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.

Suppression of Parametric Resonance of a Cantilever Beam by a Pendulum-Type Vibration Absorber

1999 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Jun Kawazoe ◽  
Nobuharu Aoshima
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Parametric Resonance ◽  
Natural Frequencies ◽  
Dominant Role ◽  
Static Friction ◽  
Equation Of Motion ◽  
Vibration Absorber ◽  
Pendulum Motion

Abstract The dynamic response of a parametically excited cantilever beam with a pendulum-type vibration absorber is presented. The equation of motion and the associated boundary conditions are derived considering the static friction for the rotating motion at the pivot of the pendulum. It is thoretically shown that the static friction plays a dominant role in the suppression of the parametric resonance. The boundary conditions are different between the cases when the motion of the pendulum is locked by the static friction and when it’s not. According to this variation of the boundary conditions depending on the pendulum motion, the natural frequencies of the system are automatically changed and the unstable regions for the parametric resonance are also shifted, so that the parametric resonace does not occur. Furthermore experimental results verify the effectiveness of the pendulum as a vibration absorber for the parametric resonance.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

Dynamic Responses of Functionally Graded Sandwich Beams Resting on Elastic Foundation Under Harmonic Moving Loads

2018 ◽  
Vol 18 (09) ◽  
pp. 1850112 ◽  
Author(s):  
Wachirawit Songsuwan ◽  
Monsak Pimsarn ◽  
Nuttawit Wattanasakulpong
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Moving Load ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Harmonic Load ◽  
Sandwich Beams

This paper investigates the free vibration and dynamic response of functionally graded sandwich beams resting on an elastic foundation under the action of a moving harmonic load. The governing equation of motion of the beam, which includes the effects of shear deformation and rotary inertia based on the Timoshenko beam theory, is derived from Lagrange’s equations. The Ritz and Newmark methods are employed to solve the equation of motion for the free and forced vibration responses of the beam with different boundary conditions. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, spring constants, etc. on natural frequencies and dynamic deflections of the beam. It was found that increasing the spring constant of the elastic foundation leads to considerable increase in natural frequencies of the beam; while the same is not true for the dynamic deflection. Additionally, very large dynamic deflection occurs for the beam in resonance under the harmonic moving load.

Piezoelectric energy harvester under parametric excitation: A theoretical and experimental investigation

2019 ◽  
Vol 31 (4) ◽  
pp. 612-631 ◽  
Author(s):  
Anshul Garg ◽  
Santosha K Dwivedy
Keyword(s):  
Experimental Investigation ◽  
Cantilever Beam ◽  
Parametric Resonance ◽  
Energy Harvester ◽  
Multiple Scales ◽  
Resonance Condition ◽  
Equation Of Motion ◽  
Attached Mass ◽  
Piezoelectric Patch ◽  
Piezoelectric Energy

In the present work, both theoretical and experimental investigation of a vertical cantilever beam–based piezoelectric energy harvester are carried out under principal parametric resonance condition. A piezoelectric patch is attached near the fixed end of the cantilever beam along with an attached mass positioned at an arbitrary location. The extended Hamilton’s principle is used to derive the spatio-temporal equation of motion, and generalized Galerkin’s approximation is used to obtain the temporal nonlinear electromechanical governing equation of motion. The method of multiple scales is used to find the reduced modulation equations. Due to large transverse deflection and effect of rotary inertia of the attached mass, the system exhibits cubic and inertial nonlinearities. An experimental setup with slider crank mechanism–based shaker and a harvester consisting of a cantilever beam with piezoelectric patch and attached mass is designed and developed. The challenges posed by parametric resonance in crack development in the PZT and in the beam are reported. The theoretical and experimental output voltage and the power obtained are found to be in good agreement. Furthermore, a qualitative and quantitative comparative study of 17 energy harvesters has been carried out, and the normalized power densities have been compared.

scholarly journals Effect of Clamping Torque on Large Deflection Static and Dynamic Response of a Cantilever Beam: An Experimental Study

2018 ◽  
Vol 15 ◽  
pp. 1-16
Author(s):  
Soumen Mondal ◽  
Sushanta Ghuku ◽  
Kashi Nath Saha
Keyword(s):  
Experimental Study ◽  
Dynamic Response ◽  
Cantilever Beam ◽  
Strain Gauge ◽  
Large Deflection ◽  
Static Load ◽  
Natural Frequencies ◽  
Dynamic Strain ◽  
Load Step ◽  
Different Thickness

