Vibration Analysis Of Thick Plates Research Articles

An extended separation-of-variable method for free vibration of rectangular Reddy plates

The Reddy plate theory is widely used in the vibration analysis of thick plates, but there are few closed-form analytical solutions for free vibration of rectangular Reddy plates with arbitrary homogenous boundary conditions. This work is to develop the extended separation-of-variable (SOV) method for the free vibration analysis of rectangular Reddy plates. In the present method, the mode functions are in an explicit and closed form, and the natural frequencies corresponding to two-direction eigenfunctions are mathematically assumed to be independent of each other. According to two pairs of boundary conditions, the closed-form mode functions and frequency equations are achieved. The present method is numerically compared with other approximate and analytical methods, and some valuable observations are presented. The present solutions are exact for the plates with at least two opposite sides simply supported, and agree well with the results in literatures for other boundary conditions.

Eigenvector and eigenvalue analysis of thick plates resting on elastic foundation with first order finite element

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin’s theory with first order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency parameters of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using first order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 4-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 4-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

Using fourth order element for free vibration parametric analysis of thick plates resting on elastic foundation

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin\'s theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

A high-performance parametrized mixed finite element model for bending and vibration analyses of thick plates

Based on the parametrized mixed variational principle, a high-performance finite element model has been developed for bending and vibration analysis of thick plates. The proposed mixed variational formulation combines the concept of Reissner’s mixed variational theorem and Rong’s generalized mixed variational theorem. In addition to unknown parameters of the displacement fields, the transverse normal component of the stress tensor is also assumed as the independent field variable in the present variational formulation. The latter allows the fulfillment of the boundary conditions of the transverse normal stress at the top and bottom surfaces of the plate in a natural way. The variational constraint of the transverse normal strain–displacement relations is relaxed via the parametrized Lagrange multipliers method. The functional of the proposed variational formulation contains an arbitrary free parameter, called the splitting factor. Simple formulations have been proposed for selecting the splitting factor which leads to the results of higher precision. The numerical results obtained from the proposed mixed formulation have been compared with the results of three-dimensional (3D) theory of elasticity and other plate theories available in the literature. The comparison study shows that the proposed parametrized mixed plate theory is capable of achieving the accuracy of nearly exact 3D solutions.

Analytical Approaches to Vibration Analysis of Thick Plates Subjected to Different Supports, Loadings and Boundary Conditions - A Literature Survey

Plates are one of the most important structural components used in many industries like aerospace, marine and various other engineering fields and thus motivate designers and engineers to study the vibrational characteristics of these structures. A lot of research work and studies have been done to study its vibration characteristics. This paper is a review of existing literature on vibration analysis of plates. Focus has been kept on prominent studies related to isotropic plates based on Mindlin plate theory; however few citations on orthotropic plates and higher order shear deformation theories have also been included. All citations are in English language. This review is aimed to provide contemporarily relevant survey of papers on vibrational characteristics of thick plates and identification of various methods and approaches that have been used to study the vibration characteristics. This paper will not only be useful for scientists, designers and researchers to locate important and relevant literature/research quickly but will also help them to identify and apply some of these methods and approaches to study the vibration characteristics of various other 2D and 3D structures.

A new finite element formulation for vibration analysis of thick plates

A new procedure for determining properties of thick plate finite elements, based on the modified Mindlin theory for moderately thick plate, is presented. Bending deflection is used as a potential function for the definition of total (bending and shear) deflection and angles of cross-section rotations. As a result of the introduced interdependence among displacements, the shear locking problem, present and solved in known finite element formulations, is avoided. Natural vibration analysis of rectangular plate, utilizing the proposed four-node quadrilateral finite element, shows higher accuracy than the sophisticated finite elements incorporated in some commercial software. In addition, the relation between thick and thin finite element properties is established, and compared with those in relevant literature.

Free vibration analysis of thick plates resting on Winkler elastic foundation

The purpose of this study is to determine the effects of various parameters such as the aspect ratio, subgrade reaction modulus and thickness/span ratio on the frequency parameters of thick plates resting on Winkler-type elastic foundations. For this purpose, 4-noded (PBQ4) and 8-noded (PBQ8) Mindlin plate elements are adopted for the analysis using Winkler foundation model. Two different integration rules, namely the full integration (FI) and the selective reduced integration (SRI) techniques, are used to obtain stiffness matrix of plates. The results obtained in this study are compared with the results that are obtained by SAP2000 structural analysis software.

