The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems^#

Abstract

The rapid growth in anisotropic material (such as composite materials) usage marks a new era in material science. Obviously, in order to understand the physical behavior of structural systems constituted by composite materials, several parameters, such as natural frequencies, mode shapes, and transmissiblities, must be incorporated into anisotropic elastic analyses. Orthotropy, as a special case of anisotropy, is common in almost all fields of civil and mechanical engineering. The objective of this effort is to investigate the effect of orthotropy on the behavior of vibrating plate systems near degenerate modes. A degenerate plate may be lack of geometric stability since the plate may exhibit a qualitatively different behavior under an arbitrarily small change in special parameters. The special parameters considered in this study are orthotropy and the location of additional mass, which have the effect of removing the system symmetry. The method, which depends on a variational procedure in conjunction with a finite difference method, is employed to examine free vibration characteristics as well as to characterize steady state response to a sinusoidally varying force applied to orthotrophic elastic rectangular plate. The problem is reduced to the solution of a system consisting of algebraic equations by using the variational difference method (VDM). In order to sort the effect of orthotropy on the vibration behavior from other factors, locations of external force, and mass are treated as additional parameters 364 Altintas and Goktepe in the analyses. Furthermore, supports are constituted as elastic so as to be able to obtain force transmissibility curves. Finally, plate systems having two different boundary conditions, namely elastically supported and elastically point supported, are utilized to observe the generalization of the outcomes. Results reveal that in case of material orthotropy existence in a plate system, there are several keynote issues that must be taken into account in vibration analyses, which are not important under isotropic conditions. Obviously, these effects are of theoretical importance and should be considered in practical applications.

Effect of application area distributions of mass, force, and support on free and forced vibration behavior of viscoelastically supported plates

“…The method with implementation of an interlacing grid technique which is about vibrating plate problems was examined by Aksu and Felemban (1992) and Aksu and Al-Kaabi (1987). Using a similar technique, free and forced vibration analysis of viscoelastically supported plates was investigated by Kocatu¨rk and Altintas ( 2003), Altintas andBagci (2004, 2005), Altintas and Goktepe (2007) and Altintas (2009). The numerical method based on VDM by which the analyses have been applied in this study is described briefly.…”

“…In the three particular cases studied by Wong (2002), it was reported that the added mass would reduce the amplitude of an antinode close to it and all vibration antinodes around the added mass would appear to be shifted towards the loaded region. Altintas and Goktepe (2007) studied free vibration analysis for the location of mass and forced vibration analysis for both the location of mass and force. The findings of the free vibration part of that study support those of Wong's (2002) study.…”

“…The findings of the free vibration part of that study support those of Wong's (2002) study. Crucially, the distinct differences between the effects of mass and force location on vibrating plate were found by Altintas and Goktepe (2007), where the location of the additional mass was reported to be a more significant parameter than external force location for the occurrence of the peaks on the force transmissibility curves. Altintas and Bagci (2005) analyzed the effects of variation of the distributed mass area on the characteristics of free and also forced vibrations in the range of the fundamental mode.…”

Analysis of human-induced vibrations in a lightweight framework

“…The structural damping also decreases due to the lack of vibration-absorbing materials. Moreover, these kinds of frameworks usually employ orthotropic materials, whose dynamic behavior varies significantly from isotropic ones [1]. All these factors can produce an inappropriate vibration response to daily activity loads, i.e., human walking forces, machinery, etc.…”