This study examines the vibration response of imperfect functionally graded (FG) cylindrical shells reinforced with different types of eccentrically placed stiffeners. The material composition follows a power-law distribution, varying with different grading indices. The analysis is conducted analytically under simply supported boundary conditions, considering longitudinal and transverse stiffeners of circular, rectangular, and triangular cross-sections. The cylindrical shell, resting on an elastic foundation, is subjected to thermo-mechanical loading. The governing equations are derived using the first-order shear deformation theory, incorporating von Kármán-Donnell nonlinear geometric formulation and the smeared stiffener method. A numerical approach combining the fourth-order Runge-Kutta method and Galerkin's procedure is employed to evaluate the dynamic response and natural frequencies. Results reveal that increasing foundation stiffness enhances natural frequencies by 15% and reduces vibration amplitude. Conversely, elevated temperature leads to a 12% reduction in natural frequencies and a decrease in structural rigidity, highlighting the coupled effects of thermal and mechanical loads on the shell's dynamic behavior.

The purpose of this paper is developed a new model of photothermoelastic with memory-dependent derivatives (PMDD) under non-local (NL) parameter, dual phase lag (DPL) and hyperbolic two temperature (HTT). The governing coupled equations of the considered model with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of a half-space. Integral transform involving Laplace and Fourier transforms reduced the governing equations into ordinary differential equation. The arbitrary constants in the solution are determined by considering the loading environment on the surface. Three different categories of the sources are taken to explore the application as (i) normal force (ii) thermal source (iii) carrier density source. In the new domain, the closed form expressions of physical quantities like displacement, normal stress, conductive temperature field and carrier density distribution are derived. The numerical inversion method is employed to recover the results in a physical domain. The impact of non-local parameter, dual phase lag and hyperbolic two-temperature with and without MDD (memory dependent derivative) along with variations of all kernel functions on physical field variables are presented in form of graphs. Unique cases are also explored. The problem assumes great significance in an earthquake region when we think of variation of particle motion as a possible precursor for earthquake prediction. The results obtained are also helpful in designing the semiconductor materials in the course of coupled elastic, thermal, plasma waves and also find the application in the material and engineering sciences.

This paper addresses the plane stress problem of a cantilever functionally graded beam subjected to concentrated load. The material properties of the beam vary continuously through thickness, according to a power-law distribution of volume fraction. The existing solution focuses on resolving differential equations, but a new Airy function proposal is proposed. The paper examines the effect of material graduation on the degree of polynomial degree. A simple formulation developed to predict stress and displacement distributions relative to structural problems. The proposed model validated by comparison with existing literature, ensuring stability and resistance of the materials. A numerical example presented to show the effect of material inhomogeneity on the elastic field in a functionally graded cantilever beam.

This study uniquely investigates functionally graded nanoplates under combined partial loading and non-uniform elastic support, developing a quasi-3D model, a unified analytical framework for complex foundations, and novel closed-form solutions, thereby addressing a critical yet underexplored area in structural mechanics. A simplified quasi-3D high-order shear deformation theory incorporating integral terms is used. The governing equilibrium equations consider the interaction between the loading type and the variation of Winkler-Pasternak and Kerr foundation parameters. The numerical results for non-dimensional stresses and displacements are obtained using the virtual displacement principle and Navier's solution technique. The accuracy of the non-dimensional formulas is validated against existing literature, demonstrating excellent agreement. Additionally, several parametric studies examine the effects of various geometric and material factors. This analytical model is well suited for analyzing the bending behaviour of simply supported FG plates in specific engineering applications.