• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.2
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• pp.72-79
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• 2021

The present paper aims to set forth a two-dimensional theory for the dynamics of plates that is valid over a large range of excitation. To construct a dynamic plate theory within the long-wavelength approximation, two dimensional-reduction procedures must be used for analyzing the low- and high-frequency behaviors under the dynamic variational-asymptotic method. Moreover, a separate and logically independent step for the short-wavelength regime is introduced into the present approach to avoid violation of the positive definiteness of the derived energy functional and to facilitate qualitative description of the three-dimensional dispersion curve in the short-wavelength regime. Two examples are presented to demonstrate the capabilities and accuracy of all of the formulas derived herein by using various dispersion curves through comparison with the three-dimensional finite element method.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.7
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• pp.35-40
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• 2020

This work is concerned with various planar deformations of an isotropic sandwich beam, which generally consists of three layers: two stiff skin layers and one soft core layer. When one layer of the sandwich beam is modeled as a beam, the variational-asymptotic method is rigorously used to construct a zeroth-order beam model, which is similar to a generalized Timoshenko beam model capable of capturing the transverse shear deformations but still carries out the zeroth-order approximation. To analyze the planar sandwich beam, the sum of the energies of the two skin layers and one core layer is then formulated with different material and geometric properties and represented by a universal beam model in terms of the core-layer kinematics through interface displacement and stress continuity conditions. As a preliminary validation, two extreme examples are presented to demonstrate the capability and accuracy of this present approach.