Trapped modes in an infinite tube with inhomogeneity

Symmetric and anti-symmetric trapped modes in a cylindrical tube with a segment of higher density are studied. The problem is reduced to an eigenvalue problem of the spatial Helmholtz equation subject to vanishing Dirichlet boundary condition in the cylindrical coordinate system. Through the domain decomposition method and matching technique, multiple frequency parameters are determined by solving the characteristic equation, and the corresponding n-fold periodic trapped modes can be constructed. It is found that in addition to the fundamental mode, the second- and higher-order trapped modes exist, which depend on the density ratio and length of the inhomogeneity. The local inhomogeneity leads to a decrease of the cutoff frequencies of the homogeneous tube and the corresponding vibration mode is localized near the inhomogeneous segment.

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Single Vibration Mode Standing Wave Tubular Piezoelectric Ultrasonic Motor

10.32920/ryerson.14664675.v1 ◽

2021 ◽

Author(s):

Soonho Park

Keyword(s):

Standing Wave ◽

Vibration Mode ◽

Cylindrical Tube ◽

Electrical Energy ◽

High Energy ◽

High Energy Density ◽

Ultrasonic Frequency ◽

Ultrasonic Motors ◽

Piezoelectric Motors ◽

Piezoelectric Effects

The objective of this thesis is to report the single vibration mode standing wave tubular piezoelectric ultrasonic motors developed. Piezoelectric motors are driven by reverse piezoelectric effects which converts an input of ultrasonic frequency of electrical energy into an output of mechanical movement. There are many advantages of piezoelectric ultrasonic motors compared to electromagnetic motors such as simple structure, high energy density, and high torque at low speed. Three prototypes are designed and fabricated. Two motors are fabricated using PZT cylindrical tube; one with PZT teeth and the other with metal teeth. A third motor using brass tube with PZT plates attached is fabricated. After design and fabrication of three prototypes, the performances of the motors are tested using a test apparatus for speed and torque.

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Generalized Brinkman Type Dusty Fluid Model for Blood Flow

Advanced Applications of Fractional Differential Operators to Science and Technology - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-7998-3122-8.ch007 ◽

2020 ◽

pp. 154-170

Author(s):

Muhammad Saqib ◽

Sharidan Shafie ◽

Ilyas Khan

Keyword(s):

Blood Flow ◽

Magnetic Parameter ◽

Fluid Model ◽

Cylindrical Tube ◽

Hankel Transform ◽

Governing Equations ◽

Two Phase ◽

Cylindrical Coordinate ◽

Long Time ◽

Fractional Parameter

This chapter is dedicated to studying the magnetic blood flow with uniformly distributed magnetite dusty particles (MDP) in a cylindrical tube. For this purpose, the two-phase fractional Brinkman type fluid model is considered. The fractional governing equations are modeled in the cylindrical coordinate system taking into consideration the magnetization of the fluid due to the applied magnetic field. The fractional governing equations are subjected to physical initial and boundary conditions. The joint Laplace and Hankel transform is employed to develop exact analytical solutions. The obtained solutions are computed numerically and plotted in different graphs. It is noticed that for a long time the blood and MDP velocities increase with increasing values of the fractional parameter. In contrast, this effect reverses for a shorter time. In the case of the magnetic parameter, both velocities are decreased with increasing values of the magnetic parameter.

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Single Vibration Mode Standing Wave Tubular Piezoelectric Ultrasonic Motor

10.32920/ryerson.14664675 ◽

2021 ◽

Author(s):

Soonho Park

Keyword(s):

Standing Wave ◽

Vibration Mode ◽

Cylindrical Tube ◽

Electrical Energy ◽

High Energy ◽

High Energy Density ◽

Ultrasonic Frequency ◽

Ultrasonic Motors ◽

Piezoelectric Motors ◽

Piezoelectric Effects

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Trapped modes in an infinite or semi-infinite tube with a local enlargement

Ultrasonics ◽

10.1016/j.ultras.2016.05.021 ◽

2016 ◽

Vol 71 ◽

pp. 59-68 ◽

Cited By ~ 2

Author(s):

Wei-Sha Li ◽

Jiaqi Zou ◽

Kang Yong Lee ◽

Xian-Fang Li

Keyword(s):

Trapped Modes ◽

Infinite Tube

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Complex Trapped Modes of the Helmholtz Equation in Cross, S, and U Bends

International Journal of Applied Mechanics ◽

10.1142/s1758825115500246 ◽

2015 ◽

Vol 07 (02) ◽

pp. 1550024

Author(s):

C. Y. Wang

Keyword(s):

Boundary Conditions ◽

Helmholtz Equation ◽

Domain Decomposition ◽

Eigenfunction Expansion ◽

Decomposition Method ◽

Domain Decomposition Method ◽

Local Effect ◽

Trapped Modes ◽

Simply Supported ◽

Quantum Waveguides

The Helmholtz equation with zero boundary conditions is important in the vibration of membranes, simply-supported plates, and electromagnetic and quantum waveguides. Trapped modes, with a lowered frequency and limited local effect, may exist for infinite strips with local bends or enlargements. Infinite strips with a cross bulge, with an S bend and with a U bend are studied using an efficient eigenfunction expansion and domain decomposition method. As the bulge become larger, more trapped modes with more complexity appear. Some geometries do not support trapped modes at all. These results are new.

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