Abstract
In this work, we study the effect of the thickness variation of viscoelastic layer inserted in a laminated multi-layer beam in forced vibration on the vertical displacements and on the natural frequencies. The new structure is a sandwich structure composed by two external layers (top and bottom facesheets) of aluminum and viscoelastic core of 3M ISD112 polymers. The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. The finite element method including the viscoelastic model of fractional derivatives for modeling the sandwich structure is used. The system resolution of the nonlinear equations of motion of the sandwich structure is required to use a numerical integration method as the explicit method of Newmark to obtain the transient response. Also, ANSYS finite element modeling is applied to the sandwich structure to calculate the frequency response in harmonic vibration. The increase in the thickness of the viscoelastic layer leads to a decrease in the amplitudes of vibration. The natural frequencies found by the two methods are very close to the frequencies found experimentally in the literature.
Highlights
In recent years the research community has manifested a sound interest in the investigation of dynamic behavior of slightly damped structures [1,2,3]
In this work, we study the effect of the thickness variation of viscoelastic layer inserted in a laminated multi-layer beam in forced vibration on the vertical displacements and on the natural frequencies
The finite element method including the viscoelastic model of fractional derivatives for modeling the sandwich structure is used
Summary
In recent years the research community has manifested a sound interest in the investigation of dynamic behavior of slightly damped structures [1,2,3]. Galucio et al [17] developed a finite element formulation to analyze the transient dynamics of a sandwich beam with viscoelastic embedded layer whose material behavior was modeled with fractional derivative operators. They used the four-parameters model of Bagley and Torvik [15] to characterize the frequency-dependence of the viscoelastic layer. The algorithm of the Newmark method is already programmed in MATLAB to obtain the temporal response of the sandwich beam in transient vibration for different thicknesses of viscoelastic layer Another finite element modeling with ANSYS applied on the sandwich structure in free vibration to calculate the natural frequencies and harmonic vibration to calculate the frequency response.
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