scholarly journals NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM

2009 ◽  
pp. 259-272
Author(s):  
M. Abdel-Jaber ◽  
◽  
A.A. Al-Qaisia ◽  
M.S. Abdel-Jaber ◽  
◽  
...  
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Tapered Cantilever Beam

Nondestructive Detection of a Crack in a Triangular Cantilever Beam Based on Frequency Measurement

2007 ◽  
Vol 353-358 ◽  
pp. 2285-2288
Author(s):  
Fei Wang ◽  
Xue Zeng Zhao
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Frequency Measurement ◽  
Crack Size ◽  
Force Sensors ◽  
Rotational Spring ◽  
Cantilever Deflection ◽  
Crack Location ◽  
Small Force ◽  
Point Of Intersection

Triangular cantilevers are usually used as small force sensors in the transverse direction. Analyzing the effect of a crack on transverse vibration of a triangular cantilever will be of value to users and designers of cantilever deflection force sensors. We present a method for prediction of location and size of a crack in a triangular cantilever beam based on measurement of the natural frequencies in this paper. The crack is modeled as a rotational spring. The beam is treated as two triangular beams connected by a rotational spring at the crack location. Formulae for representing the relation between natural frequencies and the crack details are presented. To detect crack details from experiment results, the plots of the crack stiffness versus its location for any three natural modes can be obtained through the relation equation, and the point of intersection of the three curves gives the crack location. The crack size is then calculated using the relation between its stiffness and size. An example to demonstrate the validity and accuracy of the method is presented.

Vibration of Triangular Cantilever Plates by the Ritz Method

1954 ◽  
Vol 21 (4) ◽  
pp. 365-370
Author(s):  
B. W. Andersen
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Plan View ◽  
Modes Of Vibration ◽  
Accuracy Of Results ◽  
Isosceles Triangles

Abstract Using the method published by Ritz in 1909, natural frequencies and corresponding node lines have been determined for two symmetric and two antisymmetric modes of vibration of isosceles triangular plates clamped at the base and having length-to-base ratios of 1, 2, 4, and 7 and for the two lowest modes of right triangular plates clamped along one leg and having ratios of the length of the free leg to that of the clamped one of 2, 4, and 7. A nonorthogonal co-ordinate system was used which gave constant limits of integration over the area of the triangle. The co-ordinate transformation made it necessary to modify the functions used by Ritz in approximating deflections and to consider cross products in the integration. The integration was done numerically, using tables compiled by Young and Felgar in 1949. To check the accuracy of results, a solution was obtained to the problem of a vibrating cantilever beam of uniform depth and triangular plan view. The results obtained were found to be consistent with those obtained for the plates by using an eight-term series to approximate the deflections of the symmetric plates (isosceles triangles) and a six-term series to approximate the deflections of the unsymmetric plates (right triangles).

scholarly journals Cantilever Beam Metastructure for Active Broadband Vibration Suppression

2020 ◽  
Author(s):  
Ratiba Fatma Ghachi ◽  
Wael Alnahhal ◽  
Osama Abdeljaber
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Vibration Suppression ◽  
Research Work ◽  
Peak Frequency ◽  
Experimental Frequency ◽  
Transmission Frequency ◽  
Vibration Attenuation ◽  
The Masses ◽  
Zigzag Structure

This paper presents a beam structure of a new metamaterial-inspired dynamic vibration attenuation system. The proposed experimental research presents a designed cantilevered zigzag structure that can have natural frequencies orders of magnitude lower than a simple cantilever of the same scale. The proposed vibration attenuation system relies on the masses places on the zigzag structure thus changing the dynamic response of the system. The zigzag plates are integrated into the host structure namely a cantilever beam with openings, forming what is referred to here as a metastructure. Experimental frequency response function results are shown comparing the response of the structure to depending on the natural frequency of the zigzag structures. Results show that the distributed inserts in the system can split the peak response of the structure into two separate peaks rendering the peak frequency a low transmission frequency. These preliminary results provide a view of the potential of research work on active-controlled structures and nonlinear insert-structure interaction for vibration attenuation.

