Wave Propagation in Structures

Doyle, James F.

doi:10.1007/978-1-4684-0344-2_6

Cited by 236 publications

(296 citation statements)

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“…This will be done in the next section. The equilibrium equations for the circular beam in cylindrical coordinates may be written as [3,4]:…”

Section: Circular Beam Spectral Elementmentioning

confidence: 99%

“…The spectral components of the axial force, bending moment and transverse shear force are given by [3],…”

Section: Circular Beam Spectral Elementmentioning

confidence: 99%

“…Simple ring models are derived using the spectral element approach [3] and the implementation of a rotating force in such a model is discussed. First, a simple circular beam spectral element is derived and validated by comparing the frequency response to a point force with the analytical solution.…”

Section: Introductionmentioning

confidence: 99%

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Simple Models for the Dynamic Modeling of Rotating Tires

Delamotte

Nascimento

Arruda

2008

Shock and Vibration

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Abstract. Large Finite Element (FE) models of tires are currently used to predict low frequency behavior and to obtain dynamic model coefficients used in multi-body models for riding and comfort. However, to predict higher frequency behavior, which may explain irregular wear, critical rotating speeds and noise radiation, FE models are not practical. Detailed FE models are not adequate for optimization and uncertainty predictions either, as in such applications the dynamic solution must be computed a number of times. Therefore, there is a need for simpler models that can capture the physics of the tire and be used to compute the dynamic response with a low computational cost. In this paper, the spectral (or continuous) element approach is used to derive such a model. A circular beam spectral element that takes into account the string effect is derived, and a method to simulate the response to a rotating force is implemented in the frequency domain. The behavior of a circular ring under different internal pressures is investigated using modal and frequency/wavenumber representations. Experimental results obtained with a real untreaded truck tire are presented and qualitatively compared with the simple model predictions with good agreement. No attempt is made to obtain equivalent parameters for the simple model from the real tire results. On the other hand, the simple model fails to represent the correct variation of the quotient of the natural frequency by the number of circumferential wavelengths with the mode count. Nevertheless, some important features of the real tire dynamic behavior, such as the generation of standing waves and part of the frequency/wavenumber behavior, can be investigated using the proposed simplified model.

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“…This will be done in the next section. The equilibrium equations for the circular beam in cylindrical coordinates may be written as [3,4]:…”

Section: Circular Beam Spectral Elementmentioning

confidence: 99%

“…The spectral components of the axial force, bending moment and transverse shear force are given by [3],…”

Section: Circular Beam Spectral Elementmentioning

confidence: 99%

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Simple Models for the Dynamic Modeling of Rotating Tires

Delamotte

Nascimento

Arruda

2008

Shock and Vibration

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“…For 1-d problems describing the axial and flexural waves in bars and beams, there is one element, called Spectral Element (SE), which may satisfy analytically the SRC [20]. The complex non-standing solution described in figure 4 represents a combination of a vibrating mode and a wave propagation phenomena.…”

Section: Casementioning

confidence: 99%

Numerical methods for the dynamics of unbounded domains

Mesquita¹,

Pavanello²

2005

Mat. apl. comput.

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“…[2][3][4][5] To regard local non-uniformities in waveguides, a finite element model would be employed and combined with spectral elements. That is, a beam is separated into two uniform regions with SEs and a local region with a FE.…”

Section: Introductionmentioning

confidence: 99%

Propagation of Structural Waves along Waveguides with Non-Uniformities Using Wavenumber Domain Finite Elements

Ryue¹

2014

The Journal Of The Acoustical Society Of Korea

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Wave reflection and transmission characteristics in waveguides are an important issue in many engineering applications. A combined spectral element and finite element (SE/FE) method is used to investigate the effects of local non-uniformities but limited at relatively low frequencies because the SE is formulated by using a beam theory. For higher frequency applications, a method named a combined spectral super element and finite element (SSE/FE) method was presented recently, replacing spectral elements with spectral super elements. This SSE/FE approach requires a long computing time due to the coupling of SSE and FE matrices. If a local non-uniformity has a uniform cross-section along its short length, the FE part could be further replaced by SSE, which improves performance of the combined SSE/FE method in terms of the modeling effort and computing time. In this paper SSEs are combined to investigate the characteristics of waves propagating along waveguides possessing geometric non-uniformities. Two models are regarded: a rail with a local defect and a periodically ribbed plate. In the case of the rail example, firstly, the results predicted by a combined SSE/FE method are compared with those from the combined SSEs in order to justify that the combined SSEs work properly. Then the SSEs are applied to a ribbed plate which has periodically repeated non-uniformities along its length. For the ribbed plate, the propagation characteristics are investigated in terms of the propagation constant.

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Wave Propagation in Structures

Cited by 236 publications

References 0 publications

Simple Models for the Dynamic Modeling of Rotating Tires

Simple Models for the Dynamic Modeling of Rotating Tires

Numerical methods for the dynamics of unbounded domains

Propagation of Structural Waves along Waveguides with Non-Uniformities Using Wavenumber Domain Finite Elements

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