Vibration and Damping Analysis of Rectangular Plate With Partially Covered Constrained Viscoelastic Layer

1987 ◽  
Vol 109 (3) ◽  
pp. 241-247 ◽  
Author(s):  
A. K. Lall ◽  
N. T. Asnani ◽  
B. C. Nakra
Keyword(s):  
Loss Factor ◽  
Ritz Method ◽  
Viscoelastic Damping ◽  
Viscoelastic Layer ◽  
Transverse Displacement ◽  
Modal System ◽  
Resonant Frequencies ◽  
Simply Supported ◽  
The Core ◽  
Single Term

The Rayleigh-Ritz method is applied for the damping analysis offlexural vibrations of a simply supported plate, partially covered with constrained viscoelastic damping treatment. The anaysis is carried out in terms of resonant frequencies and associated modal system loss factors. Single-term solutions for respective modes are assumed for the longitudinal displacements of the constraining layer and the transverse displacement of the plate. The variations of the resonant frequency and the associated modal loss factor with the coverage percentage, the coverage location, the core shear modulus and the thickness of the constrained and the constraining layers have been reported.

THE SELF-DAMPING CHARACTERISTICS OF A MAGNETIC CONSTRAINED FULLY COVERED SANDWICH CANTILEVER BEAM

2005 ◽  
Vol 29 (3) ◽  
pp. 333-341 ◽  
Author(s):  
Ming Li ◽  
Zeng He
Keyword(s):  
Cantilever Beam ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Geometrical Parameters ◽  
Transverse Displacement ◽  
Constrained Layer Damping ◽  
Resonant Frequencies ◽  
Damping Characteristics ◽  
Single Term ◽  
Sandwich Type

The Rayleigh-Ritz method is applied for the damping analysis of flexural vibration of a fully covered double sandwich-type cantilever beam with the attraction arrangement magnets on the constraining layers root. The analysis is carried out in terms of resonant frequencies and associated modal system loss factors. Single-term solutions for respective modes are assumed for the longitudinal displacements of the constraining layer and the transverse displacement of the beam. The modeling is validated experimentally. The improvement of damping characteristics using the magnetic constrained layer damping treatment under different physical and geometrical parameters has been reported.

Accurate Vibration Analysis of Simply Supported Rhombic Plates by Considering Stress Singularities

1995 ◽  
Vol 117 (3A) ◽  
pp. 245-251 ◽  
Author(s):  
C. S. Huang ◽  
O. G. McGee ◽  
A. W. Leissa ◽  
J. W. Kim
Keyword(s):  
Ritz Method ◽  
Mode Shapes ◽  
Transverse Displacement ◽  
Algebraic Polynomials ◽  
Stress Singularities ◽  
Simply Supported ◽  
Free Transverse Vibration ◽  
Skewed Plates ◽  
Convergence Of Solution ◽  
Skew Angles

This is the first known work which explicitly considers the bending stress singularities that occur in the two opposite, obtuse corner angles of simply supported rhombic plates undergoing free, transverse vibration. The importance of these singularities increases as the rhombic plate becomes highly skewed (i.e., the obtuse angles increase). The analysis is carried out by the Ritz method using a hybrid set consisting of two types of displacement functions, e.g., (1) algebraic polynomials and (2) corner functions accounting for the singularities in the obtuse corners. It is shown that the corner functions accelerate the convergence of solution, and that these functions are required if accurate solutions are to be obtained for highly skewed plates. Accurate nondimensional frequencies and normalized contours of the vibratory transverse displacement are presented for simply supported rhombic plates with skew angles ranging to 75 deg. (i.e., obtuse angles of 165 deg.). Frequency and mode shapes of isosceles and right triangular plates with all edges simply supported are also available from the data presented.

Nonlinear, Damped Vibrations of Sandwich Plates With Time-Dependent Temperature

1993 ◽  
Author(s):  
S. Lukasiewicz ◽  
Z. Q. Xia
Keyword(s):  
Sandwich Plate ◽  
Rapid Change ◽  
Time Dependent ◽  
Viscoelastic Damping ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Geometrical Nonlinearities ◽  
The Core

Abstract The paper studies the effect of the rapid change of temperature on the vibrations of simply supported sandwich plates. It has been taken into consideration that the properties of the facings and of the core of the sandwich plate materials change with the change of the temperature. The effects of the viscoelastic damping and geometrical nonlinearities on the behaviour of the plate have also been included. It was found that the rapid change of temperature affects the amplitude and frequency of the vibrations.