Application of the Modified Vlasov Model to the Free Vibration Analysis of Thick Plates Resting on Elastic Foundations

The Modified Vlasov Model is applied to the free vibration analysis of thick plates resting on elastic foundations. The effects of the subsoil depth, plate dimensions and their ratio, the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. A four-noded, twelve degrees of freedom quadrilateral finite element (PBQ4) is used for plate bending analysis based on Mindlin plate theory which is effectively applied to the analysis of thin and thick plates when selective reduced integration technique is used. The first ten natural frequency parameters are presented in tabular and graphical forms to show the effects of the parameters considered in the study. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on elastic foundation is generally larger than that of the other parameters considered in the study.

Application of the Modified Vlasov Model to the Free Vibration Analysis of Thick Plates Resting on Elastic Foundations

The Modified Vlasov Model is applied to the free vibration analysis of thick plates resting on elastic foundations. The effects of the subsoil depth, plate dimensions and their ratio, the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. A four-noded, twelve degrees of freedom quadrilateral finite element (PBQ4) is used for plate bending analysis based on Mindlin plate theory which is effectively applied to the analysis of thin and thick plates when selective reduced integration technique is used. The first ten natural frequency parameters are presented in tabular and graphical forms to show the effects of the parameters considered in the study. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on elastic foundation is generally larger than that of the other parameters considered in the study.

A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported

This paper is introducing a semi-analytical differential quadrature element method (DQEM) based on first-order shear deformation theory for free vibration analysis of thick plates. By decomposing the plate into a series of sub-domains or elements, any discontinuity in geometry, material properties, and elastic foundations in one direction can be handled conveniently. Classical, as well as non-classical boundary conditions can be imposed. One benefits of this semi-analytical DQEM is reducing the storage requirements and the computational efforts needed to assemble the global equations. The method would also increase the computational efficiency in comparison with the finite element method (FEM) or differential quadrature method (DQM) analysis of such problems. The accuracy, versatility, stability, and convergence of the algorithm are certified.

Vibration of non-uniform thick plates on elastic foundation by differential quadrature method

This paper presents a differential quadrature (DQ) solution for free vibration analysis of thick plates of continuously varying thickness on two-parameter elastic foundations. The formulations are based on the first-order shear deformation theory taking into account the effects of rotary inertia. The thickness of the plate may vary in one or two directions. The thickness variation might be assumed linear or non-linear. Different types of boundary conditions, including free edges and corners, loaded edges with in-plane forces are formulated. The accuracy, convergence and versatility of the DQ procedure for the type of plate problems, with complicated governing differential equations and boundary conditions are examined and verified.

Spline選点最小二乗法を用いた厚板の振動解析

This paper presents vibration analysis of thick plates on the basis of the Mindlin plate theory and the theory of elasticity by using the spline collocation least square method which is an alternative free mesh method. No numerical integration is required in the formulation and the resulting matrix has the advantage of always being symmetrical To demonstrate an accuracy and convergence of the present numerical method, some numerical examples are solved and the results are compared with those obtained by analytical method and other numerical methods. It is seen that good accuracy and stable convergence are obtained.

Vibration of thick plates using finite strip-elements

This paper develops a finite strip-element method for the vibration analysis of thick plates. The method uses a combined polynomial and trigonometric interpolation scheme that enables all boundary conditions to be correctly treated. The global equations are derived in the usual manner of the finite element method, and natural frequencies of vibration can be found by solving a linear eigenvalue problem.

VIBRATION OF SYMMETRICALLY LAMINATED THICK SUPER ELLIPTICAL PLATES

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and thep-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition.

Research on thick plate vibration: a literature survey

This paper is a review of existing literature on the vibration analysis of thick plates: 132 publications are cited, mostly recent and nearly all in the English language. Attention is mainly devoted to studies based on the Mindlin theory and the modified Mindlin plate theories for laminated plates, while some papers using high order shear deformation plate theories are also included. The aim of this paper is to provide a contemporarily relevant survey of studies on the vibration of thick plates. Studies are categorized by different plate shapes. This review paper should be useful for scientists and researchers in assisting them to locate relevant existing literature quickly.

Frequency analysis of thick orthotropic plates on elastic foundation using a high precision triangular plate bending element

AbstractA high precision triangular thick orthotropic plate bending element on an elastic foundation is developed for the free vibration analysis of thick plates on elastic foundation. The element has three nodes with twelve degrees‐of‐freedom per node, and takes into account the shear deformation and rotatory inertia. The accuracy of the element is established by comparison of the natural frequencies of certain thick and thin plates, determined from a consistent mass matrix formulation, with available results.