Determination of the Steady-State Response of Viscoelastically Supported                 Rectangular Orthotropic Mass Loaded Plates by an Energy-Based Finite Difference Method

Journal of Vibration and Control

2009

The principal objective in this study is to investigate the special behaviors of linear vibrating plates with special parameters near degenerate modes. Near degenerate modes, plates may lack geometric stability because they exhibit a qualitatively different behavior under an arbitrarily small change in special parameters. The special parameters considered in this study are the location and quantity of an additional mass, which have an effect on removing the system symmetry. To this end, analyses are carried out for three plate systems with each having different boundary conditions. The effect of the location and the quantity of additional mass on degenerate modes are significantly different from those of other mode types. Clearly, these effects are of theoretical importance and should be taken into consideration in practical applications. With the view of the deterministic approach, it can be stated that the study determines some unspecified parts of forced vibration behaviors of mass loaded plates.

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Mass Based Imperfections on Behavior of Linear Vibrating Plates Near Degenerate Modes

Journal of Vibration and Control

2009

“…In another study carried out by Kocaturk et al (2005), point support as well as forced vibration analyses were applied to orthotropic rectangular plates by applying symmetric mass location for free and forced vibration analyses. Finally, Altintas and Bagci (2005) analyzed the free and forced vibration on viscoelastically supported anisotropic plates for different mass location and force application details.…”

Section: Introductionmentioning

confidence: 99%

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

Mechanics Based Design of Structures and Machines

Göktepe²

2007

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.

“…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. The results of the free vibration analysis showed that the increase of the non-structural additional mass could lead to the increase of the fundamental frequency value.…”

Section: Introductionmentioning

confidence: 99%

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

Ergüt

Journal of Vibration and Control

2012

In real world systems, implementation areas of mass, force and supports have considerable quantity, unlike homogenized areas in numerical solutions. In this study, the effect of area distributions of non-structural additional mass, external force and supports on linear vibrating plate systems are analyzed. There are two key questions addressed in this study. First, the majority of the previous works cover the range of a fundamental mode, and do not answer the question of how results of the fundamental analyses can be generalized for the higher modes based on investigated parameters, particularly for the case of forced vibration. Second, how structural safety is threatened by focused idealizations has not been adequately studied before. Numerical results of this study are obtained by using the variational difference method (VDM), which is based on a variational procedure in conjunction with traditional finite difference method. VDM is applied for determining free vibration characteristics and steady-state responses to a sinusoidally varying force applied to a viscoelastically supported plate. Because the results of the investigated systems showed that the vibration characteristics had a high sensitivity to analyzed parameters (the amount of area distributions of non-structural additional mass, external force and supports), the idealization process of areas must be attentively employed. The study provides insight not only for a fundamental mode but also for higher modes. Obviously the results of this deterministic study have showed that theoretical importance shall be considered in practical applications.