frequencies of the plate under thermal load decreases as the temperature increases and they are influenced significantly by the nature of temperature field. Variations in free vibration mode shapes of the square plates found with not significant change as temperature increases. However, free vibration modes of the rectangular plates are sensitive to the nature of temperature field whenever there is a free edge associated with the boundary condition. Influence of functional grading on the free vibration mode shapes is not significant in contrast with the free vibration natural frequencies. The magnitude of free vibration natural frequencies of functional grade-X type carbon nanotube reinforcement showed higher in comparison with other two types of reinforcements considered here.

scholarly journals Vibrations of Complete Spherical Shells With Imperfections

2007 ◽  
Vol 129 (3) ◽  
pp. 363-370 ◽  
Author(s):  
Thomas A. Duffey ◽  
Jason E. Pepin ◽  
Amy N. Robertson ◽  
Michael L. Steinzig ◽  
Kimberly Coleman
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Spherical Shells ◽  
The Past ◽  
Dynamic Holography ◽  
Theoretical Investigations ◽  
Modes Of Vibration ◽  
Geometrical Imperfections ◽  
Theoretical Results

Numerous theoretical investigations on the natural frequencies for complete spherical shells have been reported over the past four decades. However, attempts at correlating the theoretical results with either experimental or simulated results (both for axisymmetric and nonaxisymmetric modes of vibration) are almost completely lacking. In this paper, natural frequencies and mode shapes obtained from axisymmetric and nonaxisymmetric theories of vibration of complete spherical shells and from finite element computer simulations of the vibrations, with and without geometrical imperfections, are presented. Modal tests reported elsewhere on commercially available, thin spherical marine floats (with imperfections) are then utilized as a basis for comparison of frequencies to both the theoretical and numerical results. Because of the imperfections present, “splitting” of frequencies of nonaxisymmetric modes is anticipated. The presence of this frequency splitting phenomenon is demonstrated. In addition, results of a “whole field” measurement on one of the imperfect shells using dynamic holography are presented.

scholarly journals Structural Dynamics of Real and Modeled Solanum Stamens: Implications for Pollen Ejection by Buzzing Bees

2021 ◽  
Author(s):  
Mark Jankauski ◽  
Riggs Ferguson ◽  
Avery L Russell ◽  
Stephen Buchmann
Keyword(s):  
Material Properties ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Element Model ◽  
Flowering Plant ◽  
Mode Shapes ◽  
Bending Vibration ◽  
Solanum Elaeagnifolium ◽  
Flowering Plant Species ◽  
Poricidal Anthers

An estimated 10% of flowering plant species conceal their pollen within tube-like anthers that dehisce through small apical pores (poricidal anthers). Bees extract pollen from poricidal anthers through a complex motor routine called floral buzzing, whereby the bee applies large vibratory forces to the flower stamen by rapidly contracting its flight muscles. The resulting deformation and pollen expulsion depend critically on the stamen's natural frequencies and vibration mode shapes, yet these properties remain unknown. We performed experimental modal analysis on Solanum elaeagnifolium stamens to quantify their natural frequencies and vibration modes. Based on morphometric and dynamic measurements, we developed a finite element model of the stamen to identify how variable material properties, geometry and bee weight could affect its dynamics. In general, stamen natural frequencies fell outside the reported floral buzzing range, and variations in stamen geometry and material properties were unlikely to bring natural frequencies within this range. However, inclusion of bee mass reduced natural frequencies to within the floral buzzing frequency range and gave rise to an axial-bending vibration mode. We hypothesize that floral buzzing bees exploit the large vibration amplification factor of this mode to increase anther deformation, which may facilitate pollen ejection.

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