Tunable chirping of a fibre Bragg grating using a tapered cantilever beam

1994 ◽  
Vol 30 (25) ◽  
pp. 2163-2165 ◽  
Author(s):  
M. Le Blanc ◽  
R.M. Measures ◽  
M.M. Ohn ◽  
S.Y. Huang
Keyword(s):  
Cantilever Beam ◽  
Bragg Grating ◽  
Fibre Bragg Grating ◽  
Tapered Cantilever Beam

Natural frequencies of a rotating curved cantilever beam: A perturbation method-based approach

2020 ◽  
Vol 234 (9) ◽  
pp. 1706-1719
Author(s):  
Ajinkya Baxy ◽  
Abhijit Sarkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Perturbation Method ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Analytical Formula ◽  
Industrial Applications ◽  
Curved Beam ◽  
Straight Beam ◽  
Element Method

The blades of propellers, fans, compressor and turbines can be modeled as curved beams. In general, for industrial application, finite element method is employed to determine the modal characteristics of these structures. In the present work, a novel formula for determining the natural frequencies of a rotating circularly curved cantilever beam is derived. Rayleigh–Ritz approach is used along with perturbation method to obtain the analytical formula. In the first part of the work, a formula for natural frequencies of a non-rotating curved beam vibrating in its plane of curvature is presented. This formula is derived as a correction to the natural frequencies of its straight counterpart. The curvature is treated as a perturbation parameter. In the next part of the work, the effect of rotation on the curved beam is captured as an additional perturbation. Thus, the formula for a curved rotating beam is derived as a correction (involving two perturbation parameters) to the non-rotating straight beam. The results obtained using the derived formula are compared with the finite element method results. It is found that the frequency estimates from the formula are valid over a fairly large range of curvature and rotation speed. Thus, the derived formula can provide a faster alternative for design iterations in industrial applications.

scholarly journals Effect of Dead Load on Dynamic Characteristics of Rotating Timoshenko Beams

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yan-Qi Yin ◽  
Bo Zhang ◽  
Yue-ming Li ◽  
Wei-Zhen Lu
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Experimental Result ◽  
Dead Load ◽  
Rotating Speed ◽  
Experimental Apparatus ◽  
The Dead

The dynamic characteristics of a rotating cantilever Timoshenko beam under dead load are investigated in this paper. Considering the predeformation caused by dead load and centrifugal force, governing equation of rotating cantilever Timoshenko beam is derived based on Hamilton’s principle, and the influence of the load on natural vibration is revealed. A suit of modal experimental apparatus for cantilever beam is designed and used to test the natural frequencies under the dead load, and the natural frequencies under rotation condition are calculated with a commercial finite element code. Both the experimental result and numerical result are utilized to compare with the present theoretical result, and the results obtained by present modeling method show a good agreement with those obtained from the experiment and finite element method. It is found that the natural frequencies of cantilever beam increase with both the dead load and the rotating speed.

Suppression of Parametric Resonance in Cantilever Beam With a Pendulum (Effect of Static Friction at the Supporting Point of the Pendulum)

2004 ◽  
Vol 126 (1) ◽  
pp. 149-162 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Tomohiko Murakami ◽  
Jun Kawazoe ◽  
Nobuharu Aoshima
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Parametric Resonance ◽  
Natural Frequencies ◽  
Dominant Role ◽  
Static Friction ◽  
Equation Of Motion ◽  
Pendulum Motion ◽  
Supporting Point

The dynamic response of a parametrically excited cantilever beam with a pendulum is theoretically and experimentally presented. The equation of motion and the associated boundary conditions are derived considering the static friction of the rotating motion at the supporting point (pivot) of the pendulum. It is theoretically shown that the static friction at the pivot of the pendulum plays a dominant role in the suppression of parametric resonance. The boundary conditions are different between two states in which the motion of the pendulum is either trapped by the static friction or it is not. Because of this variation of the boundary conditions depending on the pendulum motion, the natural frequencies of the system are automatically and passively changed and the bifurcation set for the parametric resonance is also shifted, so that parametric resonance does not occur. Experimental results also verify the effect of the pendulum on the suppression of parametric resonance in the cantilever beam.

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