Design of Corrugated Plates for Optimal Fundamental Frequency

Abstract

This paper investigates shifting the fundamental frequency of plate structures by corrugation. Creating corrugations significantly improves the flexural rigidities of plate and hence increases its natural frequencies. Two types of corrugations are investigated: sinusoidal and trapezoidal corrugations. The finite element method (FEM) is used to model the corrugated plates and extract the natural frequencies and mode shapes. The effects of corrugation geometrical parameters on simply supported plate fundamental frequency are studied. To reduce the computation time, the corrugated plates are modeled as orthotropic flat plates with equivalent rigidities. To demonstrate the validity of modeling the corrugated plates as orthotropic flat plates in studying the free vibration characteristics, a comparison between the results of finite element model and equivalent orthotropic models is made. A correspondence between the results of orthotropic models and the FE models is observed. The optimal designs of sinusoidal and trapezoidal corrugated plates are obtained based on a genetic algorithm. The optimization results show that plate corrugations can efficiently maximize plate fundamental frequency. It is found that the trapezoidal corrugation can more efficiently enhance the fundamental frequency of simply supported plate than the sinusoidal corrugation.

Shape adaptation of beams (1D) and plates (2D) to maximise eigenfrequencies

“…23 An optimum distribution of sinusoidal and trapezoidal corrugations was studied in order to shift the fundamental frequency to maximum values. 30…”

“…23 An optimum distribution of sinusoidal and trapezoidal corrugations was studied in order to shift the fundamental frequency to maximum values. 30 It can be concluded that many different approaches have already been studied to maximise the eigenfrequencies of different structures. However, structural optimisations like topology and shape optimisations are often time consuming and require high computational effort.…”

Optimal design of a functionally graded corrugated cylindrical shell subjected to axisymmetric loading

“…Since the longitudinal deformation implied by the external load q x is statically determinate, we study only the case of bending deformation governed by the load q z . For this purpose, the bending components of projection of the displacements u b , w b are presented as follows [30]…”

“…Therefore, the key and most important problem is formulation and then effective solution of the problem of optimal design of the FG corrugated shells. Employment of numerical approaches for optimal design of FG corrugations implies occurrence of numerous difficulties in the sense of the time-consuming computations [26][27][28][29][30][31][32][33]. The homogenization approach seems to be promising in this case [34][35][36][37].…”

Design and Numerical Analysis of Corrugated Helmet Under Impact Test

“…Where E is the modulus of elasticity of plate material, ѵ is the Poisson's ratio of plate material C is the corrugation pitch; F is the height of corrugation; λ is the developed length of unit corrugation, and h is the thickness of corrugation direction [22].…”