Vibration and Flutter of a Honeycomb Sandwich Plate with Zero Poisson’s Ratio

Junhua Zhang,Zhaochen Yan,Lili Xia

doi:10.3390/math9192528

Junhua Zhang, Zhaochen Yan + Show 1 more

Open Access

https://doi.org/10.3390/math9192528

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Abstract

A honeycomb is a kind of excellent lightweight structure and a honeycomb sandwich plate with zero Poisson’s ratio (ZPR) core is used widely in morphing structures. In this paper, a sandwich plate composed of a honeycomb core with zero Poisson’s ratio is analyzed for free vibrations and flutter under supersonic airflows. The equivalent elastic parametric formulas of the honeycomb core for zero Poisson’s ratio are proposed. The models are compared for their natural frequencies by theoretical and finite element methods respectively, which verifies the validity of the equivalent elastic parametric formulas and the model for the honeycomb sandwich plate with zero Poisson’s ratio. The influence of the geometric parameters of the honeycomb plate on the vibration frequencies is obtained. Three kinds of honeycomb cores, namely, regular hexagon, auxetic and hybrid with zero Poisson’s ratio, are compared through natural frequencies of the sandwich plate. It is found that the frequency of the zero Poisson’s ratio honeycomb sandwich plate is the second one when the other parameters are the same. The flutter of the honeycomb plate is analyzed by using the first order piston theory under supersonic flows. The critical flutter velocity of the plate is obtained, and the influence of geometric parameters of the honeycomb plate on the critical flutter velocities is obtained.

Highlights

Honeycomb structures have received extensive applications in engineering and daily life, such as aerospace, building, vehicle, and packaging, etc., as they have outstanding mechanical properties such as lightweight, low weight-to-stiffness ratios, good energy absorption characteristics, etc
The energy absorption of the honeycomb sandwich structure was increased by adding an absorbent agent to the Nomex honeycomb wall that was filled with polymer tube [1]
The model of the honeycomb sandwich plate with zero Poisson’s ratio is obtained through both the theoretical method and finite element method, which proves the accuracy of the equivalent elastic parameters of the honeycomb core layer and the validity of the model

Summary

Introduction

Honeycomb structures have received extensive applications in engineering and daily life, such as aerospace, building, vehicle, and packaging, etc., as they have outstanding mechanical properties such as lightweight, low weight-to-stiffness ratios, good energy absorption characteristics, etc. Olympio and Gandhi [7] proposed a sandwich skin for morphing aircraft, comprised of cellular honeycomb core with zero Poisson’s ratio and studied mechanical properties of the honeycomb. Liu et al [11] proposed a trapezoidal honeycomb with close-to-zero Poisson’s ratio and the effects of geometric parameters on the elastic properties of the structure were studied. Free vibrations and flutter under supersonic airflows of a honeycomb sandwich plate with zero Poisson’s ratio are analyzed. By substituting Equation (12) into Equation (11), the nonlinear dynamic equation of honeycomb sandwich plate with zero Poisson’s ratio in the form of displacement can be obtained

Calculation of Equivalent Elastic Parameters

Vibrational Frequencies of ZPR Honeycomb Plate

Flutter Analysis under Aerodynamic Forces

Conclusions