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.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

Vibration Analysis of a Stepped Beam by Using Adomian Decomposition Method

2012 ◽  
Vol 160 ◽  
pp. 292-296
Author(s):  
Qi Bo Mao ◽  
Yan Ping Nie ◽  
Wei Zhang
Keyword(s):  
Decomposition Method ◽  
Natural Frequencies ◽  
Adomian Decomposition Method ◽  
Free Vibrations ◽  
Continuity Condition ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Stepped Beam ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam

The free vibrations of a stepped Euler-Bernoulli beam are investigated by using the Adomian decomposition method (ADM). The stepped beam consists two uniform sections and each section is considered a substructure which can be modeled using ADM. By using boundary condition and continuity condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions are presented. Comparing the results using ADM to those given in the literature, excellent agreement is achieved.

scholarly journals Transverse Vibration of Clamped-Pinned-Free Beam with Mass at Free End

2019 ◽  
Vol 9 (15) ◽  
pp. 2996 ◽  
Author(s):  
Jonathan Hong ◽  
Jacob Dodson ◽  
Simon Laflamme ◽  
Austin Downey
Keyword(s):  
Transverse Vibration ◽  
Theoretical Calculations ◽  
Beam Theory ◽  
High Rate ◽  
Harsh Environments ◽  
Mode Shapes ◽  
Engineering Systems ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam ◽  
Free Beam

Engineering systems undergoing extreme and harsh environments can often times experience rapid damaging effects. In order to minimize loss of economic investment and human lives, structural health monitoring (SHM) of these high-rate systems is being researched. An experimental testbed has been developed to validate SHM methods in a controllable and repeatable laboratory environment. This study applies the Euler-Bernoulli beam theory to this testbed to develop analytical solutions of the system. The transverse vibration of a clamped-pinned-free beam with a point mass at the free end is discussed in detail. Results are derived for varying pin locations and mass values. Eigenvalue plots of the first five modes are presented along with their respective mode shapes. The theoretical calculations are experimentally validated and discussed.

scholarly journals Natural Frequencies and Mode Shapes of Statically Deformed Inclined Risers

2016 ◽  
Author(s):  
Feras K. Alfosail ◽  
Ali H. Nayfeh ◽  
Mohammad I. Younis
Keyword(s):  
Natural Frequencies ◽  
Equilibrium Configuration ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Galerkin Approach ◽  
Inclination Angles ◽  
Linear Vibrations ◽  
Euler Bernoulli Beam ◽  
Beam Mode ◽  
Good Agreement

In this work, we investigate numerically the linear vibrations of inclined risers using the Galerkin approach. The riser is modeled as an Euler-Bernoulli beam accounting for the nonlinear mid-plane stretching and self-weight. After solving for the initial deflection of the riser due to self-weight, a Galerkin expansion of fifteen axially loaded beam mode shapes are used to solve the eigenvalue problem of the riser around the static equilibrium configuration. This yields the riser natural frequencies and exact mode shapes for various values of inclination angles and applied tension. The obtained results are validated against a boundary-layer analytical solution and are found in good agreement. This constructs a basis to study the nonlinear forced vibrations of inclined risers.

scholarly journals Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

2011 ◽  
Vol 18 (5) ◽  
pp. 709-726 ◽  
Author(s):  
Yusuf Yesilce
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural Elements ◽  
Mass System ◽  
Assembly Technique

The structural elements supporting motors or engines are frequently seen in technological applications. The operation of machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. This paper aims at determining the exact solutions for the natural frequencies and mode shapes of Reddy-Bickford beams. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using Reddy-Bickford Beam Theory (RBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Reddy-Bickford single-span and multi-span beams calculated by using the numerical assembly technique and the secant method are compared with the natural frequencies of single-span and multi-span beams calculated by using Timoshenko Beam Theory (TBT); the mode shapes are presented in graphs.

