scholarly journals Discussion: “Natural Frequencies of Continuous Beams of Uniform Span Length” (Ayre, R. S., and Jacobsen, L. S., 1950, ASME J. Appl. Mech., 17, pp. 391–395)

1951 ◽  
Vol 18 (2) ◽  
pp. 217-218
Author(s):  
L. E. Goodman ◽  
J. G. Sutherland
Keyword(s):  
Natural Frequencies ◽  
Span Length ◽  
Continuous Beams

Natural Frequencies of Continuous Beams of Uniform Span Length

1950 ◽  
Vol 17 (4) ◽  
pp. 391-395
Author(s):  
R. S. Ayre ◽  
L. S. Jacobsen
Keyword(s):  
Natural Frequencies ◽  
Flexural Vibration ◽  
Span Length ◽  
Continuous Beams

Abstract A simple graphical network is used to determine the natural frequencies of flexural vibration of continuous beams having any number of spans of uniform length. The network is based upon a relatively few calculated values.

scholarly journals Effect of intermediate supports location on natural frequencies of multiple cracked continuous beams

2018 ◽  
Author(s):  
Do Nam ◽  
Nguyen Tien Khiem ◽  
Le Khanh Toan ◽  
Nguyen Thi Thao ◽  
Pham Thi Ba Lien
Keyword(s):  
General Solution ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Continuous Beam ◽  
Cracked Beam ◽  
Continuous Beams ◽  
Simplified Method ◽  
Rigid Supports ◽  
Natural Frequency Analysis ◽  
Eigenfrequency Spectrum

The present paper deals with free vibration of multiple cracked continuous beams with intermediate rigid supports. A simplified method is proposed to obtain general solution of free vibration in cracked beam with intermediate supports that is then used for natural frequency analysis of the beam in dependence upon cracks and support locations. Numerical results show that the support location or ratio of span lengths in combination with cracks makes a significant effect on eigenfrequency spectrum of beam. The discovered effects of support locations on eigenfrequency spectrum of cracked continuous beam are useful for detecting not only cracks but also positions of vanishing deflection on the beam.

scholarly journals Dynamic tests of composite footbridge segment – experimental and numerical studies

2019 ◽  
Vol 285 ◽  
pp. 00021 ◽  
Author(s):  
Tomasz Wiczenbach ◽  
Tomasz Ferenc ◽  
Łukasz Pyrzowski ◽  
Jacek Chróścielewski
Keyword(s):  
Numerical Model ◽  
Cross Section ◽  
Natural Frequencies ◽  
Foam Core ◽  
Span Length ◽  
Dynamic Tests ◽  
Numerical Studies ◽  
Reinforced Polymer ◽  
Fibre Reinforced Polymer ◽  
Dynamic Excitations

Experimental dynamic tests and numerical simulations of a 3 meters long segment of a footbridge made of polymer composites are presented in the paper. The span-length is reduced, however dimensions of cross-section are the same as the target footbridge. The segment structure is made of sandwich panels, which consist of fibre reinforced polymer (GFRP) laminates (skins) and a PET foam (core). The first part of the paper contains description and results of experimental dynamic tests, which were subjected to the structure. The excitations during these tests was realised by a group of people standing or jumping on the structure deck. The obtained results allowed to determine natural frequencies as well as damping ratios. Moreover, cyclic loading was applied to the structure deck to check the possibility of delamination or debonding occurrence, as a result of repetitive dynamic excitations. The second part contains validation of numerical model - results of numerical analysis and its comparison with the experimental ones.

EXACT VIBRATION FREQUENCIES AND MODES OF BEAMS WITH INTERNAL RELEASES

2002 ◽  
Vol 02 (01) ◽  
pp. 63-75 ◽  
Author(s):  
M. EISENBERGER
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Beam Element ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Dynamic Stiffness Matrix ◽  
Continuous Beams ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

The exact vibration frequencies of continuous beams with internal releases are found using the dynamic stiffness method. Two types of releases are considered: hinge and sliding discontinuities. First, the exact dynamic stiffness matrix for a beam element with a release is derived and then used in the assembly of the structure dynamic stiffness matrix. The natural frequencies are found as the values of frequency that make this matrix singular. Then the mode shapes are found exactly. Examples are given for continuous beams with different releases.