The present paper reports an experimental study on the effect of finite clamping on static and dynamic characteristics of cantilever beam. The experiment is carried out with two different beams, each of which is clamped at two different locations resulting in two different geometry settings. Under each of these four settings, specimen is clamped under two different torque ratings giving rise to different finite clamping effect. Under the eight settings, coordinates of tip point under static loading are measured directly using scales and plumb at each load step; whereas, complete deflection profiles of loaded beam under each static load step are obtained through post-processing of images captured during experimentation. Such image processing is carried out manually using AutoCAD®and in-built AutoLISP®software. Strain measurements at each static load step are carried out by using strain gauge, a universal data acquisition system and the associated Catman Easy®software. To obtain loaded free vibration characteristics, loaded beam under each setting is disturbed by a rubber hammer and its dynamic response is recorded from strain gauge signal through Catman Easy®software. These dynamic strain readings of loaded beam are post-processed and FFT plots are generated in MATLAB®software and first two loaded natural frequencies of beam under each setting are obtained. Finally, effects of clamping torques on the static strain and deflection results and loaded natural frequencies for beam settings with the four different thickness to length ratios are reported in a suitable manner. The result reported may be useful as ready reference to develop a theoretical model of clamped beam like structures incorporating the effect of finite clamping.

Dynamic Behavior of Sandwich FGM Beams

2020 ◽  
Vol 22 (4) ◽  
pp. 919-930
Author(s):  
Mohamed Bouamama ◽  
Kaddour Refassi ◽  
Abbes Elmeiche ◽  
Abdelkader Megueni
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Material Properties ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Equation Of Motion ◽  
Sandwich Beams ◽  
Thickness Direction ◽  
Base Materials ◽  
Fgm Layer

AbstractThis work is consisted to investigate the vibration behavior of FGM beams under different boundary conditions with diverse volume fraction. The main objective in this paper is to study the thickness influence of the sandwich beams skin on the frequencies of the structures. The classical Euler-Bernoulli theory (CLBT) with assuming that the material properties of the FGM layer will evaluated continuously in the thickness direction according to the power law (P-FGM) is used to derived the equation of motion. The frequencies obtained are compared with the natural frequencies of a two-material and those of the base materials.

The Study of the Vibration Characteristics of the Cantilever Beam with a Surface Crack

2013 ◽  
Vol 394 ◽  
pp. 121-127
Author(s):  
Li Hua Chen ◽  
Jian Wei Duan ◽  
Yue Sun ◽  
Jing Li
Keyword(s):  
Theoretical Analysis ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Surface Crack ◽  
Natural Frequencies ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Internal Boundary ◽  
Cracked Beam

In this paper, the physical model of the cantilever beam with a surface crack is established to study the free vibration of the cracked beam from three aspects that are theoretical analysis, FEM analysis, and experiment. At the same time, the relation between the crack parameter and the vibration characteristics, which are natural frequencies and the modes of each order, is obtained through analysis. The theoretical analysis is on the basis of the mode analysis theory and applied mechanics. The crack is regarded as a flexible hinge. Utilizing the external boundary conditions and internal boundary conditions at the crack, the free vibration characteristics are obtained combining with the vibration mechanics. With the ANSYS software, a finite element model of the cracked beam is established by the beam element. During the process of calculation, it calculates the natural frequencies and the modes of cracked beam with different parameters of crack. The results obtained from the experiment are in agreement with the results obtained from the theoretical and the FEM analysis. So the accuracy of the theoretical analysis and the numerical simulation is verified by the experiment. At last, the effects of the crack location and depth on the natural frequencies and modes of each order are shown, and it could provide the theoretical, numerical and experimental basis for the identification of cracked materials and the relevant study.

Analysis of the Dynamic Response of a Cracked Beam Structure

2012 ◽  
Vol 187 ◽  
pp. 58-62 ◽  
Author(s):  
D. N. Thatoi ◽  
J. Nanda ◽  
H.C. Das ◽  
D.R. Parhi
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Cantilever Beam ◽  
Crack Detection ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Cracked Beam ◽  
Local Flexibility ◽  
Good Agreement

In this research, dynamic behaviour of a cracked cantilever beam has been analysed using finite element and experimental analysis. Deviations in mode shapes and natural frequencies have been noticed due to the presence of crack in the beam. The variation in the dynamic response is due to change in local flexibility because of the presence of crack in the beam. Finite element and experimental analyses have been carried out to find out the vibration indices of the cracked cantilever beam for validating the robustness of the theoretical model used for crack detection. The numerical results obtained through FEA are in good agreement with experimental results.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

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