Influence of cross-sectional discontinuity on the damping characteristics of viscoelastically supported rectangular plates
Introduction
Vibrations of a structure excited by an impact source produce unwanted noises. Damping of these noises by attaching viscoelastic materials to a variety of mechanical structures has become a common method to reduce vibration and sound radiation [1], [2]. Selection of an optimal position for the attached constrained damping material was found to minimize the transverse vibration levels in a plate structure [3]. However, the mechanical properties of the absorbing materials (e.g., stiffness and damping ratio) can be easily affected by ambient temperature and excitation frequencies [1], [4]. In addition, this passive damping method may increase the size of the structure and manufacturing cost.
Another approach to reduce structural vibration is to change the cross-sectional geometry of the structures. Unlike attaching damping materials, changes in geometry are an efficient way to minimize vibration and noise generation or transmission without increasing weight. Vibration and sound radiation of stiffened structures has primarily been analyzed using numerical simulations [5], [6], [7].
Stiffened geometries have been adopted in many engineering applications. For instance, a stiffened plate was applied to reduce structure-borne sound in a gearbox housing [8]. An effective stiffener layout designed to provide low vibration and noise was investigated using a finite element model. Geometrical modifications of automotive-type panels were analyzed using a finite element model and were compared to the measured results [9]. Optimal geometries and respective locations were obtained to reduce radiated sound power. Sound transmission performance of stiffened curved aircraft panels [10] and sandwich panels [11] were also analyzed.
Recently, various periodic structures [12], [13], [14], [15] have been studied for vibration and noise reduction within the band stop frequencies based on locally resonant materials. Piezoelectric actuators [14], [15] were utilized to control the vibration localization. In this strategy, the propagating longitudinal and flexural waves were blocked by periodic structures, and transmission of energy was isolated accordingly. In the above studies, interactions between the structure and the boundaries were not considered because these works focused on vibration reduction in the structure itself.
Large mechanical systems such as automobiles, trains, and airplanes contain many sub-structures. Thinner panels made of high strength steels have been widely applied in such complex structures. These panels have various cross-sections that serve to enhance structural rigidity and improve acoustic performance. Vibration and sound radiation characteristics of these systems are significantly affected by both the cross-sectional geometry and boundary conditions. Optimal support conditions for minimum vibration response were obtained in a previous study for a viscoelastically supported plate [16]. An analytic model showed that energy dissipation at the plate edges was strongly related to the vibration response. Therefore, structural interactions among the sub-structures should be considered to increase damping.
In this paper, the influence of cross-sectional discontinuities on the damping characteristics of viscoelastically supported plates was investigated. To understand the different vibration responses due to discontinuity, experimental studies were performed using steel plates with continuous and discontinuous cross-sections. The tested plates were sub-panels in the body structure of an automotive vehicle. In the experiments, the plates were supported by viscoelastic materials at the edges to simulate the actual installation. The change in vibration response and damping characteristics were analyzed as a function of stiffness using a numerical model. Flexural wave propagation through the discontinuous cross-sections was analyzed to quantify the dissipation of vibration energy at the edge. The results showed an influence of the geometric parameters on the reflection ratios and the damping characteristics.
Section snippets
Measurement of forced vibration response of a continuous and discontinuous plate
Experiments were conducted to determine the effect of cross-sectional geometry in a rectangular plate on its vibration response. The experimental setups used to measure the responses of steel plates excited by a point impact source with and without discontinuities in the cross-section is shown in Fig. 1. A test plate – continuously stiffened in the length-wise direction (plate A1) is shown in Fig. 1(a). Plate B1 shown in Fig. 1(b), had discontinuous cross-sectional geometries contrary to plate
Numerical analysis
The Rayleigh–Ritz method was used to predict the vibration and damping of plates with and without discontinuous cross-sections. Fig. 5 shows models for the simplified plates used in the experiments as illustrated in Fig. 1(c) and (d). The variation in cross-sectional geometry in the length-wise and width-wise directions was analyzed by the change in the bending stiffness. The complex translational and rotational stiffnesses at the edges of the plates were used to analyze the boundary damping.
Numerical results
Fig. 7 shows the measured and predicted mode shapes of the simplified continuous and discontinuous plates A2 and B2. The plates were fastened by bolts at the edges and were excited by an impact hammer. The measured mode shapes are shown in Fig. 7(a) and (c). The predicted mode shapes shown in Fig. 7(b) and (d) were directly obtained from Eq. (10).
In the numerical analysis, the plate length (a), width (b), and thickness (h) were 1.04, 0.15 and 0.0012 m, respectively. The material density (ρ) of
Conclusions
In this study, the influence of cross-sectional discontinuities on the vibration characteristics of a viscoelastically supported plate was investigated. A systematically stiffened cross-section reduced the vibration and sound radiation of the plate. Using numerical analysis, the damping from the boundary was affected by the length-wise discontinuity of the plate. Changes in the damping characteristics induced from the viscoelastic support stiffness were analyzed using a flexural wave
Acknowledgments
This work was supported by a research program through the Hyundai Motor Company. The comments from reviewers are sincerely appreciated.
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