Analysis of natural frequencies and modal loss factors of simply supported beams with adhesively bonded double‐strap joints

1992 ◽  
Vol 92 (1) ◽  
pp. 268-276 ◽  
Author(s):  
Mohan D. Rao ◽  
Shulin He
Keyword(s):  
Natural Frequencies ◽  
Adhesively Bonded ◽  
Simply Supported ◽  
Loss Factors

Lateral Vibrations of a Damped Laminated Hollow Circular Cross-Section Beam

1974 ◽  
Vol 96 (3) ◽  
pp. 845-852
Author(s):  
R. A. Ditaranto
Keyword(s):  
Cross Section ◽  
Viscoelastic Material ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Material Loss ◽  
Simply Supported ◽  
Elastic Beams ◽  
Mass Moment ◽  
Elastic Layers ◽  
Loss Factors

The free lateral bending vibrations of an “infinitely” long or simply-supported thin-walled circular cross-section beams having elastic-viscoelastic-elastic layers are investigated to determine the natural frequencies and associated composite loss factors. The analysis considers the inner and outer beams to behave as elastic beams in which the mass and mass-moment of inertia are both considered along with the interaction of the two elastic beams through the viscoelastic material. The results indicate that there are two natural frequencies. The lower one associated with the two elastic beams moving together so that little damping is obtained in this mode of vibration; the higher mode in which the two elastic beams vibrate in opposite directions so that there is an amount of damping comparable to the material loss factor of the viscoelastic material. A simplified model analysis is performed which is used to corroborate the trends obtained in the computer solutions of the more rigorous analysis. A series of curves are obtained for equal thickness elastic layers which can be used to obtain natural frequencies and composite loss-factors for a realistic range of geometrical and physical properties of a laminated circular cross-section simply supported beam.

scholarly journals Vibration Analysis of Viscoelastically Damped Sandwich Shells

1996 ◽  
Vol 3 (6) ◽  
pp. 403-417 ◽  
Author(s):  
Ji-Fan He ◽  
Bang-An Ma
Keyword(s):  
Asymptotic Solution ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Governing Equations ◽  
Modal Strain Energy ◽  
Simply Supported ◽  
Modal Strain Energy Method ◽  
Sandwich Shells ◽  
Method Accuracy ◽  
Loss Factors

The simplified governing equations and corresponding boundary conditions of vibration of viscoelastically damped unsymmetrical sandwich shells are given. The asymptotic solution to the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the modal strain energy method. By taking more terms of the asymptotic solution with successive calculations and use of the Padé approximants method, accuracy of natural frequencies and modal loss factors of sandwich shells can be improved. The lowest three or four natural frequencies and modal loss factors of simply supported cylindrical sandwich shells are calculated.

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.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

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.

The Natural Frequency Calculation Method of Simply-Supported Beam in the Sunshine Temperature Field

2013 ◽  
Vol 394 ◽  
pp. 364-367
Author(s):  
Yong Chun Cheng ◽  
Yu Ping Shi ◽  
Guo Jin Tan
Keyword(s):  
Temperature Field ◽  
Calculation Method ◽  
Natural Frequencies ◽  
Bernoulli Model ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Frequency Calculation ◽  
Natural Frequency Calculation ◽  
Beam Bridge ◽  
T Beam

The related researches show that , the sunshine temperature field can cause the changes of the natural frequencies of the simply-supported beam. In order to recover the influence law of the temperature field on the natural frequencies, the calculation method of the natural frequencies of the simply-supported beam bridge is formed. First, according to the principles of stress equivalence, transform the sunshine temperature field to the partiality axis forces. Based on the Bernoulli model, the calculation method of the natural frequencies of the simply-supported beam under the partiality axis forces at both ends is formed. At last, take one simply-supported T beam as the object of numerical modeling and verify the validity and the reliability of this method.

Computation of natural frequencies of skewed slabs using equivalent rectangular slab concept

1980 ◽  
Vol 7 (2) ◽  
pp. 384-388 ◽  
Author(s):  
T. I. Campbell ◽  
W. H. Siu
Keyword(s):  
Isotropic Material ◽  
Natural Frequencies ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Linear Elastic ◽  
Rectangular Slab

The natural frequencies of skewed slabs (in the shape of a parallelogram) of uniform thickness and linear elastic isotropic material are considered. It is shown that the natural frequencies of a skewed slab can be related to those of the corresponding rectangular slab by means of an equivalent rectangular slab concept. Charts are presented to allow the computation of the natural frequencies of one-, two-, and three-span symmetric skewed slabs, which are simply supported at each end and free along each edge.

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