Incorporating Compressional and Shear Wave Types Into Fuzzy Structure Models for Plates

1995 ◽  
Author(s):  
Judith L. Rochat ◽  
Victor W. Sparrow
Keyword(s):  
Thin Plate ◽  
Shear Waves ◽  
Wave Theory ◽  
Structure Theory ◽  
Detailed Knowledge ◽  
Bending Waves ◽  
Incident Plane ◽  
Dependent Mass ◽  
Mass Spring ◽  
Bending Wave

Abstract Although realistic complex structures are usually difficult to model theoretically, fuzzy structure theory enables one to produce such a model without a detailed knowledge of the entire structure. Using the theory established by Pierce et al. [A. D. Pierce, V. W. Sparrow, and D. A. Russell, J. Vib. Acoust. (to be published), also ASME 93-WA/NCA-17.] regarding fundamental structural-acoustic idealizations for structures with imprecisely known or fuzzy internals, the effects that fuzzy attachments have on different wave types in a primary (or master) structure are examined in this paper. In the theory by Pierce et al., the primary structure that undergoes vibrations is a thin plate mounted in an infinite baffle. On one side of the plate are fuzzy attachments, represented as an array of attached mass-spring-dashpot systems, which are excited by an incident plane pulse. This known theory explains the effects of these attachments on bending waves in the plate. In this paper, the theory is extended to isolated compressional and shear waves in a plate. While studying this new problem, it is discovered that coupling effects occur when the plate and attachment properties are not uniform in the direction perpendicular to the wave propagation. Hence, unlike the bending wave theory which models a finite thin plate with point attached oscillators, the new wave type theory uses a thin plate infinite in one direction with line attached oscillators also infinite in the same direction. For both the compressional and shear waves, it is found that the fuzzy attachments add an apparent frequency dependent mass and damping to the plate. These results are similar to those for the bending wave theory.

Design of a Variable Thickness Plate to Focus Bending Waves

2012 ◽  
Author(s):  
Noah H. Schiller ◽  
Sz-Chin Steven Lin ◽  
Randolph H. Cabell ◽  
Tony Jun Huang
Keyword(s):  
Numerical Simulations ◽  
Thin Plate ◽  
Traveling Waves ◽  
Variable Thickness ◽  
Focal Point ◽  
Frequency Range ◽  
Additional Energy ◽  
Broad Frequency Range ◽  
Bending Waves ◽  
Energy Dissipated

This paper describes the design of a thin plate whose thickness is tailored in order to focus bending waves to a desired location on the plate. Focusing is achieved by smoothly varying the thickness of the plate to create a type of lens, which focuses structure-borne energy. Damping treatment can then be positioned at the focal point to efficiently dissipate energy with a minimum amount of treatment. Numerical simulations of both bounded and unbounded plates show that the design is effective over a broad frequency range, focusing traveling waves to the same region of the plate regardless of frequency. This paper also quantifies the additional energy dissipated by local damping treatment installed on a variable thickness plate relative to a uniform plate.

Propagation of bending waves in a thin plate with an ensemble of randomly located holes of non-canonical form

2020 ◽  
Vol 18 (0) ◽  
Author(s):  
Ya. I. Kunets' ◽  
V. V. Matus ◽  
V. O. Mishchenko ◽  
V. V. Porokhovs'kyi
Keyword(s):  
Thin Plate ◽  
Canonical Form ◽  
Bending Waves

scholarly journals A Study on the Minimization of Mooring Load in Fish-Cage Mooring Systems with a Damping Buoy

2020 ◽  
Vol 8 (10) ◽  
pp. 814
Author(s):  
Gun-Ho Lee ◽  
Bong-Jin Cha ◽  
Hyun-young Kim
Keyword(s):  
Numerical Simulations ◽  
Wave Theory ◽  
Line Length ◽  
Stokes Wave ◽  
Mooring Line ◽  
Spring Model ◽  
Mass Spring Model ◽  
Wave Conditions ◽  
Mass Spring ◽  
Fifth Order

