Buckling Behavior of Thick Porous FGM Toroidal Shell Segments Under External Pressure and Elevated Temperature Including Tangential Edge Restraint

Owing to mathematical and geometrical complexities, there is an evident lack of stability analyses of thick closed shell structures with porosity. The present work aims to analyze the effects of porosities, elasticity of edge constraint and surrounding elastic media on the buckling resistance capacity of thick functionally graded material (FGM) toroidal shell segments subjected to external pressure, elevated temperature and the combined action of these loads. The volume fractions of constituents are varied across the thickness according to power law functions and effective properties of the FGM are determined using a modified rule of mixture. The porosities exist in the FGM through even and uneven distributions. Governing equations are based on a higher order shear deformation theory taking into account interactive pressure from surrounding elastic media. These equations are analytically solved and closed-form expressions of buckling loads are derived adopting the two-term form of deflection along with Galerkin method. Parametric studies indicate that the porosities have beneficial and deteriorative influences on the buckling resistance capacity of thermally loaded and pressure loaded porous FGM toroidal shell segments, respectively. Furthermore, tangential constraints of edges lower the buckling resistance capacity of the shells, especially at elevated temperatures.

Functionally graded viscoelastic core characteristics on vibroacoustic behavior of double-walled cylindrical shells in a subsonic external flow

The present study is concerned with an analytical solution for calculating sound transmission loss through an infinite double-walled circular cylindrical shell with two isotropic skins and a polymeric foam core. Accordingly, the two-walled cylindrical shell is stimulated applying an acoustic oblique plane wave. The equations of motion are derived according to Hamilton’s principle using the first-order shear deformation theory for every three layers of the construction. Additionally, by the aid of employing the Zener mathematical model for the core of polymeric foam, mechanical properties are determined. To authenticate the results of this study, the damping of the core layer goes to zero. Therefore, the numerical results in this special case are compared with those of isotropic shells. The results prove that the presented model has high accuracy. It is also designated that decreasing the power-law exponent of the core leads to improving the sound transmission loss through the thickness of the construction. Besides, in addition to probe some configurations versus alterations of frequencies and dimensions, the convergence algorithm is provided. Consequently, it is realized that by increasing the excitation frequency, the minimum number of modes to find the convergence conditions is enhanced. The results also contain a comparison between the sound transmission loss coefficient for four different models of a core of a sandwiched cylindrical shell. It is comprehended that the presented model has a transmission loss coefficient more than the other types of the core at high frequencies.

Free Vibration of Composite Cylindrical Shells Based on Third-Order Shear Deformation Theory

The focus of this study is to analyse the free vibration of cylindrical shells under third-order shear deformation theory (TSDT). The constitutive equations of the cylindrical shells are obtained using third-order shear deformation theory (TSDT). The surface and traverse displacements are expected to have cubic and quadratic variation. Spline approximation is used to approximate the displacements and transverse rotations. The resulting generalized eigenvalue problem is solved for the frequency parameter to get as many eigenfrequencies as required starting from the least. From the eigenvectors, the spline coefficients are computed from which the mode shapes are constructed. The frequency of cylindrical shells is analysed by varying circumferential node number, length dimension, layer number, and different materials. The authenticity of the present formulation is established by comparing with the available FEM results.

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

Forced Vibration Analysis of Laminated Composite Plates under the Action of a Moving Vehicle

This paper provides a finite element analysis of laminated composite plates under the action of a moving vehicle. The vehicle is modeled as a rigid body with four suspension systems, each consisting of a spring-dashpot. Overall, the vehicle possesses three degrees of freedom: vertical, rolling, and pitching motions. The equations of motion of the plate are deduced based on first-order shear deformation theory. Using the Euler-Lagrange equations, the system of coupled equations of motion is extracted and solved by using the Newmark time discretization scheme. The algorithm is validated through the comparison of both the free and forced vibration results provided by the present model and exact or numerical results reported in the literature. The effects are investigated of several system parameters on the dynamic response.

Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

This research is based on higher-order shear deformation theory to analyse the free vibration of composite annular circular plates using the spline approximation technique. Equilibrium equations are derived, and differential equations in terms of displacement and rotational functions are obtained. Cubic or quantic spline is used to approximate the displacement and rotational functions depending upon the order of these functions. A generalized eigenvalue problem is obtained and solved numerically for eigenfrequency parameter and associated eigenvector of spline coefficients. Frequency of annular circular plates with different numbers of layers with each layer consisting of different materials is analysed. The effect of geometric and material parameters on frequency value is investigated for simply supported condition. A comparative study with existing results narrates the validity of the present results. Graphs and tables depict the obtained results. Some figures and graphs are drawn by using Autodesk Maya and Matlab software.