• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.24 no.12
• /
• pp.999-1006
• /
• 2014

Mindlin plate theory includes the shear deformation and rotatory inertia effects which cannot be negligible as exciting frequency increases. The statistical methods such as energy flow analysis(EFA) and statistical energy analysis(SEA) are very useful for estimation of structure-borne sound of various built-up structures. For the reliable vibrational analysis of built-up structures at high frequencies, the energy transfer relationship between out-of-plane waves and in-plane waves exist in Mindlin plates coupled at arbitrary angles must be derived. In this paper, the new wave transmission analysis is successfully performed for various energy analyses of Mindlin plates coupled at arbitrary angles.

• Structural Engineering and Mechanics
• /
• v.44 no.3
• /
• pp.267-288
• /
• 2012

Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy's third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1996.04a
• /
• pp.127-134
• /
• 1996

In this paper, the effect of neglecting the own weight of the composite plate on the natural frequency of vibration of the laminated plates is presented. The method used has been developed by the author since 1974. This method is very effective for the plates with arbitrary boundary conditions and irregular sections. When the attached mass is equal to the weight of the plate, the effect of neglecting the plate weight is 9.26 percent

• Structural Engineering and Mechanics
• /
• v.56 no.5
• /
• pp.835-854
• /
• 2015

In this paper, the modified form of shear deformation plate theories is proposed. First, the displacement field geometry of classical and the first order shear deformation theories are compared with each other. Using this comparison shows that there is a kinematic relation among independent variables of the first order shear deformation theory. So, the modified forms of rotation functions in shear deformation theories are proposed. Governing equations for rectangular and circular thick laminated plates, having been analyzed numerically so far, are solved by method of separation of variables. Natural frequencies and mode shapes of the plate are determined. The results of the present method are compared with those of previously published papers with good agreement obtained. Efficiency, simplicity and excellent results of this method are extensible to a wide range of similar problems. Accurate solution for governing equations of thick composite plates has been made possible for the first time.

• Structural Engineering and Mechanics
• /
• v.74 no.1
• /
• pp.105-119
• /
• 2020

In this work, a novel higher-order shear deformation theory (HSDT) for static and free vibration analysis of functionally graded (FG) plates is proposed. Unlike the conventional HSDTs, the proposed theory has a novel displacement field which includes undetermined integral terms and contains fewer unknowns. Equations of motion are obtained by using Hamilton's principle. Analytical solutions for the bending and dynamic investigation are determined for simply supported FG plates. The computed results are compared with 3D and quasi-3D solutions and those provided by other plate theories. Numerical results demonstrate that the proposed HSDT can achieve the same accuracy of the conventional HSDTs which have more number of variables.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.16 no.2
• /
• pp.1-7
• /
• 1979

The authors had done theoretical analysis of the vibration of rectangular elastic plates in contact with water. In this analysis, using the elliptic cylindrical coordinate system, they investigated the effects of mass density ratios, chord-length to thickness ratios, aspect ratios, boundary conditions and mode shapes on the added mass of plates. The results are reported in papers quoted as the reference [4] and [5] of this paper. In this report the results of experiments conducted to verify the above theoretical analysis are presented. It shows that numerical results derived from the theoretical analysis are generally in good agreement with the experimental results.

• Steel and Composite Structures
• /
• v.3 no.3
• /
• pp.213-229
• /
• 2003

A high precision shear deformable triangular element has been proposed for free vibration analysis of composite trapezoidal plates. The element has twelve nodes at the three sides and four nodes inside the element. Initially the element has fifty-five degrees of freedom, which has been reduced to forty-eight by eliminating the degrees of freedom of the internal nodes through static condensation. Plates having different side ratios (b/a), boundary conditions, thickness ratios (h/a=0.01, 0.1 and 0.2), number of layers and fibre angle orientations have been analyzed by the proposed shear locking free element. Trapezoidal laminate with concentrated mass at the centre has also been analyzed. An efficient mass lumping scheme has been recommended, where the effect of rotary inertia has been included. For validation of the present element and formulation few results of isotropic trapezoidal plate and square composite laminate have been compared with those obtained from open literatures. The numerical results for composite trapezoidal laminate have been given as new results.

• Steel and Composite Structures
• /
• v.46 no.5
• /
• pp.659-667
• /
• 2023

Nonlinear forced vibration behaviors of sandwich plates having graphene platelets (GPL) based face sheets have been researched in this article. Possessing low weight together with low stiffness, square honeycomb cores are mostly constructed by aluminum. Herein, the square shaped core has been fortified by two skins of GPL-based type in such a way that the skins have uniform and linearly graded GPL dispersions. The square shaped core has the effective material specification according to the relative density concept. The whole formulation has been represented based upon classical plate theory (CPT) while harmonic balance approach is applied for solving the problem and plotting the amplitude-frequency curves. The forced vibration behaviors of such plates are influenced by square-shaped core and the relative density, skin's height and GPL fortification.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11a
• /
• pp.309.2-309
• /
• 2002

This paper is concerned with the development of the vibration isolation system using piezoelectric actuators and sensors. The active vibration absorber system consists of 4 pairs of PZT actuators bonded on aluminum plates making s- shaped device. Hence, the active system is directly connected to the passive system. The rubber attached to the end of the beam is connected to the upper base as a structural member. It allows bending thus maximizing the vertical movement generated by the piezoceramic actuators. (omitted)

• Steel and Composite Structures
• /
• v.17 no.1
• /
• pp.21-46
• /
• 2014

This paper presents a simple n-order four variable refined theory for the bending and vibration analyses of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.