An Analytical Solution for Nonlinear Vibrations Analysis of Functionally Graded Plate Using Modified Lindstedt–Poincare Method

Abstract

In this research, the nonlinear free vibrations analysis of functionally graded (FG) rectangular plate which simply supported all edges are investigated analytically using modified Lindstedt–Poincare (MLP) method for the first time. For this purpose, with the aid of von Karman nonlinearity strain-displacement relations, the partial differential equations of motion are developed based on first-order shear deformation theory (FSDT). Afterward, by applying Galerkin method, the nonlinear partial differential equations are transformed into the time-dependent nonlinear ordinary differential equations. The nonlinear equation of motion is then solved analytically by MLP method to determine the nonlinear frequencies of the FG rectangular plate. The material properties are assumed to be graded through the direction of plate thickness according to power law distribution. The effects of some system parameters such as vibration amplitude, volume fraction index and aspect ratio on the nonlinear to linear frequency ratio are discussed in detail. To validate the analysis, the results of this paper are compared with both the published data and numerical method, and good agreements are found.

Experimental investigation of mechanical properties of Kevlar fiber composite sandwich panel with truss core reinforced bynano‐SiO2

“…To find the compression strength of the composite sandwich panel, single laps flatwise compression test is implemented on the sandwich panels according to the guidelines presented in the ASTM‐C365. [ 44 ] To perform the uniform compression test, the samples with an area of 100 mm × 100 mm × 38 mm are put on a self‐aligning spherical bearing block. The movable head of the machine applies pressure on the top of the sandwich panel until the failure of the core occurs.…”

Experimental and numerical investigation of high‐velocity impact effects on composite sandwich panel with M‐shaped core reinforced by nano‐SiO2

“…Sandwich panels are widely used in various applications, including transportation, automotive, ship industries, civil infrastructures, wind turbine blades, owing to their extraordinary mechanical properties and multifunctional design ability. A typical sandwich panel is often manufactured by bonding two thin, stiff, and robust plates [1][2][3][4][5][6][7] to both sides of a thick lightweight core. Skins are frequently made of metal alloys and fiber-reinforced polymers (e.g., CFRP [carbon fiber reinforced polymer] and GFRP [glass fiber reinforced polymer]) to bear flexural and compressive loads.…”

An experimental and numerical study on the vibration characteristics of glass fiber composite sandwich panel with lattice cores

“…Correspondingly, large quantities of research have been performed on the vibration and dynamic behavior of continuous structures such as plates. 2–8 Some researchers have specifically worked on the vibration characteristics of the composite sandwich panels, some of which are mentioned in this section. Li et al 9 investigated the vibration response of metallic sandwich panels with hourglass truss cores by comparing it with the traditional pyramidal sandwich structure.…”