An Analysis of Viscoelastic Damping Characteristics of a Simply-Supported Sandwich Beam

1971 ◽  
Vol 93 (4) ◽  
pp. 1239-1244 ◽  
Author(s):  
A. Chatterjee ◽  
J. R. Baumgarten
Keyword(s):  
Energy Method ◽  
Sandwich Beam ◽  
Core Material ◽  
Viscoelastic Damping ◽  
Experimental Measurements ◽  
Simply Supported ◽  
The Core ◽  
Damping Characteristics ◽  
Viscoelastic Core ◽  
Theoretical Predictions

An energy method is employed to analyze the damping in the fundamental mode of a simply-supported sandwich beam with viscoelastic core material sandwiched between two elastic metallic layers called the facings. The theory developed herein enables one to predict the damped natural frequency and the damping (in terms of logarithmic decrement) of the transverse vibration of a beam of known dimensions, provided the moduli-frequency characteristics of the core material are known. Experimental measurements bear out the accuracy of the theoretical predictions. The theory can very easily be extended for the analysis of higher discrete modes.

scholarly journals Research on the Dynamic Responses of Simply Supported Horizontal Pipes Conveying Gas-Liquid Two-Phase Slug Flow

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 83
Author(s):  
Gang Liu ◽  
Zongrui Hao ◽  
Yueshe Wang ◽  
Wanlong Ren
Keyword(s):  
Slug Flow ◽  
Peak Frequency ◽  
Dynamic Responses ◽  
Piping System ◽  
Transverse Displacement ◽  
Vibration Acceleration ◽  
Two Phase ◽  
Horizontal Pipes ◽  
Simply Supported ◽  
Superficial Gas Velocity

The dynamic responses of simply supported horizontal pipes conveying gas-liquid two-phase slug flow are explored. The intermittent characteristics of slug flow parameters are mainly considered to analyze the dynamic model of the piping system. The results show that the variations of the midpoint transverse displacement could vary from periodic-like motion to a kind of motion whose amplitude increases as time goes on if increasing the superficial gas velocity. Meanwhile, the dynamic responses have certain relations with the vibration acceleration. By analyzing the parameters in the power spectrum densities of vibration acceleration such as the number of predominant frequencies and the amplitude of each peak frequency, the dynamic behaviors of the piping system like periodicity could be calculated expediently.

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.

Post-Buckling of Piezoelectric Thin Plates

2015 ◽  
Vol 15 (07) ◽  
pp. 1540020 ◽  
Author(s):  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Nonlinear Behavior ◽  
Dirichlet Boundary Conditions ◽  
Thin Plates ◽  
Governing Equations ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Single Term ◽  
Post Buckling ◽  
Special Case

In the present paper, the geometrically nonlinear behavior of piezoelastic thin plates is studied. First, the governing equations for the electromechanically coupled problem are derived based on the von Karman–Tsien kinematic assumption. Here, the Berger approximation is extended to the coupled piezoelastic problem. The general equations are then reduced to a single nonlinear partial differential equation for the special case of simply supported polygonal edges. The nonlinear equations are approximated by using a problem-oriented Ritz Ansatz in combination with a Galerkin procedure. Based on the resulting equations the buckling and post-buckling behavior of a polygonal simply supported plate is studied in a nondimensional form, where the special geometry of the polygonal plate enters via the eigenvalues of a Helmholtz problem with Dirichlet boundary conditions. Single term as well as multi-term solutions are discussed including the effects of piezoelectric actuation and transverse force loadings upon the solution. Novel results concerning the buckling, snap through and snap buckling behavior are presented.

Consideration of Both Extensional and Shear Strain of Core Material in Modal Property Estimation of Sandwich Plates

1995 ◽  
Author(s):  
Byung-Chan Lee ◽  
Kwang-Joon Kim
Keyword(s):  
Shear Strain ◽  
Layer Thickness ◽  
Sandwich Beam ◽  
Base Layer ◽  
Core Material ◽  
Viscoelastic Layer ◽  
Sandwich Plates ◽  
Modal Parameter ◽  
The Core ◽  
Plate Length

Abstract In vibration analysis of sandwich beam/plates, it is often assumed that there occurs shear deformation only, i.e. no extension or compression, in the core viscoelastic layer. Certainly, this assumption may have limitations, for example, with increase of the core thickness or frequency range of vibration. The purpose of this paper is to consider the extentional as well as shear strain of the core for modal parameter estimation of the sandwich plates and to investigate how much error will be caused by neglecting the extension or compression in the core material. Natural frequencies and modal loss factors are estimated for a simply supported square plates under each of the above two assumptions. Nondimensional characteristic equations are formulated and solved for various ratios of the base layer thickness to plate length, core to base layer thickness, and constraining layer to base layer thickness.

scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

Vibration Analysis of Anisotropic Simply Supported Plates by Using Variable Kinematic and Rayleigh-Ritz Method

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Erasmo Carrera ◽  
Fiorenzo Adolfo Fazzolari ◽  
Luciano Demasi
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Virtual Displacement ◽  
Simply Supported ◽  
Order Expansion ◽  
Thickness Layer ◽  
Made In

This work deals with accurate free-vibration analysis of anisotropic, simply supported plates of square planform. Refined plate theories, which include layer-wise, equivalent single layer and zig-zag models, with increasing number of displacement variables are take into account. Linear up to fourth N-order expansion, in the thickness layer-plate direction have been implemented for the introduced displacement field. Rayleigh-Ritz method based on principle of virtual displacement is derived in the framework of Carrera’s unified formulation. Regular symmetric angle-ply and cross-ply laminates are addressed. Convergence studies are made in order to demonstrate that accurate results are obtained by using a set of trigonometric functions. The effects of the various parameters (material, number of layers, and fiber orientation) upon the frequencies and mode shapes are discussed. Numerical results are compared with available results in literature.

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