Modal Analysis of Composite Structures With Damping Material

Abstract

Modal Analysis of Composite Structures with Damping Material Kellie TremaineThe purpose of this study is to develop an analytical solution for modal analysis of actively damped orthotropic composite plates in bending and to verify it with experimental analysis.The analytical modal analysis solution for composite plate dynamics is derived using Euler theory. This analysis applies to structures with orthotropic lamina of uniform material properties at any lamination angle. The bending-extensional coupling can be neglected for plates that are symmetric or approximately symmetric, which allows an exact solution for natural frequency and mode shape to be obtained. An exact solution can be found for natural vibration and in general.The active control is modeled analytically by combining the Lagrange equation with the Ritz Assumed Mode method. This analysis produces a generalized coordinate vector that correlates the assumed mode to the particular amplitude of a particular case. The kinetic energy dissipated by the piezoelectric actuator from the system over one oscillation can be calculated from the generalized coordinate vector and the assumed mode. The equivalent damping ratio of the active control system is calculated as the ratio between the kinetic energy absorbed by the piezoelectric actuator from the system in one oscillation and the maximum strain energy of the system during that oscillation.A point mass on the plate, such as an accelerometer mass, can also be modeled as a single layer of uniform mass, that is an isotropic layer, by equating the potential energy of the point mass with the potential energy of the uniform mass layer. It is important to note that the mass of the isotropic layer is frequency dependent, and it has no effect on the plate stiffness.The analytical model is validated by comparison to experimental work. The samples studied were aluminum and composite plates of various lengths. The active control predictions were also validated using previous experimental work completed at California Polytechnic State University in San Luis Obispo. These cases included active control of an aluminum beam with a patch of piezoelectric material and an aluminum sailplane with a patch of piezoelectric material.v Results indicate that while the analytical mode solutions are in good agreement with the experimental results, they are also systematically higher than the experimental results. The analytical active control solutions match previous work when the piezoelectric effects are linear. The main result of adding an active control system is approximately a 5-10% increase in modal frequencies and a 200-800% increase of damping ratio.

Analysis of Impacting Wave using Piezoelectric Sensor for a Pressurized Thin Aluminum Plate Covered with a Composite Material

“…Impulsive forces are those generated when a steel ball hit a metallic aluminum plate (with and without coating), typical time intervals of impulses occur during the impact start from 0.18-0.2 msec for steel impacted test (Young and Budynas, 2002;Peraire and Widnall, 2003). Piezoelectric sensor is used in experiments with an error between 3.0 and 7.5% error in the experimental frequencies which is lower than the analytical solution using vibrational equations for the aluminum plate shaker testing and the dynamics parameters of composites plate with the bending modal frequencies are solved by Euler theory which predicts tends to be about 5% larger than experimental results in deflection for any amplitude and frequency in plate testing with the Ritz assumption mode method for analytical solution for the effective of damping ratio as a ratio of energy absorbed to total system energy which predicts linear piezoelectric effects (Tremaine, 2012). Polystyrene, low density polyethylene, polypropylene and poly methacrylate are the polymer materials which are investigated under the impact test and performed at room temperature according to ISO 179 each sample was tested for 3 times and average results have been reported and represented that the increasing of PP content in polymer makes the impact properties and fracture toughness increases for blends system (Salih et al, 2015).…”

Effects of stacking sequences and longitudinal parameter on the dynamic characteristics of multilayer glass epoxy composite

“…In this regard, Hemanshu et al [2] carried out an analysis to understand the dynamic behaviour of composite beams considering the different boundary configurations and stacking sequences. Another study was conducted by Tremaine et al [3] in which analytical formulation was proposed for the damped orthotropic composite material to determine the vibrational characteritics and later they compared the analytical solution with the experiment. For this study, glass fibers and epoxy resin are combined.…”

The Effect of Sensor Mass, Sensor Location, and Delamination Location of Different Composite Structures Under Dynamic Loading

“…The damping materials implemented in the composite plates provided changes in damping characteristics and the coupled resonance response. [14] Rider discovered the effects of damage arrestment devices (DADs) on the structural response of composite plates and composite sandwiches. The DADs greatly improved vibration and flexural characteristics of delaminated and impacted composite specimens.…”

“…Poisson's ratio was similar to those found in previous research efforts. [12][13] [14] The experimental Poisson's ratio was the value used in material properties for theoretical analysis of the test specimen.…”