This study established the conditions in which mooring load is minimized in a fish cage that includes a damping buoy in specific wave conditions. To derive these conditions, numerical simulations of various mooring contexts were conducted on a fish cage (1/15 scale) using a simplified mass-spring model and fifth-order Stokes wave theory. The simulation conditions were as follows: (1) bridle-line length of 0.8–3.2 m; (2) buoyancy of 2.894–20.513 N for the damping buoy; and (3) mooring-rope thickness of 0.002–0.004 m. The wave conditions were 0.333 m in height and 1.291–2.324 s of arrival period. Consequently, the mooring tensions tended to decrease with decreasing mooring line thickness and increasing bridle-line length and buoyancy of the buoy. Accordingly, it was assumed to be advantageous to minimize the mooring tension by designing a thin mooring line and long bridle line and for the buoyancy of the buoy to be as large as possible. This approach shows a valuable technique because it can contribute to the improvement of the mooring stability of the fish cage by establishing a method that can be used to minimize the load on the mooring line.

Formation of Bending-Wave Band Structures in Bicoupled Beam-Type Phononic Crystals

2013 ◽  
Vol 81 (1) ◽  
Author(s):  
Y. Q. Guo ◽  
D. N. Fang
Keyword(s):  
Dispersion Relation ◽  
Closed Form ◽  
Phononic Crystals ◽  
Formation Mechanisms ◽  
Wave Band ◽  
Band Structures ◽  
Bending Waves ◽  
Beam Type ◽  
Thickness Shear ◽  
Bending Wave

Beam-type phononic crystals as one kind of periodic material bear frequency bands for bending waves. For the first time, this paper presents formation mechanisms of the phase constant spectra in pass-bands of bending waves (coupled flexural and thickness-shear waves) in bicoupled beam-type phononic crystals based on the model of periodic binary beam with rigidly connected joints. Closed-form dispersion relation of bending waves in the bicoupled periodic binary beam is obtained by our proposed method of reverberation-ray matrix (MRRM), based on which the bending-wave band structures in the bicoupled binary beam phononic crystal are found to be generated from the dispersion curves of the equivalent bending waves in the unit cell due to the zone folding effect, the cut-off characteristic of thickness-shear wave mode, and the wave interference phenomenon. The ratios of band-coefficient products, the characteristic times of the unit cell and the characteristic times of the constituent beams are revealed as the three kinds of essential parameters deciding the formation of bending-wave band structures. The MRRM, the closed-form dispersion relation, the formation mechanisms, and the essential parameters for the bending-wave band structures in bicoupled binary beam phononic crystals are validated by numerical examples, all of which will promote the applications of beam-type phononic crystals for wave filtering/guiding and vibration isolation/control.

Transient Bending Wave Propagation in Anisotropic Plates

1998 ◽  
Vol 65 (4) ◽  
pp. 930-938 ◽  
Author(s):  
K.-E. Fa¨llstro¨m ◽  
O. Lindblom
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Integral Representation ◽  
Orthotropic Plate ◽  
Representation Formula ◽  
Rotary Inertia ◽  
Anisotropic Plates ◽  
Bending Waves ◽  
Integral Representation Formula ◽  
Bending Wave

In this paper we study transient propagating bending waves. We use the equations of orthotropic plate dynamics, derived by Chow about 25 years ago, where both transverse shear and rotary inertia are included. These equations are extended to include anisotropic plates and an integral representation formula for the bending waves is derived. Chow’s model is compared with the classical Kirchoff’s model. We also investigate the influence of the rotary inertia. Comparisons with experimental data are made as well.

scholarly journals Cable Force Identification Based on Bending Waves in Substructures

