scholarly journals Assessment of Theories for Free Vibration Analysis of Homogeneous and Multilayered Plates

2004 ◽  
Vol 11 (3-4) ◽  
pp. 261-270 ◽  
Author(s):  
Erasmo Carrera
Keyword(s):  
Vibration Analysis ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Normal Stresses ◽  
Displacement Fields ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Vibrational Response ◽  
Multilayered Plates ◽  
Electric Materials

This paper assesses classical and advanced theories for free vibrational response of homogeneous and multilayered simply supported plates. Closed form solutions are given for thick and thin geometries. Single layer and multilayered plates made of metallic, composite and piezo-electric materials, are considered. Classical theories based on Kirchhoff and Reissner-Mindlin assumptions are compared with refined theories obtained by enhancing the order of the expansion of the displacement fields in the thickness directionz. The effect of the Zig-Zag form of the displacement distribution inzas well as of the Interlaminar Continuity of transverse shear and normal stresses at the layer interface were evaluated. A number of conclusions have been drawn. These conclusions could be used as desk-bed in order to choose the most valuable theories for a given problem.

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.

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.

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

Modeling and Free Vibration Analysis of a Complex Cable-Stayed Bridge

2012 ◽  
Author(s):  
D. Q. Cao ◽  
M. T. Song ◽  
W. D. Zhu
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Longitudinal Vibrations ◽  
Simply Supported ◽  
Cable Stayed Bridge ◽  
Linear Partial Differential Equations ◽  
Localized Mode ◽  
Linearized Model

A complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern the motions of the cables and segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge, which includes both the transverse and longitudinal vibrations of the cables, are determined. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for a symmetrical case with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies and localized mode shapes.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

Free Vibration Analysis of Cable Structures Using Isogeometric Approach

2017 ◽  
Vol 14 (03) ◽  
pp. 1750033 ◽  
Author(s):  
Son Thai ◽  
Nam-Il Kim ◽  
Jaehong Lee
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Penalty Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Displacement Fields ◽  
Numerical Examples ◽  
B Splines ◽  
Cable Structures

This paper presents a free vibration analysis of cable structures based on the isogeometric approach. The nonuniform rational B-splines (NURBS) basis functions are employed to represent both the exact geometry of cable and displacement fields. In order to enrich the basis functions, the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-refinement strategies are implemented. Therefore, these refinement schemes increase the accuracy of solution fields. For determining the static configuration of slack cables as a reference configuration, the well-known penalty method is used. Three numerical examples for slack and taut cable structures are presented in which different refinement schemes are utilized to obtain the converged results. The accuracy and reliability of the present numerical method are verified by comparing the natural frequencies with the results given by other researchers.

Sign in / Sign up

Export Citation Format

Share Document