scholarly journals Flexural Vibration Test of a Beam Elastically Restrained at One End: A New Approach for Young’s Modulus Determination

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Rafael M. Digilov ◽  
Haim Abramovich
Keyword(s):  
Young Modulus ◽  
Flexural Vibration ◽  
Force Sensor ◽  
Frequency Equation ◽  
Bending Vibrations ◽  
Flexural Vibration Test ◽  
Elastically Restrained ◽  
Fixed End ◽  
Partially Restrained

A new vibration beam technique for the fast determination of the dynamic Young modulus is developed. The method is based on measuring the resonant frequency of flexural vibrations of a partially restrained rectangular beam. The strip-shaped specimen fixed at one end to a force sensor and free at the other forms the Euler Bernoulli cantilever beam with linear and torsion spring on the fixed end. The beam is subjected to free bending vibrations by simply releasing it from a flexural position and its dynamic response detected by the force sensor is processed by FFT analysis. Identified natural frequencies are initially used in the frequency equation to find the corresponding modal numbers and then to calculate the Young modulus. The validity of the procedure was tested on a number of industrial materials by comparing the measured modulus with known values from the literature and good agreement was found.

The impact of root flexibility on the fundamental frequency of a restrained cantilever beam

2017 ◽  
Vol 45 (2) ◽  
pp. 184-193 ◽  
Author(s):  
Rafael M Digilov ◽  
Haim Abramovich
Keyword(s):  
Fundamental Frequency ◽  
Cantilever Beam ◽  
Experimental Studies ◽  
Force Sensor ◽  
Modal Number ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
Strip Shape ◽  
Elastically Restrained ◽  
The Impact

This study presents the theoretical and experimental studies of the impact of root flexibility on the fundamental frequency of the free bending vibration of a uniform Euler–Bernoulli cantilever beam elastically restrained at the root. The dispersion relation between the natural frequency and modal number has been derived and solved numerically and approximately using the series method of the expansion in terms of the modal number. It is shown that the approximate solution is reduced to the empirical Dunkerley rule, which is sound not universally true. A commercial force sensor is used for the experimental detection of the effect of root flexibility on the fundamental frequency of bending vibrations of a cantilevered beam. The strip-shape specimen attached to the force sensor forms a cantilever beam restrained at the root against rotation and translation and it fundamental frequency is identified. The results of measurements for a series of industrial materials are compared with exact calculations and those predicted by Dunkerley’s formula and an excellent agreement is observed.

Comparison of the viscoelastic penetration and tensile behaviour of poly(methyl acrylate) and poly(ethyl acrylate)

1979 ◽  
Vol 44 (6) ◽  
pp. 1942-1948 ◽  
Author(s):  
Jaroslav Hrouz ◽  
Michal Ilavský ◽  
Ivan Havlíček ◽  
Karel Dušek
Keyword(s):  
Methyl Acrylate ◽  
Poisson Ratio ◽  
Young Modulus ◽  
Ethyl Acrylate ◽  
Sample Volume ◽  
Viscoelastic Behaviour ◽  
Tensile Behaviour ◽  
Temperature Superposition ◽  
Main Transition

The viscoelastic penetration and tensile behaviour of poly(methyl acrylate) and poly(ethyl acrylate) in the main transition region have been investigated. It was found that the time-temperature superposition could be carried out in the case of the penetration viscoelastic behaviour; the temperature dependence of the penetration and tensile shift factors was the same. The superimposed curves of the penetration and Young modulus allowed us to calculate the dependence of the Poisson ratio and thus to characterize the change in sample volume with deformation. It was demonstrated that the penetration method of determination of the viscoelastic behaviour is equivalent to the tensile method.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

Comparison of results obtained by static 3- and 4-point bending and flexural vibration tests on solid wood, MDF, and 5-plywood

Holzforschung ◽  
2013 ◽  
Vol 67 (8) ◽  
pp. 941-948 ◽  
Author(s):  
Hiroshi Yoshihara
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Medium Density Fiberboard ◽  
Flexural Vibration ◽  
Solid Wood ◽  
Bending Tests ◽  
Four Point Bending ◽  
Flexural Vibration Test ◽  
The Difference ◽  
Vibration Tests

Abstract The flexural Young’s modulus of western hemlock, medium-density fiberboard, and 5-plywood (made of lauan) has been determined by conducting three- and four-point bending tests with various span lengths and by flexural vibration test. The Young’s modulus was significantly influenced by the deflection measurement method. In particular, the Young’s modulus was not reliable based on the difference between the deflections at two specific points in the specimen, although this test is standardized according to ISO 3349-1975 and JIS Z2101-2009.

