On the frequency equation of a combined system consisting of a simply supported beam and in-span helical spring–mass with mass of the helical spring considered

2006 ◽  
Vol 295 (1-2) ◽  
pp. 436-449 ◽  
Author(s):  
M. Gürgöze ◽  
O. Çakar ◽  
S. Zeren
Keyword(s):  
Frequency Equation ◽  
Helical Spring ◽  
Combined System ◽  
Simply Supported Beam ◽  
Simply Supported

Exact Frequency Equation of a Linear Structure Carrying Lumped Elements Using the Assumed Modes Method

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Philip D. Cha ◽  
Siyi Hu
Keyword(s):  
Linear Structure ◽  
Frequency Equation ◽  
Governing Equations ◽  
Linear Structures ◽  
Combined System ◽  
Digamma Function ◽  
Simply Supported ◽  
Lumped Elements ◽  
Finite Sum ◽  
Infinite Sum

Combined systems consisting of linear structures carrying lumped attachments have received considerable attention over the years. In this paper, the assumed modes method is first used to formulate the governing equations of the combined system, and the corresponding generalized eigenvalue problem is then manipulated into a frequency equation. As the number of modes used in the assumed modes method increases, the approximate eigenvalues converge to the exact solutions. Interestingly, under certain conditions, as the number of component modes goes to infinity, the infinite sum term in the frequency equation can be reduced to a finite sum using digamma function. The conditions that must be met in order to reduce an infinite sum to a finite sum are specified, and the closed-form expressions for the infinite sum are derived for certain linear structures. Knowing these expressions allows one to easily formulate the exact frequency equations of various combined systems, including a uniform fixed–fixed or fixed-free rod carrying lumped translational elements, a simply supported beam carrying any combination of lumped translational and torsional attachments, or a cantilever beam carrying lumped translational and/or torsional elements at the beam's tip. The scheme developed in this paper is easy to implement and simple to code. More importantly, numerical experiments show that the eigenvalues obtained using the proposed method match those found by solving a boundary value problem.

Dimensionless wave numbers evolution of a three spans simply supported beam when the intermediate supports are moving along the whole beam

2021 ◽  
Vol 66 (1) ◽  
pp. 17-24
Author(s):  
Zeno-Iosif Praisach ◽  
Dorel Ardeljan ◽  
Constantin-Viorel Pașcu
Keyword(s):  
Vibration Mode ◽  
Frequency Equation ◽  
Wave Number ◽  
Continuous Beam ◽  
Dimensionless Wave Number ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Continuous Beams ◽  
Maximum Value ◽  
Wave Numbers

Continuous beams simply supported with several intermediate supports are very common in engineering achievements everywhere. The paper shows the evolution of the dimensionless wave number in 3D format, respectively of the eigenfrequencies for a continuous beam with three openings when the intermediate supports take any position inside the beam. The frequency equation for calculating the dimensionless wave number is presented and the modal function is given with an example for the case where the eigenfrequency has the maximum value at fist vibration mode.

scholarly journals Study on the improvement of the torsional bracing system designing process for steel shaped I simply supported beam bridge

2021 ◽  
Vol 682 (1) ◽  
pp. 012045
Author(s):  
K V Nguyen ◽  
C A L Huynh ◽  
H D H Nguyen ◽  
N D Van ◽  
N T Nguyen ◽  
...  
Keyword(s):  
Simply Supported Beam ◽  
Simply Supported ◽  
Bracing System ◽  
Beam Bridge

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.

Experimental Study on the Dynamic Deformation of Simply Supported Beam in Chinese High-speed Railway

2018 ◽  
Author(s):  
Gonglian Dai ◽  
Meng Wang ◽  
Tianliang Zhao ◽  
Wenshuo Liu
Keyword(s):  
High Speed ◽  
Structure Design ◽  
Dynamic Coefficient ◽  
Bridge Structure ◽  
High Speed Railway ◽  
Simply Supported Beam ◽  
Vertical Stiffness ◽  
Simply Supported ◽  
Speed Up ◽  
Design Speed

<p>At present, Chinese high-speed railway operating mileage has exceeded 20 thousand km, and the proportion of the bridge is nearly 50%. Moreover, high-speed railway design speed is constantly improving. Therefore, controlling the deformation of the bridge structure strictly is particularly important to train speed-up as well as to ensure the smoothness of the line. This paper, based on the field test, shows the vertical and transverse absolute displacements of bridge structure by field collection. What’s more, resonance speed and dynamic coefficient of bridge were studied. The results show that: the horizontal and vertical stiffness of the bridge can meet the requirements of <b>Chinese “high-speed railway design specification” (HRDS)</b>, and the structure design can be optimized. However, the dynamic coefficient may be greater than the specification suggested value. And the simply supported beam with CRTSII ballastless track has second-order vertical resonance velocity 306km/h and third-order transverse resonance velocity 312km/h by test results, which are all coincide with the theoretical resonance velocity.</p>

Large Deflections of a Simply Supported Beam Subjected to Moment at One End

1984 ◽  
Vol 51 (3) ◽  
pp. 519-525 ◽  
Author(s):  
P. Seide
Keyword(s):  
Linear Theory ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Large Deflections ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastica Theory ◽  
Angle Of Rotation

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

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