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

Abstract

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.

Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support

“…For one-dimensional beam structure, Şimşek and Kocatürk (2009) investigated the free and forced vibrations of an FG simply supported beam subjected to concentrated moving harmonic load. Ergut and Altintas (2013) presented the effect of application area distributions of mass, force, and support on free and forced vibration behaviors of viscoelastically supported plates. Demir and Oz (2014) exploited the finite element method (FEM) to investigate resonance frequencies of the FG beam under viscoelastic boundary conditions.…”

Quality factor of circular microdiaphragm with surface effects in contact with liquids

“…Later, Lamb’s model was revised by Amabili and Kwak [33] to study the coupled free vibration of circular plates. In recent years, various extended coupling vibration models have been developed to investigate the vibrations of rectangular and circular plates at the macroscale [34, 35]. Experiments have proved that Lamb’s theoretical vibration model of plates is also applicable to microscale structures [36].…”