Vibro-acoustic response of sandwich plates with functionally graded core

A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates

This paper analyzes the sound radiation behavior of a clamped thin, functionally graded material plate using the classical plate theory and Rayleigh Integral with the elemental radiator approach. The material properties of the plate are assumed to vary according to the power-law distribution of the constituent materials in the transverse direction. The functionally graded material is modeled using a physical neutral surface instead of a geometric middle surface. The effects of the power-law index, elastic modulus ratio, different constituent materials, and damping loss factor on the sound radiation of functionally graded plate are analyzed. It was found that, for the considered plate, the power-law index significantly influences sound power level and radiation efficiency. There exists a critical value of the power-law index for which the corresponding peak of sound power level is minimum. In a wide operating frequency range, approximately 500–1500 Hz, this research suggests that the radiation efficiency is lower for the power-law index equal to 0 and 1. However, for very low frequencies (less than 250 Hz), the power-law index does not affect radiation efficiency significantly. Further, as the modulus ratio increases, the sound power peak decreases for a given power-law index. For the given material constituents of the functionally graded plate, the different values of damping loss factors do not significantly influence radiation efficiency. However, the selection of material constituents affects the radiation efficiency peak.

This paper uses a quasi-3D refined shear deformation plate theory to investigate the buckling response of supported functionally graded (FG) porous sandwich (SW) plates. The material properties of FG sandwich porous plates (SWPPs) are defined by a modified mixing rule, supplemented by an additional term representing the porosity in the thickness of the FG layer. By incorporating indefinite integral variables, the number of unknowns and governing equations of the current theory is reduced, making it easier to use. Three common types of sandwich porous plates are considered in the analysis: an isotropic FG porous plate, an FG face plate with a homogeneous core, and a homogeneous face plate with an FG core. The current method considers both normal and shear deformations and satisfies the transverse shear stress-free boundary conditions at the top and bottom surfaces of the plate. The equilibrium equations are derived using the principle of virtual displacements. These equations are then solved using the Navier-type method. The influence of thickness strain and several parameters, including mechanical loads, porosity coefficients, layer thickness ratios, geometric parameters, and gradient indices, are studied. The numerical results of the present theory are similar to the predictions of quasi-3D theories with more unknowns, in addition to being more accurate than those obtained by higher-order shear deformation theories. The findings support the idea that the suggested theory offers an easy and effective method for predicting the buckling behavior of FG porous sandwich plates. The results show that, without taking into account transverse normal deformations, the plate is softer and the critical buckling load decreases. On the other hand, with transverse normal deformations, the plate is stiffer, which increases the critical buckling load.

Analytical non-linear analysis of functionally graded sandwich solid/annular sector plates

On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

In the present work, the inverse trigonometric shear deformation theory (ITSDT) is applied to analytically perform the free vibration and buckling analysis of functionally graded (FG) sandwich plate. The governing equations are derived using the principle of virtual work, incorporating linear structural kinematics and the generalized Hooke’s law. These equations are solved in closed form for simply supported boundary conditions to obtain the buckling and vibration response. For the analysis, two types of FG sandwich plates are considered i.e., Type – A and Type – B. For the Type – A plate, the core and face sheets of the FG sandwich plate are made up of Ceramic and FG material, respectively. Whereas in case of Type- B plate, the core is composed of FG material, while the top and bottom face sheets are made up of ceramic and metal, respectively. The power law is employed to vary the material properties in the FG material. The evaluated results for the FG sandwich Type – A plate are compared with the already reported results in the literature wherever possible and are found in good agreement. The influence of the various parameters such as span to thickness (a/h), aspect ratio (a/b), power law index (p) and core thickness (schemes) are investigated on the dimensionless fundamental frequency and dimensionless critical buckling load of the FG sandwich plate, on those basis, noteworthy conclusions are drawn.

This paper considers the critical buckling and free vibration of functionally graded (FG) plates whose material properties vary continuously through the thickness. Such plates can be regarded as consisting of two phases, known as the matrix and reinforcement. The volume fraction of the reinforcement varies from zero to unity through the thickness of the plate, e.g. according to a power law, so that the composition is pure matrix material on the top surface and pure reinforcement material on the bottom surface. Applications include metal or ceramic components in aerospace and industrial applications which are required to withstand high temperature gradients. It has previously been shown [1,2] that critical buckling loads and natural frequencies of FG plates are proportional to those for homogeneous isotropic plates. Moreover, coupling between in-plane and out-of-plane behaviour can be eliminated by an appropriate choice of the neutral surface [3,4]. These ideas are extended in this paper to obtain an equivalent isotropic model for a FG plate so that it can be analysed using existing methods based on classical plate theory for homogeneous plates. Analytical expressions are derived for the thickness, Young's modulus, Poisson's ratio and (for a vibration problem) the density of the equivalent isotropic plate. The position of its neutral surface is defined in terms of an offset above the geometric mid-surface. These expressions are shown to give an exact equivalence when the matrix and reinforcement materials have the same Poisson's ratio, and otherwise a small approximation is introduced. The equivalent isotropic model is used to obtain critical buckling and undamped free vibration results for a simply supported square FG plate. The correctness and accuracy of the model are confirmed by comparing these results with well converged solutions from an approximate model in which the plate is divided into isotropic layers. Agreement is also demonstrated with theoretical predictions and results from the literature.

This paper presents a new active control method of sound radiated from a double-walled structure. The purpose of this study is to control of sound radiation power level using both of active noise control and active vibration control. First, modal coupling method is introduced which is required to model a vibro-acoustic coupling system. Then, optimal control laws of active noise control and active vibration control for minimizing the sound radiation power are derived in a vector form. Next, some numerical simulations are carried out to demonstrate the validity of the proposed method. As a result of the analysis, reduction of the sound power level is succeeded by feedforward control. Some numerical results show that active noise control is more effective than active vibration control for minimizing the sound power level. In addition, it is shown that by combination of the both control methods, improvement of a control performance is achieved. Furthermore, it is found that control effect rely on the relationship between placement of control sound sources and the disturbance location, while placement of control vibration source does not have significant impact on the control performance.

Transient response of rotating laminated functionally graded cylindrical shells in thermal environment

Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory

Material optimization of tri-directional functionally graded plates by using deep neural network and isogeometric multimesh design approach

Optimum distribution of materials for functionally graded rectangular plates considering thermal buckling

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

This paper is concerned with the coupled thermo-mechanical stress analysis of functionally graded (FG) gas turbine rotor shaft system. Gas turbine shaft may expose in high temperature environments which demands to use functionally graded materials (FGMs). The aim of the present work is to study the stresses developed in the FG turbine shaft due to temperature variations and mechanical loading due to unbalance masses. For the present analysis aluminum oxide (Al2O3) and stainless steel (SUS304) are taken as shaft materials, power law gradation is used for the determination of FG material properties of the turbine shaft. Three nodded Timoshenko beam element with six degree of freedom (DOF) per node is considered for the finite element modelling of FG shaft. First order shear deformation theory (FSDT) is used with rotary inertia, strain and kinetic energy. Solution for governing equation of motion is obtained by the Hamilton principle. Complete MATLAB code has been developed for thermosmechanical stress analysis. Comparative study between steel shaft and FG shaft have been carried out. Normal stress (σxx) on plane perpendicular to axial direction, shear stress (τxr) on plane perpendicular to axial direction in radial direction and shear stress (τxθ) on plane perpendicular to axial direction in circumferential direction are obtained against time and along radius of shaft. Also these stresses are obtained for different parameters like power law indexes and speed of rotation of shaft.