Young’s and shear moduli of glued laminated timber composed of different species obtained by a flexural vibration test

Holzforschung ◽  
2012 ◽  
Vol 66 (7) ◽  
pp. 871-875 ◽  
Author(s):  
Yoshitaka Kubojima ◽  
Mario Tonosaki
Keyword(s):  
Elastic Constants ◽  
Pinus Densiflora ◽  
Flexural Vibration ◽  
Japanese Cedar ◽  
Picea Sitchensis ◽  
Vibration Test ◽  
Shear Moduli ◽  
Glued Laminated Timber ◽  
Flexural Vibration Test ◽  
Lamination Theory

Abstract The applicability of the flexural vibration test to determine the elastic constants of glued laminated timber (GLT) composed of five wood species (ash, Fraxinus spaethiana Lingelsh.; balsa, Ochroma pyramidale Urban.; Japanese cedar, Cryptomeria japonica D. Don; Japanese red pine, Pinus densiflora Sieb. et Zucc.; Sitka spruce, Picea sitchensis Carr.) has been investigated. GLT models were prepared from four laminae with dimensions of 30 (R)×5 (T)×300 (L) mm3. The suitability of Japanese cedar for inner layers in GLTs was tested by flexural vibration test to determine the elastic constants of the laminae and the glued laminated timber. The Young’s and shear moduli were calculated by the Goens-Hearmon regression method based on the Timoshenko theory of bending (TGH method), and the results were compared with the estimated values based on the Young’s and shear moduli measured individually of each lamina. The simple lamination theory was found to be applicable for Young’s modulus but not to shear modulus. The result obtained based on the lamination theory from the shear strain energy was similar to that obtained by the TGH method.

Free Vibration of a Circular Cylindrical Shell Elastically Restrained by Axially Spaced Springs

1983 ◽  
Vol 50 (3) ◽  
pp. 544-548 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Muramoto
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Circular Cylindrical Shell ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Governing Equations ◽  
Structure Matrix ◽  
The Matrix ◽  
Circular Cylindrical Shells ◽  
Elastically Restrained

An analysis is presented for the free vibration of a circular cylindrical shell restrained by axially spaced elastic springs. The governing equations of vibration of a circular cylindrical shell are written as a coupled set of first-order differential equations by using the transfer matrix of the shell. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrices and the point matrices at the springs, and the frequency equation is derived with terms of the elements of the structure matrix under the boundary conditions. The method is applied to circular cylindrical shells supported by axially equispaced springs of the same stiffness, and the natural frequencies and the mode shapes of vibration are calculated numerically.

Flatwise Young’s modulus and flatwise shear modulus of plywood measured by flexural vibration test

Holzforschung ◽  
2013 ◽  
Vol 67 (6) ◽  
pp. 683-690 ◽  
Author(s):  
Hiroshi Yoshihara
Keyword(s):  
Finite Element Analysis ◽  
Shear Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Flexural Vibration ◽  
Vibration Test ◽  
Specimen Length ◽  
Element Analysis ◽  
Flexural Vibration Test ◽  
Vibration Tests

Abstract The flatwise Young’s modulus and the flatwise shear modulus of 3-, 5-, and 7-ply plywoods made of Lauan (Shorea sp.) veneers have been determined by conducting flexural vibration tests with various specimen lengths and by finite element analysis. The results indicate that the flatwise Young’s modulus decreases with decreasing specimen length, whereas the opposite is true for the flatwise shear modulus.

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