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jing Huang ◽  
Jun Xiao ◽  
Jinxiang Zhang ◽  
Fanying Jiang ◽  
Yang Dai ◽  
...  
Keyword(s):  
Least Squares Method ◽  
External Disturbance ◽  
Sampling Point ◽  
Frequency Method ◽  
Force Identification ◽  
Bending Waves ◽  
Axial Tension ◽  
Cable Force ◽  
The Impact ◽  
Bending Wave

A method is proposed to study the dynamic characteristics of cable structures from the perspective of traveling waves based on the modified Timoshenko beam axial tension model. Considering the propagation characteristics of the bending wave in a beam structure, once the frequency response of the three measuring points is measured, the wave component coefficients can be obtained by the least squares method, and then the cable force and bending stiffness can be identified with the aim of minimizing the fitting residual. The accuracy of this method is verified by a numerical simulation experiment of the cable vibration. Compared with the traditional frequency method, this method focuses on the cable force identification of the substructure, so the effect of the shock absorber is invalid. Moreover, the cable force of each position of the cable can be calculated reversely by static analysis with the identified cable force of the substructure, which breaks the concept that the cable force is a single value. Furthermore, the cable force can be identified at each frequency sampling point, reducing the impact of the external disturbance.

scholarly journals Critical Frequencies of Composite Cylindrical Shells

2020 ◽  
Vol 25 (1) ◽  
pp. 79-87
Author(s):  
K. Renji ◽  
S. Josephine Kelvina Florence
Keyword(s):  
Cylindrical Shell ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Critical Frequency ◽  
Composite Panel ◽  
Transverse Shear Deformation ◽  
Composite Cylindrical Shell ◽  
Composite Cylinder ◽  
Bending Waves ◽  
Bending Wave

The sound radiation characteristics of a structure depend on its critical frequency. The expression for theoretically estimating the critical frequency of a composite cylindrical shell has not yet been reported. Thus, the practice is to use the expression for the composite panel for determining the critical frequency of a composite shell. In this work, critical frequencies of composite shells are investigated. As the critical frequency depends on the speed of the bending wave, an expression for the speed of the bending wave is first derived. It is seen that the curvature causes an increase in the speed of the bending wave and the orthotropic nature of the cylinder reduces the speed. An expression for the critical frequency of a composite cylindrical shell is then derived. The curvature causes a reduction in the critical frequency and the influence is significant in acoustically thick cylinders. Hence, the critical frequencies of such cylinders cannot be determined by using the expression for the panels. Effects of transverse shear deformation on the speed of the bending wave as well as the critical frequency are then investigated. Transverse shear deformation causes both reduction in the speed of the bending wave and an increase in the critical frequency. The orthotropic nature of the cylindrical shell increases the critical frequency further. The critical frequency of a typical composite cylinder is determined through a numerical simulation and the results are in agreement with the results obtained using the expressions derived. The critical frequency of a typical composite cylinder obtained through an experiment is presented. With this work, expressions for theoretically estimating the speeds of the bending waves and critical frequencies are derived for a composite cylindrical shell considering transverse shear deformation.

Streamwise Gate Vibration

2017 ◽  
pp. 204-229
Keyword(s):  
Wave Theory ◽  
Mass Effect ◽  
Added Mass ◽  
Wave Radiation ◽  
Theory Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Long Span ◽  
Mass Spring

Streamwise vibrations of gates due to the bending flexibility of the skinplate of Tainter gates or the weir plate of long-span gates result in pushing-and-drawing of the water in the reservoir. During each cycle of vibration, the gate's motion must accelerate and then decelerate the water mass in contact with the vibrating gate surface, resulting in a substantial added mass effect. From simple single degree-of-freedom mass-spring-damper vibration theory, one understands that the effect of added mass is to lower the frequency of gate vibration. In addition to the push-and-draw effect, streamwise motion can also result in discharge fluctuation for inclined gates, providing a source of gate excitation. Rayleigh's wave theory analysis from the previous chapter is applied to provide an analysis framework for determining the magnitude of wave radiation damping and to calculate the added mass.

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