Vibration Analysis of One-Dimensional Structures with Discontinuities Using the Acoustical Wave Propagator Technique

2004 ◽  
Vol 127 (6) ◽  
pp. 604-607
Author(s):  
S. Z. Peng
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Elastic Waves ◽  
Vibration Analysis ◽  
Fourier Transforms ◽  
Numerical Technique ◽  
Sudden Change ◽  
Computationally Efficient ◽  
Exact Analytical Solutions ◽  
One Dimensional

A numerical technique, named the acoustical wave propagator technique, is introduced to describe the dynamic characteristics of one-dimensional structures with discontinuities. A scheme combining Chebyshev polynomial expansion and fast Fourier transforms is introduced in detail. Comparison between exact analytical solutions and predicted results obtained by the acoustical wave propagator technique shows that this scheme has highly accurate and computationally efficient. Furthermore, this technique is extended to investigate the wave propagation and reflection of elastic waves in beams at the location of a sudden change in cross section.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

2D in-plane elastic waves in curved-tapered square lattice frame structure

2021 ◽  
pp. 1-12
Author(s):  
Rajan Prasad ◽  
Ajinkya Baxy ◽  
Arnab Banerjee
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Cross Sections ◽  
Elastic Waves ◽  
Dynamic Stiffness ◽  
Frame Structure ◽  
Square Lattice ◽  
Wave Localization ◽  
Finite Structure ◽  
Complete Bandgap

Abstract This work proposes a unique configuration of two-dimensional metamaterial lattice grid comprising of curved and tapered beams. The propagation of elastic waves in the structure is analyzed using the dynamic stiffness matrix (DSM) approach and the Floquet-Bloch theorem. The DSM for the unit cell is formulated under the extensional theory of curved beam considering the effects of shear and rotary inertia. The study considers two types of variable rectangular cross-sections, viz. single taper and double taper along the length of the beam. Further, the effect of curvature and taper on the wave propagation is analysed through the band diagram along the irreducible Brillouin zone. It is shown that a complete band gap, i.e. attenuation band in all the directions of wave propagation, in a homogeneous structure can be tailored with a suitable combination of curvature and taper. Generation of the complete bandgap is hinged upon the coupling of axial and transverse component of the lattice grid. This coupling emerges due to the presence of the curvature and further enhanced due to tapering. The double taper cross-section is shown to have wider attenuation characteristics than single taper cross-sections. Specifically, 83.36% and 63% normalized complete bandwidth is achieved for the double and single taper cross-section for a homogeneous metamaterial, respectively. Additional characteristics of the proposed metamaterial in time and frequency domain of the finite structure, vibration attenuation, wave localization in the equivalent finite structure are also studied.

Free Vibration Response of Thin and Thick Nonhomogeneous Shells by Refined One-Dimensional Analysis

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Alberto Varello ◽  
Erasmo Carrera
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cross Section ◽  
Vibration Analysis ◽  
Plane Deformation ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Variable Order ◽  
Vibrational Modes ◽  
One Dimensional

The free vibration analysis of thin- and thick-walled layered structures via a refined one-dimensional (1D) approach is addressed in this paper. Carrera unified formulation (CUF) is employed to introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the cross section. Classical Euler–Bernoulli (EBBM) and Timoshenko (TBM) beam theories are obtained as particular cases. Different kinds of vibrational modes with increasing half-wave numbers are investigated for short and relatively short cylindrical shells with different cross section geometries and laminations. Numerical results of natural frequencies and modal shapes are provided by using the finite element method (FEM), which permits various boundary conditions to be handled with ease. The analyses highlight that the refinement of the displacement field by means of higher-order terms is fundamental especially to capture vibrational modes that require warping and in-plane deformation to be detected. Classical beam models are not able to predict the realistic dynamic behavior of shells. Comparisons with three-dimensional elasticity solutions and solid finite element solutions prove that CUF provides accuracy in the free vibration analysis of even short, nonhomogeneous thin- and thick-walled shell structures, despite its 1D approach. The results clearly show that bending, radial, axial, and also shell lobe-type modes can be accurately evaluated by variable kinematic 1D CUF models with a remarkably lower computational effort compared to solid FE models.

Absorbing boundary layer control for linear one-dimensional wave propagation problems

2016 ◽  
Vol 24 (6) ◽  
pp. 1019-1031 ◽  
Author(s):  
Daniel Ritzberger ◽  
Alexander Schirrer ◽  
Stefan Jakubek
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Absorbing Boundary Conditions ◽  
Boundary Layer Control ◽  
Reference Trajectory ◽  
Computationally Efficient ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Layer Control ◽  
Dimensional Wave

In this work, a boundary layer control scheme for one-dimensional wave propagation problems is presented that provides reflection-less absorption of incident waves in numerical simulations. The desired absorption properties are formulated as an optimization problem. By using the dispersion relation to predict the unbounded wave propagation as a reference trajectory, a constant-gain state-feedback boundary layer controller is found. Since no additional auxiliary variables are introduced, this approach is highly computationally efficient, making it suitable for simulations under real-time requirements. The performance of the boundary layer controller is first evaluated and demonstrated on the scalar wave equation (vibrating string), for which reference absorbing boundary conditions are well established. Afterward, the moving Euler–Bernoulli beam under axial tension is considered, for which a good absorbing performance is achieved.

