Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

Zhou, Ding; Ji, Tianjian

doi:10.1155/2012/983576

Cited by 10 publications

(6 citation statements)

References 21 publications

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“…Thus, the problems of solving the modal parameters (eigenfrequencies and eigenvectors) of the floor can be translated into those of solving eigenvalues from equation 7. 21 According to equation 7, one can find that the eigenfrequencies of the floor are affected by the stiffness of the elastic supports. Therefore, tuning the stiffness of the elastic supports will change the eigenfrequencies of the floor, and the eigenfrequencies of the floor may shift from its original frequency range of the resonance.…”

Section: Floor Vibration Reduction Analysismentioning

confidence: 99%

“…The differential equation of the wood plank can be written as follows 21 where ∇4=∂4/∂x4+2∂4/∂x2∂y2+∂4/∂y4 is the differential operator; wtrue(x,ytrue) is the vertical displacement of the floor; D is the bending stiffness of the floor; ρ is the density of the floor material; trueh¯ is the thickness; ω is the circular frequency. Boundary conditions are introduced to solve equation (5).…”

Section: Floor Vibration Reduction Analysismentioning

confidence: 99%

“…Thus, the problems of solving the modal parameters (eigenfrequencies and eigenvectors) of the floor can be translated into those of solving eigenvalues from equation (7). 21…”

Section: Floor Vibration Reduction Analysismentioning

confidence: 99%

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Car body floor vibration of high-speed railway vehicles and its reduction

Gong

Wang

Duan

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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An on-site test has been performed to address the problem of feet numbness caused by the floor vibration of high-speed railway vehicles. Analysis of the floor vibration performance indicates that the vibration of the car body chassis transmitted to the floor by the elastic supports is significantly amplified in the frequency range of 20-50 Hz. This overlaps with the frequency range in which human lower extremities are most sensitive, leading to feet numbness. A refined finite element model of the car body, including the floor panels is developed to further study the vibration mechanism of the floor. Results show that due to the inappropriate design of the elastic support stiffness, the deformations of the floor above the bogie centre for several typical modes in the frequency range of 20-50 Hz are significantly amplified. When the excitation frequencies transmitted from the car body chassis were close to the eigenfrequencies of the floor, the local resonance of the floor will occur, which is the root cause of human feet numbness. The dynamic stiffness of the elastic support is further optimised, and the experimental verification shows that the vibration transmissibility from the car body chassis to the floor in the frequency range of 20-50 Hz has been significantly reduced, and the problem of feet numbness has been solved.

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Section: Floor Vibration Reduction Analysismentioning

confidence: 99%

Section: Floor Vibration Reduction Analysismentioning

confidence: 99%

See 1 more Smart Citation

Car body floor vibration of high-speed railway vehicles and its reduction

Gong

Wang

Duan

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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show abstract

“…Depending on the types of structural elements (rod and shell), two methods were developed, namely asymptotic and variational, which are presented by Le [7] from a mathematical point of view, emphasizing the formulation of boundary-value problems. Zhou [8] presents an exact solution of free vibration of a thin rectangular plate attached with sprung masses based on differential equations.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of a Guitar considered as a Symmetrical Mechanical System

2019

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This paper aimed to use the symmetry that exists to the body of a guitar to ease the analysis behavior to vibrations. Symmetries can produce interesting properties when studying the dynamic and steady-state response of such systems. These properties can, in some cases, considerably decrease the effort made for dynamic analysis at the design stage. For a real guitar, these properties are used to determine the eigenvalues and eigenvectors. Finite element method (FEM) is used for a numerical modeling and to prove the theoretically determined properties in this case. In this paper, different types of guitar plates related to symmetrical reinforcement patterns were studied in terms of modal analysis performed using finite element analysis (FEA). The dynamic response differs in terms of amplitude, eigenvalues, modal shapes in accordance with number and pattern of stiffening bars. In this study, the symmetrical and asymmetric modes of modal analysis were highlighted in the case of constructive symmetrical structures.Symmetry 2019, 11, 727 2 of 16 symmetrical system of the guitar is analyzed and the vibration properties that are the result of considering this symmetry are revealed. An example for a real system is made in the second part of the paper. Derveaux et al. [9] developed a guitar model based on advanced numerical methods to simulate the three-dimensional sound-pressure field of a guitar in the time domain. Due to the complexity of the problem, the main parts of guitar (plates, body, strings, air from cavity, holes) that are implied in acoustic radiation and vibration were simplified in terms of mathematical models and interactions. Compare to [9], in this paper, the frequency spectrum and eigenmodes of different symmetric types of guitar plates were analyzed and in future works, the guitars bodies with different bars pattern will be numerical modeled. Elejabarrieta et al. [10] analyzed the influence of each component from acoustic box of guitar on the vibrational behavior using finite element method in a progressive manner of constructive system.These types of problems occur frequently in practical applications; many mechanical systems exhibit different kinds of symmetry properties, resulting from a design process for constructive, simplistic, logistic or cost considerations. Knowing these properties allows to increase the precision of calculations in such issues. Properties determined by symmetries have been observed by researchers and are mainly used in the static analysis. They are presented in the classical courses of Strength of Material or Structural Analysis. From a historical point of view, the symmetries in mechanics have been studied by mathematicians [11,12]. Symmetry effects occur in the writing the motion equations, but the solutions can be symmetric and antisymmetric according to the assumed boundary conditions [7]. In accordance with [13], the methods of mechanics (Lagrangian and Hamiltonian) use symmetry to solve complex problems. Moreover, these methods and symmetry principles are based on the ...

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“…It is therefore important for design engineers to have a broad understanding on the dynamic behaviour of thin plate when submerged in fluid and when it is rested on an elastic foundation. In the study of free vibration of rectangular plates, Zhous and Ji [1] applied exact method to determine the analytical solution. Merneedi and Raonalluri [2] investigated vibration analysis of plate with cut-out using semi-analytical method.…”

Section: Introductionmentioning

confidence: 99%