Vibro-Acoustic Response of Aerospace Structure Under Non-Uniform Edge Loads: an Analytical Investigation

Abstract

Analytical investigation carried on vibro-acoustic characteristics of plates under different non-uniform uniaxial edge loads, subjected to steady-state mechanical and acoustic waves excitation is presented. Owing to their high stiffness to weight ratio, these functionally graded-graphene reinforced nanocomposites (FG-GRC) are used as structural members in unified wing aircrafts, space launchers etc., these Graphene reinforced nanocomposites plate is assumed to be a layered structure, in which weight fraction (WGNP) of the graphene nanoplatelets (GNPs) continuously vary in each layer through the plate thickness. It is also assumed that GNPs are evenly distributed in longitudinal direction, but randomly slanted towards the transverse direction of plate. By using 2D continuum orthotropic plate model, the effective material properties of graphene reinforced nanocomposites with different grading pattern/weight fraction of GNPs are obtained by combining the modified Halpin-Tsai model and rule of mixture. In order to model the porous graphene reinforced nanocomposites, closed-cell cellular solids under Gaussian Random Field (GRF) are used. An analytical method based on the strain energy approach is adopted to estimate the buckling load (Pcr). Free and forced vibration responses of the plate are obtained, by using an analytical method based on Reddy’s third-order shear deformation theorem (TSDT). Further, vibration response of the plate is given as an input to the Rayleigh integral code built-in-house using MATLAB® to obtain the acoustic response characteristics. Validation studies carried out to ensure the accuracy of results based on 2D continuum orthotropic plate model. The predicted buckling, vibration and acoustic characteristic results of graphene reinforced nanocomposites plates by using the 2D continuum orthotropic plate model is compared with the published results and shows the good agreement with the present approach. iv Initially, influence of non-uniform uniaxial edge (NUE) loads on vibration and acoustic response isotropic plates is investigated. The results reveals that the buckling load (Pcr) is significantly influenced by the nature of NUE loads. Similarly, natural frequencies reduce with an increase in axial compressive load due to a reduction in structural stiffness. Vibration and acoustic resonant amplitudes are affected by the intensity of the compressive load. Sound transmission loss reduces with an increase in compressive load magnitude and the effect is significant in the stiffness dominant region. Followed by this, free vibration and buckling characteristics of graphene reinforced nanocomposites under the different NUE loads, four distinctive gradings (i.e., UD, X, O, and C patterns of GNPs) and different WGNP are studied. Results revealed that buckling and free vibration behaviour of the plate is significantly influenced by the GNPs dispersion pattern and weight fraction under non-uniform edge loads. It is also observed that buckling mode and the fundamental vibration mode of the plate under combined tensile-compression load (i.e., load factor (α) = 2) is entirely different from the other NUE load cases. Furthermore, to understand the vibro-acoustic characteristics of graphene reinforced nanocomposites under the different NUE loads, same grading patterns and different WGNP have been selected from the previous studies on free vibration and buckling characteristics. It is found that, the nature of edge load variation on buckling and vibro-acoustic response is significant. Free vibration mode shape changes with an increase in edge load and consequently affects the resonant amplitude of responses also especially for the plates with a higher aspect ratio. WGNP and dispersion grading pattern of GNPs also influences the resonance amplitudes. Plate with FG-GRCC dispersion pattern and higher WGNP has improved buckling and vibro-acoustic response behaviour. Similarly, change in sound transmission loss level is significant in the stiffness region compared to the damping and mass dominated region. Finally, a detailed investigation of porosity grading and coefficients on vibro- acoustic characteristics of graphene reinforced nanocomposites under the different NUE loads is presented. Three types of porous distribution patterns, in which the porosity changes latterly the thickness bearing of the graphene reinforced v nanocomposites, are considered. Plates with porosity is less at the surface and more at the centre is termed as VPC (increasing porosity towards the centre). Plates with less porosity at the centre and more at the surfaces is termed as VPS (increasing porosity towards the surface) and the plate with uniform porosity is termed as UP. It is observed that, the WGNP and grading pattern of GNPs reinforcement causes the stiffness hardening effect, whereas porosity distribution and coefficients cause the stiffness softening effect on the graphene reinforced nanocomposite plate. It is found that the plate with symmetric distribution of GNPs with more concentration at the surface and symmetric porosity variation with more porosity at the centre radiates less sound power (i.e., with higher WGNP%).