Quantitative Assessment of Mass Discretization in Structural Dynamic Modeling

1986 ◽  
Vol 108 (4) ◽  
pp. 401-405 ◽  
Author(s):  
K. M. Vashi
Keyword(s):  
Degrees Of Freedom ◽  
Quantitative Assessment ◽  
Natural Frequencies ◽  
Exact Analytical Solution ◽  
Discrete Problem ◽  
Span Length ◽  
Structural Dynamic ◽  
Simply Supported ◽  
Parametric Studies ◽  
Modeling Rule

For dynamic analysis of majority of structures, a dynamic model is developed by discretizing the distributed mass and elastic properties. For assessing the adequacy of mass discretization, several procedures are used. These procedures include a comparison of analysis with test, parametric studies using finer mass discretizations, and lump mass spacing according to a frequency-controlled span length of a simply supported beam. This paper presents a quantitative assessment of mass discretization by utilizing exact analytical solution to the discrete problem of beam and bar vibrations. The assessment examines the effect of mass discretization on the accuracy of natural frequencies, modes and participation factors. In one modeling rule, the total number of dynamic degrees of freedom is taken to be twice the number of lower frequencies to be computed with a reasonable amount of accuracy. The assessment in this paper provides support for this rule.

Dynamic Responses of Two Beams Connected by a Spring-Mass Device

2012 ◽  
Vol 29 (1) ◽  
pp. 143-155 ◽  
Author(s):  
H.- P. Lin ◽  
D. Yang
Keyword(s):  
Natural Frequencies ◽  
Beam Theory ◽  
Free Vibrations ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Entire System ◽  
Bernoulli Beam ◽  
Continuous Beams ◽  
Experimental Validations ◽  
Euler Bernoulli Beam

AbstractThis paper deals with the transverse free vibrations of a system in which two beams are coupled with a spring-mass device. The dynamics of this system are coupled through the motion of the mass. The entire system is modeled as two two-span beams and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements across each spring con-nection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Some numerical results and experimental validations are presented to demonstrate the method proposed in this article.

scholarly journals Exact Dynamic Characteristic Analysis of Steel-Concrete Composite Continuous Beams

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Qikai Sun ◽  
Nan Zhang ◽  
Guobing Yan ◽  
Xinqun Zhu ◽  
Xiao Liu ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Concrete Slab ◽  
Beam Theory ◽  
Interfacial Interaction ◽  
Span Length ◽  
Characteristic Analysis ◽  
Elastic Boundary ◽  
Continuous Beams ◽  
Direct Stiffness ◽  
Lumped Masses

The free vibration characteristics of steel-concrete composite continuous beams (SCCCBs) are analyzed based on the Euler–Bernoulli beam theory. A modified dynamic direct stiffness method has been developed, which can be used to analyze the SCCCBs with some lumped masses and elastic boundary conditions. The results obtained by the proposed method are exact due to the elimination of approximated displacement and force fields in derivation. The proposed method is verified by comparing its results with those obtained by ANSYS software and laboratory tests. Then, the influencing factors on the reduction of natural frequency are analyzed and discussed in detail using the proposed method. The results show that stronger interfacial interaction results in higher values of natural frequency as well as larger steel subbeam and thinner concrete slab. The smaller the natural frequency of the SCCCBs is, the more significant effect the interfacial interaction on the natural frequency is. The reduction of natural frequency is not affected by the different numbers of spans but the equal single-span length and various ratios of the side span to the main span but equal total length, but it is influenced by the extra single-span length and different ratios of the side span to the main span but equal main span length. And it is only affected by bending stiffness. Furthermore, the reasonable ratio of the side span to the main span is 0.9∼1.0.

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