Influence of boundary conditions on the natural frequencies of nonaxisymmetric electroelastic vibrations of piezoceramic plates

2012 ◽  
Vol 48 (5) ◽  
pp. 592-601 ◽  
Author(s):  
N. A. Shul’ga ◽  
V. V. Levchenko ◽  
O. I. Makievskii
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Electroelastic Vibrations

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.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) With a Gap in Mindlin Plates or Panels

2007 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Lap Joint ◽  
Bending Vibrations ◽  
Joint System ◽  
Adhesive Layers ◽  
Bonded Joint ◽  
Free Bending

In this present study, the “Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap in Mindlin Plates or Panels” are theoretically analyzed and are numerically solved in some detail. The “plate adherends” and the upper and lower “doubler plates” of the “Bonded Joint” system are considered as dissimilar, orthotropic “Mindlin Plates” joined through the dissimilar upper and lower very thin adhesive layers. There is a symmetrically and centrally located “Gap” between the “plate adherends” of the joint system. In the “adherends” and the “doublers” of the “Bonded Joint” assembly, the transverse shear deformations and the transverse and rotary moments of inertia are included in the analysis. The relatively very thin adhesive layers are assumed to be linearly elastic continua with transverse normal and shear stresses. The “damping effects” in the entire “Bonded Joint” system are neglected. The sets of the dynamic “Mindlin Plate” equations of the “plate adherends”, the “double doubler plates” and the thin adhesive layers are combined together with the orthotropic stress resultant-displacement expressions in a “special form”. This system of equations, after some further manipulations, is eventually reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in terms of the “state vectors” of the problem. Hence, the final set of the aforementioned “Governing Systems of Equations” together with the “Continuity Conditions” and the “Boundary conditions” facilitate the present solution procedure. This is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials). The present theoretical formulation and the method of solution are applied to a typical “Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap”. The effects of the relatively stiff (or “hard”) and the relatively flexible (or “soft”) adhesive properties, on the natural frequencies and mode shapes are considered in detail. The very interesting mode shapes with their dimensionless natural frequencies are presented for various sets of boundary conditions. Also, several parametric studies of the dimensionless natural frequencies of the entire system are graphically presented. From the numerical results obtained, some important conclusions are drawn for the “Bonded Joint System” studied here.

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.

NUMERICAL AND EXPERIMENTAL STUDY ON FREE VIBRATION OF DELAMINATED WOVEN FIBER GLASS/EPOXY COMPOSITE PLATES

2012 ◽  
Vol 12 (02) ◽  
pp. 377-394 ◽  
Author(s):  
J. MOHANTY ◽  
S. K. SAHU ◽  
P. K. PARHI
Keyword(s):  
Experimental Study ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Fiber Glass ◽  
Number Of Layers

This paper presents a combined experimental and numerical study of free vibration of industry-driven woven fiber glass/epoxy (G/E) composite plates with delamination. Using the first-order shear deformation theory, an eight-noded two-dimensional quadratic isoparametric element was developed, which has five degrees of freedom per node. In the experimental study, the influence of various parameters such as the delamination size, boundary conditions, fiber orientations, number of layers, and aspect ratio on the natural frequencies of delaminated composite plates are investigated. Comparison of the numerical results with experimental ones shows good agreement. Fundamental natural frequencies are found to decrease with the increase in the delamination size and fiber orientation and increases with the increase in the number of layers and aspect ratio of delaminated composite plates. The natural frequency of the delaminated composite plate varies significantly for different boundary conditions.

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.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

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