An Analytical Model for a Clamped Isotropic Beam Under Thermal Effects

2002 ◽  
Author(s):  
Rodrigo F. A. Marques ◽  
Daniel J. Inman
Keyword(s):  
Boundary Conditions ◽  
Analytical Model ◽  
Thermal Effects ◽  
Natural Frequencies ◽  
Dynamical Behavior ◽  
Beam Theory ◽  
Optimization Procedure ◽  
Temperature Changes ◽  
Thermally Expand ◽  
Spring Constants

Structures and industrial equipment often operate in environments where temperature variations take place. Although thermal effects may be negligible in some cases, they have caused the unexpected failure of mechanical systems many times. Whether or not temperature has significant effects on the dynamical behavior of such machines and structures depends upon several aspects, amongst which are geometry, material properties and boundary conditions. In this paper we investigate the dynamical behavior of a clamped beam under the influence of a uniform, quasi-statically varying temperature field. An analytical model was used, based on Euler-Bernoulli’s beam theory with the introduction of the proper boundary conditions. Temperature effects are included in terms of an axial force that shows up when the beam tends to thermally expand, but this expansion is restrained by the clamping. Preliminary results do not agree with experimental data, since perfect clamping is difficult to achieve in practice. Finally the model is updated with the inclusion of axial and torsional springs connecting the beam to the support. The spring constants were calculated through optimization procedure to minimize the differences between the natural frequencies obtained from the analytical model and the corresponding experimental ones. Agreement with experimental results is reasonable up to the 4th mode of the beam. In the future, this analytical model is to be used for design and simulation of an active controller that accounts for temperature changes in the structure.

scholarly journals Dynamic Characteristics of an Elastic Structure with Thermal Effects

2020 ◽  
Vol 25 (2) ◽  
pp. 200-208
Author(s):  
Guanhua Xu ◽  
Jianzhong Fu ◽  
Wen He ◽  
Yuetong Xu ◽  
Zhiwei Lin ◽  
...  
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Thermal Effects ◽  
Natural Frequencies ◽  
Elastic Structure ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Environmental Testing ◽  
Temperature Changes ◽  
Property Changes

The vibration table in a combination environmental testing device suffers from temperature changes, which cause the dynamic characteristics of the vibration structure to vary. The mechanism of the thermal effect on the dynamic characteristics of an elastic structure is presented, and a modal analysis with thermal effects based on the finite-element method (FEM) is carried out. The results show that the natural frequencies for each order decrease as the temperature increases, while the mode shapes of the vibrator do not change with temperature. Although thermal stress may affect natural frequencies due to the additional initial stress element stiffness, this stress can be neglected in the modal analysis because it is negligible relative to the effect of the material property changes with temperature.

scholarly journals Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Wensheng Xiao ◽  
Haozhi Qin ◽  
Jian Liu ◽  
Qi Liu ◽  
Junguo Cui ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Drill Pipe ◽  
Beam Theory ◽  
Transformation Method ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Order Partial Differential Equation ◽  
Lumped Mass ◽  
Acceleration Sensors

In this study, experimental and numerical investigations on the vibration characteristics of a drill pipe during the lowering of a subsea Xmas tree were presented. A fourth-order partial differential equation with variable coefficients was established based on Euler–Bernoulli beam theory. The natural frequencies and mode shapes are obtained by using the differential transformation method. Four drill pipe models of different sizes were used in the experiments which were measured using piezoelectric acceleration sensors and fiber Bragg grating sensors, respectively. The factors that affect the natural frequencies and mode shapes, such as length, diameter, lumped mass, and boundary conditions, were analyzed. The results show that all factors have remarkable effects on the natural frequency, but changes in the length and diameter of the pipe have little effect on the mode shapes; the main factors affecting the mode shape are the boundary conditions and lumped mass. The results of the numerical calculation were validated by a comparison with the experimental results and showed good agreement.

