Exact Solution of Thermoelastic Damping and Frequency Shifts in a Nano-Beam Resonator

2015 ◽  
Vol 15 (06) ◽  
pp. 1450082 ◽  
Author(s):  
Ibrahim A. Abbas
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Thermoelastic Damping ◽  
Frequency Shifts ◽  
Beam Resonator ◽  
Simply Supported ◽  
Thermoelastic Vibration ◽  
Modes Of Vibration ◽  
Generalized Thermoelastic ◽  
Analytical Expressions

In this study, we consider the problem of a generalized thermoelastic vibration of a bounded nano-beam resonator in the context of Green and Naghdi theory (GNIII). The first four modes of vibration in the nano-beam resonator are investigated for the beam under clamped and simply supported conditions. Analytical expressions for the deflection, temperature change, frequency shifts, and thermoelastic damping in the beam are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping and frequency shift.

Analytical Solution of Thermoelastic Damping in a Nanoscale Beam using the Fractional Order Theory of Thermoelasticity

2016 ◽  
Vol 16 (09) ◽  
pp. 1550064 ◽  
Author(s):  
Ibrahim A. Abbas ◽  
Aatef D. Hobiny
Keyword(s):  
Fractional Order ◽  
Present Model ◽  
Generalized Thermoelasticity ◽  
Order Theory ◽  
Thermoelastic Damping ◽  
Frequency Shifts ◽  
Beam Resonator ◽  
Special Cases ◽  
Analytical Expressions ◽  
Fractional Parameter

In this paper, we study the generalized thermoelastic vibration of a bounded nano-beam resonator under fractional order theory of thermoelasticity. The theory of generalized thermoelasticity with one relaxation time can be established in the limit as the special cases of the present model. The effect of fractional parameter is investigated on the nano-beam resonator for beams with clamped ends. Analytical expressions for the deflection, temperature change, frequency shift, and thermoelastic damping have been derived for the beam. The effect of the fractional parameter on the variation of frequency shifts and thermoelastic damping is analyzed graphically.

Normal Vibrations of a Uniform Plate Carrying Any Number of Finite Masses

1959 ◽  
Vol 26 (2) ◽  
pp. 210-216
Author(s):  
W. F. Stokey ◽  
C. F. Zorowski
Keyword(s):  
Natural Frequencies ◽  
Physical Characteristics ◽  
Normal Vibrations ◽  
Simply Supported ◽  
Numerical Example ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
General Method

Abstract A general method is presented for determining approximately the natural frequencies of the normal vibrations of a uniform plate carrying any number of finite masses. Its application depends on knowing the frequencies and natural modes of vibration of the unloaded plate and the physical characteristics of the mass loadings. A numerical example is presented in detail in which this method is applied to a simply supported plate carrying two masses. Results also are included of experimentally measured frequencies for this configuration and several additional cases along with the frequencies computed using this method for comparison.

Effect of guy cable constraint on structural damping of open lattice antenna towers

1980 ◽  
Vol 7 (4) ◽  
pp. 614-620
Author(s):  
J. S. Kennedy ◽  
D. J. Wilson ◽  
P. F. Adams ◽  
M. Perlynn
Keyword(s):  
Natural Frequencies ◽  
Damping Ratio ◽  
Field Tests ◽  
Full Scale ◽  
Structural Damping ◽  
Scale Field ◽  
Modes Of Vibration

This paper presents the results of full-scale field tests on two steel guyed latticed towers. The towers were approximately 83 m in height, were guyed at three levels, and were of bolted angle construction. The observed results consist of the natural frequencies of the first two modes of vibration as well as the damping ratio for the first mode. The observed results are compared with analytical predictions and observations made concerning the contributions of structural and cable action to the damping ratio.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method

1992 ◽  
Author(s):  
L. T. Lee ◽  
W. F. Pon
Keyword(s):  
Boundary Conditions ◽  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Energy Functional ◽  
Comprehensive Treatment ◽  
Energy Functionals ◽  
Simply Supported ◽  
Cartesian Coordinate

Abstract Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods with all four edges clamped boundary conditions and greet agreements are found between them. The natural frequencies for parallelogrammic plates with other boundary conditions, such as four edges simply supported, clamped-free and simply supported-free, are also obtained. This method is considered as a better and accurate comprehensive treatment for this type of problems.

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).

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

scholarly journals The Vibration of Simply Supported Non-Uniform Cross Sectional Pipe Conveying Fluid Resting on Viscoelastic Foundation

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Natural Frequencies ◽  
Flexural Vibration ◽  
Bernoulli Model ◽  
Viscoelastic Foundation ◽  
Cross Sectional ◽  
Flowing Fluid ◽  
Simply Supported ◽  
Critical Velocities ◽  
Stiffness And Damping ◽  
The Mathematical Model

The induced flexural vibration of slender pipe systems with continuous non uniform cross sectional area containing laminar flowing fluid lying on extended Winkler viscoelastic foundation is considered. The Euler Bernoulli model of the pipe has hinged ends. The inlet flow is considered constant steady that interacts with the wall of the pipe. The mathematical model is developed and its corresponding solution is obtained. The influence of the combination of variation of cross section, foundation stiffness and damping on the critical velocities, complex natural frequencies and stabilization of the system is presented.

Experimental Identification Approach of Dynamic Parameters of Precise Horizontal Machining Centre Based on Component-System

2011 ◽  
Vol 467-469 ◽  
pp. 1686-1690
Author(s):  
Zhi Feng Liu ◽  
Zhong Hua Chu ◽  
Qiang Cheng ◽  
Guang Bo Liu ◽  
Dong Sheng Xuan
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Modal Testing ◽  
Element Calculation ◽  
Element Simulation ◽  
Modes Of Vibration ◽  
Identification Approach ◽  
Comparison Of The Results ◽  
Machine Structure

This paper integrates experiment modal analysis and the analytical modal analysis to study on the vibration phenomena occurring occasionally at the different components of a precise horizontal machining centre. The paper is focused on extracting the mode shape of the major components of the machine in order to ensure resonance phenomena as a cause of vibration. At first the main natural frequencies with the corresponding modes of vibration of the machine structure are obtained by the experiment modal analysis. Then the dynamic behavior of the machine components is simulated using a finite element simulation model. The comparison of the results based on finite element calculation with their experimental counterparts shows the reasonableness. The model is evaluated and corrected with experimental results by modal testing of the machine components.

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