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.

scholarly journals Free Vibration of a Perfectly Clamped-Free Beam with Stepwise Eccentric Distributed Masses

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Gilbert-Rainer Gillich ◽  
Zeno-Iosif Praisach ◽  
Magd Abdel Wahab ◽  
Nicoleta Gillich ◽  
Ion Cornel Mituletu ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Analysis Method ◽  
Bending Vibration ◽  
Mathematical Relation ◽  
Mass Participation ◽  
Mass Increase ◽  
Free Beam

A direct approach for the calculation of the natural frequencies and vibration mode shapes of a perfectly clamped-free beam with additional stepwise eccentric distributed masses is developed, along with its corresponding equations. Firstly there is contrived influence of a mass, located on a given position along the beam, upon the modal energies, via an energy analysis method. Secondly, the mass participation coefficient is defined as a function of the mass location and the bending vibration mode number. The proposed coefficient is employed to deduce the mathematical relation for the frequencies of beams with supplementary eccentric loads, generally available for any boundary conditions. The accuracy of the obtained mathematical relation was examined in comparison with the numerical simulation and experimental results for a cantilever beam. For this aim, several finite element models have been developed, individualized by the disturbance extent and the mass increase or decrease. Also, one real system was tested. The comparisons between the analytically achieved results and those obtained from experiments proved the accuracy of the developed mathematical relation.

Dynamic Analysis of Composite Plates

2005 ◽  
Author(s):  
Stefan Sorohan ◽  
Ioan Parausanu ◽  
Adrian Motomancea ◽  
Dumitru I. Caruntu
Keyword(s):  
Material Properties ◽  
Orthotropic Plate ◽  
Natural Frequencies ◽  
Composite Plates ◽  
Experimental Tests ◽  
Element Model ◽  
Mode Shapes ◽  
Rigid Rod ◽  
Sand Particles ◽  
Research Stage

The paper presents comparatively the measured and estimated natural frequencies and mode shapes of a rectangular orthotropic panel. The experimental tests were performed using a shaker. The plate was fixed in horizontal position directly on the shaker armature using a rigid rod. The experimental modes shapes were visualized using sand particles. The measured natural frequencies and also the modes shapes correspond to the whole system in motion. So, the analytic model of the plate must include the effect of the vibrator connected to the plates. The purpose of this experimental measurements and analytic modeling of such plates is to further developing a methodology to estimate the material properties of the composite panels. At this research stage, an orthotropic plate with unknown material properties was investigated. Using an adequate finite element model, the mechanical properties of the material were estimated. Using these properties it is possible to numerically estimate the dynamic behavior of the plate for additional sets of boundary conditions.

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 The Effect of Inner Reinforcing Cores on Natural Frequencies of the Lathe Tool Body

2013 ◽  
Vol 21 (Special-Issue) ◽  
pp. 186-192 ◽  
Author(s):  
Ladislav Rolník ◽  
Milan Naď
Keyword(s):  
Material Properties ◽  
Machine Tools ◽  
Structural Modification ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Structural Modifications ◽  
Modal Properties ◽  
Machine Productivity ◽  
Lathe Tool

Abstract The contribution is mainly focused on research and development of structural modification of machine tools, lathes in particular. The main aim of the modification is to change the modal properties (mode shapes, natural frequencies) of the lathe tool. The main objective of the contribution will be to formulate, mathematical analyse and evaluate the proposed methods and procedures for structural modifications of the tool, represented by beam body. A modification of modal properties by insertion of beam cores into beam body is studied in this paper. In this paper, the effect of material properties and geometrical parameters of reinforcing cores on natural frequencies of beam body is presented. The implementation will bring benefit on machine productivity, decreasing the machine tool wear and in many cases it will lead to better conditions in the cutting process.

Vibration Response of a Thin-Walled Cylindrical Pipe with Liquid

2012 ◽  
Vol 189 ◽  
pp. 345-349
Author(s):  
Yu Lan Wei ◽  
Bing Li ◽  
Li Gao ◽  
Ying Jun Dai
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Model ◽  
Vibration Modes ◽  
Timoshenko Beam Model ◽  
Cylindrical Pipe ◽  
Bending Vibration ◽  
Beam Bending ◽  
Thin Walled

Vibration characteristics of the thin-walled cylindrical pipe are affected by the liquid within the pipe. The natural frequencies and vibration modes of the pipe without liquid are analyzed by the theory of beam bending vibration and finite element model, which is based on the Timoshenko beam model. The first three natural frequencies and vibration modes of the pipe with or without liquid are acquired by experiments. As shown in the experiment results, the natural frequencies of the containing liquid pipe are lower than the natural frequencies of the pipe without liquid.

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.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

Coupled Bending-Torsion Vibration of Geared Rotors

1995 ◽  
Author(s):  
J. S. Rao ◽  
J. R. Chang ◽  
T. N. Shiau
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Mesh Stiffness ◽  
Present Program ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Torsion Vibration ◽  
Gear Mesh Stiffness

Abstract A general finite element model is presented for determining the coupled bending-torsion natural frequencies and mode shapes of geared rotors. Uncoupled bending and torsion frequencies are obtained for examples available in literature and the present program is verified against these. The effect of the gear box is considered to determine the coupled frequencies. Parameters studied include the pressure angle, gear mesh stiffness, and bearing properties. The gear pressure angle is shown to have no effect on the natural frequencies of rotors supported on isotropic bearing supports. Several case studies with bending-torsion coupling are considered and the results obtained are compared with those available in literature. The results of a general rotor system with 8lodes are also presented.

Lightweight Design of the Welded Beam of Machining Center Based on Topology Optimization

2016 ◽  
Vol 836-837 ◽  
pp. 326-332
Author(s):  
Qin Sun ◽  
Zuo Li Li ◽  
Hui Yu ◽  
Yang Liu ◽  
Jin Sheng Zhang
Keyword(s):  
Topology Optimization ◽  
Natural Frequencies ◽  
Lightweight Design ◽  
Element Model ◽  
Machining Process ◽  
Mode Shapes ◽  
Cutting Condition ◽  
Machining Center ◽  
Maximum Stiffness ◽  
Stiffness Design

From the perspective of statics, the deformation of welded beam under the action of gravity and cutting force was studied in the paper. During the actual machining process, vibration of welded beam and even the machine can be caused due to the change of cutting condition and interference from the outside. To avoid the natural frequency, and prevent the occurrence of resonance phenomena, welded beam modal was further analyzed; the first six natural frequencies and mode shapes of the beam were achieved. Statics and modal analysis are the basis of lightweight design of the welded beam based on topology optimization. The topology optimization model of maximum stiffness design and eigenvalue problem structural dynamics was established. Finite element model of beam and its components was established in hypermesh, and the optimization objective function, constraint function and boundary conditions were also set. Compared with the structure before optimization, the weight of the beam was reduced 10%, the lightweight design of the welded beam was achieved and the comprehensive performance of the beam was significantly improved.

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