ANALYTICAL SOLUTIONS USING HIGH ORDER COMPOSITE LAMINATE THEORY FOR HONEYCOMB SANDWICH PLATES WITH VISCOELASTIC FREQUENCY DEPENDENT DAMPING

Analytical methods allow parametric changes in geometric and material properties of a honeycomb sandwich plate for studies of stiffness, mass, and damping characteristics with low computational cost. However, studies based on analytical methods are still limited with frequency independent damping models. Specifically, previous analytical models have not consider the frequency dependent damping for viscoelastic honeycomb core sandwich composites, while some work has been done on studying the honeycomb sandwich plate using finite element method, which can be computationally expensive for multiple parameter studies. Therefore, in this work, the honeycomb sandwich plate is studied analytically based on the cellular material theory, together with composite laminate theory. In initial analytical studies, first-order shear deformation theory (FSDT) is used for symmetric honeycomb sandwich plate in order to capture important transverse shear effects in the core. In order to obtain a frequency response which includes frequency dependent viscoelastic damping properties, the study is based on a time harmonic analysis of the sandwich plate in the frequency domain. Two materials are compared for the core; aluminum and polycarbonate. For the aluminum honeycomb core, frequency independent damping is included and results compared with the results of different damping ratios. For the polycarbonate honeycomb core, the viscoelastic behavior is modeled using the generalized Maxwell damping model expressed in terms of the Prony series. The study begins with a simplified case of a simply supported honeycomb sandwich plate subject to a uniform distributed transverse time harmonic loading, which has infinite length such that the deformation in the width direction is independent of the length. The undamped natural frequencies are also derived analytically based on the free vibration problem and compared to the damped resonance frequencies in the frequency response of the plate. Comparisons are made between regular and two types of auxetic honeycomb cores. Regular honeycomb is defined by cellular geometry with effective Poisson\u27s ratio of approximately one, whereas auxetic honeycomb has negative Poisson\u27s ratio. Both regular and auxetic have special orthotropic properties. The case study is then generalized to a simply-supported sandwich honeycomb plate for a two dimensional problem. The response of the sandwich plate with regular honeycomb core is then compared with the responses of the two types of auxetic cores. Results for frequency response show shifts in resonance frequencies due to differences in stiffness and mass of the sandwich plate with different cores. Results from a composite sandwich plate finite element model using ANSYS with effective honeycomb core orthotropic properties was used to validate the analytical models in the case of no damping. A refined higher order shear deformation theory (RSDT), based on a piecewise kinematic axial displacement component assumption, for sandwich honeycomb composite beam model is also compared to a model based on FSDT. Results show that the RSDT is more accurate at higher frequencies

Fine arts in Solow model: a clarification

This paper shows that the Saito version of Solow growth model contains an error. It corrects this error. It further applies some built-in functions of Mathematica to the correct version of Solow economic growth model and derives some interesting graphs from the Solow convergent paths.Solow growth model