Study on the Band Gap and its Influencing Factors for one Dimensional Phononic Crystal

2011 ◽  
Vol 121-126 ◽  
pp. 448-452
Author(s):  
Yu Yang He ◽  
Xiao Xiong Jin
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Band Gap ◽  
Cross Section ◽  
Phononic Crystal ◽  
Filling Rate ◽  
Lumped Mass ◽  
Height Ratio ◽  
One Dimensional ◽  
Lumped Mass Method

The width of band gap is calculated with lumped mass method in order to study the wave propagation of longitudinal and transverse elastic wave of one-dimensional phononic crystal. The starting and terminating frequency is analyzed by changing the filling rate, the density difference of two materials, cross-section height ratio, and the Young's modulus of the scatter.

One-Dimensional Theories of Wave Propagation and Vibrations in Elastic Bars of Rectangular Cross Section

1966 ◽  
Vol 33 (3) ◽  
pp. 489-495 ◽  
Author(s):  
M. A. Medick
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Isotropic Material ◽  
Rectangular Cross Section ◽  
One Dimensional ◽  
Anisotropic Elastic

A method for constructing rational, one-dimensional theories of various orders of approximation, descriptive of wave propagation and vibrations in anisotropic elastic bars of rectangular cross section, is presented. As illustrations, several approximate theories are derived which are applicable to extensional motion in rectangular bars of isotropic material.

Stress Wave Propagation Analysis in One-Dimensional Micropolar Rods with Variable Cross-Section Using Micropolar Wave Finite Element Method

2018 ◽  
Vol 10 (04) ◽  
pp. 1850039 ◽  
Author(s):  
Mohsen Mirzajani ◽  
Naser Khaji ◽  
Muneo Hori
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Cross Section ◽  
Variable Cross Section ◽  
Stress Wave Propagation ◽  
Rotational Degree ◽  
Variable Cross ◽  
One Dimensional ◽  
Element Method

The wave finite element method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross-section. For this purpose, two kinds of waves with fast and slow velocities are detected. For micropolar medium, an additional rotational degree of freedom (DOF) is considered besides the classical elasticity’s DOF. The proposed method is implemented to solve the wave propagation, reflection and transmission of two distinct waves and impact problems in micropolar rods with different layers. Along with new solutions, results of the micropolar wave finite element method (MWFEM) are compared with some numerical and/or analytical solutions available in the literature, which indicate excellent agreements between the results.

Wave Propagation in Exponentially Varying Cross‐Section Rods and Vibration Analysis

2008 ◽  
Author(s):  
Mansour Nikkhah‐Bahrami ◽  
Masih Loghmani ◽  
Mostafa Pooyanfar
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Vibration Analysis

Paper 4: An Investigation of Shock Wave Behaviour in Ducts with a Gradual or Sudden Enlargement in Cross-Sectional Area

1969 ◽  
Vol 184 (7) ◽  
pp. 17-27 ◽  
Author(s):  
B. E. L. Deckker ◽  
J. Gururaja
Keyword(s):  
Cross Section ◽  
Sudden Change ◽  
Stationary Wave ◽  
Finite Amplitude ◽  
Sectional Area ◽  
Wave Interactions ◽  
Cross Sectional ◽  
One Dimensional ◽  
Sudden Enlargement ◽  
Net Pressure

This paper details some investigations relating to non-stationary wave interactions and their effects on the propagation of finite amplitude waves in ducts with either a gradual or sudden change in cross-section. The influence of the angle of divergence on the wave-front and the perturbed flow behind it has been examined in different diffuser configurations using Schlieren spark photography. The variation with incident pressure of the net pressure (superimposition pressure) and the transmitted pressure are presented for incident pressure ratios up to 3·4. The results have been compared with a quasi-steady one-dimensional analysis and with the theory of Chisnell. Differences between measured and predicted results are attributed to the failure of the theories to account for the wave interactions. A complete analytical solution does not appear possible in view of the complexities of the flow and wave action, and numerical methods have to be employed.

scholarly journals Simulation of pulse wave propagation using one-dimensional models of hemodynamics

2021 ◽  
Vol 2103 (1) ◽  
pp. 012081
Author(s):  
G V Krivovichev ◽  
N V Egorov
Keyword(s):  
Wave Propagation ◽  
Analytical Solution ◽  
Cross Section ◽  
Pulse Propagation ◽  
Pulse Wave ◽  
Pulse Wave Propagation ◽  
One Dimensional ◽  
Hydrodynamic System ◽  
Dimensional Models ◽  
Inviscid Case

Abstract The models of hemodynamics, corresponding to the inviscid, Newtonian, and non-Newtonian models, are compared. The models are constructed by the averaging of the hydrodynamic system on the vessel cross-section. For the inviscid case, the analytical solution of the problem for pulse propagation is obtained. As the result of the comparison, the deviations of the solutions for non-Newtonian models from the Newtonian and inviscid cases are demonstrated.

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