The Dynamics of MEMS Arches of Non-Ideal Boundary Conditions

2011 ◽  
Author(s):  
Sami A. Alkharabsheh ◽  
Mohammad I. Younis
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Electrostatic Force ◽  
Dynamical Behavior ◽  
Experimental Investigations ◽  
Harmonic Load ◽  
Ideal Boundary ◽  
Shooting Technique ◽  
Softening Behavior ◽  
The Stability

We present an investigation into the dynamics of MEMS arches when actuated electrically including the effect of their flexible (non-ideal) supports. First, the eigenvalue problem of a nonlinear Euler-Bernoulli shallow arch with torsional and transversal springs at the boundaries is solved analytically. Several results are shown to demonstrate the possibility of tuning the theoretically obtained natural frequencies of an arch to match the experimentally measured. Then, simulation results are shown for the forced vibration response of an arch when excited by a DC electrostatic force superimposed to an AC harmonic load. Shooting technique is utilized to find periodic motions. The stability of the captured periodic motion is examined using the Floquet theory. The results show several jumps in the response during snap-through motion and pull-in. Theoretical and experimental investigations are conducted on a microfabricated curved beam actuated electrically. Results show softening behavior and superharmonic resonances. It is demonstrated that non-ideal boundary conditions can have significant effect on the qualitative dynamical behavior of the MEMS arch, including its natural frequencies, snap-through behavior, and dynamic pull-in.

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.

Free Vibration Analysis of Cracked Composite Beams Subjected to Coupled Bending-Torsion Loads Based on a First Order Beam Theory

2013 ◽  
Vol 325-326 ◽  
pp. 1318-1323 ◽  
Author(s):  
A.R. Daneshmehr ◽  
D.J. Inman ◽  
A.R. Nateghi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Order Theory ◽  
Composite Beams ◽  
First Order ◽  
First Order Theory

In this paper free vibration analysis of cracked composite beams subjected to coupled bending-torsion loads are presented. The composite beam is assumed to have an open edge crack. A first order theory is applied to count for the effect of the shear deformations on natural frequencies as well as the effect of coupling in torsion and bending modes of vibration. Local flexibility matrix is used to obtain the additional boundary conditions of the beam in the crack area. After obtaining the governing equations and boundary conditions, GDQ method is applied to solve the obtained eigenvalue problem. Finally, some numerical results are given to show the efficacy of the method. In addition, to count for the effect of coupling on natural frequencies of the cracked beams, different fiber orientations are assumed and studied.

Natural Frequencies of Out-of-Plane Vibration of Arcs

1982 ◽  
Vol 49 (4) ◽  
pp. 910-913 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Plane Vibration ◽  
Out Of Plane

The natural frequencies of out-of-plane vibration based on the Timoshenko beam theory are calculated numerically for uniform arcs of circular cross section under all combination of boundary conditions, and the results are presented in some figures.

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.

Experimental Modal Analysis of Rectangular and Circular Beams

2003 ◽  
Author(s):  
B. H. Emory ◽  
W. D. Zhu
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Mode Shapes ◽  
Euler Beam ◽  
Modal Assurance Criterion ◽  
Rectangular Beam ◽  
Circular Beam ◽  
A New Technique

Analytical and experimental methods are used to determine the natural frequencies and mode shapes of Aluminum 6061-T651 beams with rectangular and circular cross sections. A unique test stand is developed to provide the rectangular beam with different boundary conditions including clamped-free, clamped-clamped, clamped-pinned, and pinned-pinned. The first 10 bending frequencies and mode shapes for each set of boundary conditions are measured. The effects of the bolt torque on the measured frequencies of the rectangular beam are examined. The material properties of the circular beam, including the elastic modulus, shear modulus, and Poisson’s ratio, are determined by measuring its first 20 natural frequencies. A new technique is used to mount an accelerometer to measure the torsional modes of the circular beam. A roving hammer test is conducted to measure the first 10 mode shapes. The measured mode shapes of the circular and rectangular beams are compared with their thoretical predictions using the modal assurance criterion. The Timoshenko beam theory is shown to provide better predictions of the natural frequencies for the higher modes of the circular beam than the Bernoulli-Euler beam theory. The use of the rectangular and circular beam test stands as a teaching tool for undergraduate and graduate students is discussed.

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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