Free Vibrations of Beams with Arbitrary Boundary Conditions Based on Wave Propagation Method

2011 ◽  
Vol 66-68 ◽  
pp. 753-757
Author(s):  
Wan You Li ◽  
Hai Jun Zhou ◽  
Jun Dai ◽  
Bing Lin Lv ◽  
Dong Hua Wang ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Beam Theory ◽  
Free Vibrations ◽  
Bernoulli Beam ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Wave Propagation Method ◽  
Wave Numbers ◽  
Euler Bernoulli Beam

Under the Euler-Bernoulli beam theory, the wave propagation method is used for the vibration analysis of beams with arbitrary boundary conditions. The boundary conditions end the beam could be arbitrary that all the conventional homogeneous beam boundary conditions can be included by setting the stiffnesses of the springs be infinity or zero. In this paper, the flexural displacement of the beam is expressed in the wave propagation form including wave numbers. The wavenumber could be obtained in a known form for conventional boundary conditions. So the results are obtained through the boundary conditions and the known wavenumbers and compared with the numerical results. In order to validate the correctness, results with different stiffness are compared with those obtained by previous published papers.

scholarly journals The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

Dynamic Responses of Beams with a Flexible Support Under a Constant Speed Moving Load

2008 ◽  
Vol 24 (2) ◽  
pp. 195-204 ◽  
Author(s):  
H.-P. Lin
Keyword(s):  
Moving Load ◽  
Beam Theory ◽  
Constant Speed ◽  
Dynamic Responses ◽  
Entire System ◽  
Modal Expansion ◽  
Flexible Support ◽  
Expansion Theory ◽  
Forced Responses ◽  
Euler Bernoulli Beam

ABSTRACTThis paper deals with the linear dynamic responses of beams with a flexible support under a moving load with a constant speed. The entire system is modeled as a two-span beam and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements on the flexible constraint, the relationships between two segments can be obtained. By using a transfer matrix method, the characteristic equation of the entire system can then be determined. The forced responses of the system under a moving load can then be obtained through modal expansion theory. Some numerical results are presented to the effects of support stiffness and the different speeds of the moving load.

scholarly journals Free Vibration of a Carbon Nanotube-Based Mass Sensor

2011 ◽  
Vol 403-408 ◽  
pp. 1163-1167 ◽  
Author(s):  
Payam Soltani ◽  
Omid Pashaei ◽  
Mohammad Mehdi Taherian ◽  
Anoushiravan Farshidianfar
Keyword(s):  
Boundary Condition ◽  
Carbon Nanotube ◽  
Natural Frequencies ◽  
Dynamical Behavior ◽  
Beam Theory ◽  
Added Mass ◽  
Mass Sensor ◽  
Bernoulli Beam ◽  
Single Walled Carbon Nanotube ◽  
Euler Bernoulli Beam

In this paper, nonlocal Euler-Bernoulli beam theory is applied to investigate the dynamical behavior of a single-walled carbon nanotube (SWCNT) with an extra added nanoparticle. The SWCNT is assumed to be embedded on a Winkler-type elastic foundation with cantilever boundary condition. This configuration can be used as a nano-mass sensor which works on the basis of the changing the natural frequencies. The results show that the added mass causes an obvious increase in sensitivity of SWCNT-based nano-mass sensor, especially for stiff mediums, small nonlocal parameters, and stocky SWCNTs.

Calculation of the natural frequencies and mode shapes of a Euler–Bernoulli beam which has any combination of linear boundary conditions

2019 ◽  
Vol 25 (18) ◽  
pp. 2473-2479 ◽  
Author(s):  
Paulo J. Paupitz Gonçalves ◽  
Michael J. Brennan ◽  
Andrew Peplow ◽  
Bin Tang
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
New Method ◽  
Mode Shapes ◽  
Linear Boundary ◽  
Bernoulli Beam ◽  
Classical Boundary ◽  
Euler Bernoulli Beam

There are well-known expressions for natural frequencies and mode shapes of a Euler-Bernoulli beam which has classical boundary conditions, such as free, fixed, and pinned. There are also expressions for particular boundary conditions, such as attached springs and masses. Surprisingly, however, there is not a method to calculate the natural frequencies and mode shapes for a Euler–Bernoulli beam which has any combination of linear boundary conditions. This paper describes a new method to achieve this, by writing the boundary conditions in terms of dynamic stiffness of attached elements. The method is valid for any boundaries provided they are linear, including dissipative boundaries. Ways to overcome numerical issues that can occur when computing higher natural frequencies and mode shapes are also discussed. Some examples are given to illustrate the applicability of the proposed method.

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