Numerical Calculation for Complex Transcendental Equation

2012 ◽  
Vol 229-231 ◽  
pp. 1976-1979
Author(s):  
Tie Lin Sun ◽  
Hui Sun
Keyword(s):  
Numerical Calculation ◽  
Dispersion Equation ◽  
Elastic Plate ◽  
Fast Algorithm ◽  
Lamb Wave ◽  
Traditional Method ◽  
Wave Dispersion ◽  
Transcendental Equation ◽  
Fast Calculation

The traditional method to calculate complex transcendental equation is poor, which can't meet requirements of calculating imaginary answer and fast calculation at the same time. This paper proposes "modified dichotomy method" through modifying the classical dichotomy method to solve complex transcendental equation, that can not only calculates imaginary answer but also calculates fast. Algorithm is also verified through comparing with the answer to lamb wave dispersion equation in elastic plate.

Wave Propagation in a Micropolar Elastic Plate with Voids

2005 ◽  
Vol 11 (6) ◽  
pp. 849-863 ◽  
Author(s):  
S. K. Tomar
Keyword(s):  
Wave Propagation ◽  
Attenuation Coefficient ◽  
Elastic Material ◽  
Elastic Plate ◽  
Lamb Wave ◽  
Specific Model ◽  
Present Formulation ◽  
Numerical Computations ◽  
Lamb Wave Propagation ◽  
Symmetric And Antisymmetric Modes

Frequency equations are obtained for Rayleigh–Lamb wave propagation in a plate of micropolar elastic material with voids. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be free from stresses. The frequency equations are obtained corresponding to symmetric and antisymmetric modes of vibrations of the plate, and some limiting cases of these equations are discussed. Numerical computations are made for a specific model to solve the frequency equations for symmetric and antisymmetric modes of propagation. It is found that both modes of vibrations are dispersive and the presence of voids has a negligible effect on these dispersion curves. However, the attenuation coefficient is found to be influenced by the presence of voids. The results of some earlier works are also deduced from the present formulation.

scholarly journals Lamb Wave Scattering Analysis for Interface Damage Detection between a Surface-Mounted Block and Elastic Plate

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 860
Author(s):  
Mikhail V. Golub ◽  
Alisa N. Shpak ◽  
Inka Mueller ◽  
Sergey I. Fomenko ◽  
Claus-Peter Fritzen
Keyword(s):  
Damage Detection ◽  
Elastic Plate ◽  
Lamb Wave ◽  
Wave Scattering ◽  
Hybrid Approach ◽  
Guided Wave ◽  
Open Crack ◽  
Damage Indices ◽  
Impulse Function ◽  
Thin Walled

Since stringers are often applied in engineering constructions to improve thin-walled structures’ strength, methods for damage detection at the joints between the stringer and the thin-walled structure are necessary. A 2D mathematical model was employed to simulate Lamb wave excitation and sensing via rectangular piezoelectric-wafer active transducers mounted on the surface of an elastic plate with rectangular surface-bonded obstacles (stiffeners) with interface defects. The results of a 2D simulation using the finite element method and the semi-analytical hybrid approach were validated experimentally using laser Doppler vibrometry for fully bonded and semi-debonded rectangular obstacles. A numerical analysis of fundamental Lamb wave scattering via rectangular stiffeners in different bonding states is presented. Two kinds of interfacial defects between the stiffener and the plate are considered: the partial degradation of the adhesive at the interface and an open crack. Damage indices calculated using the data obtained from a sensor are analyzed numerically. The choice of an input impulse function applied at the piezoelectric actuator is discussed from the perspective of the development of guided-wave-based structural health monitoring techniques for damage detection.

A Fast Algorithm to Choose Delay Time for Strange Attractors

2011 ◽  
Vol 230-232 ◽  
pp. 1379-1383
Author(s):  
Peng Yao ◽  
Gai Rong Chen ◽  
Shao Hong Xu
Keyword(s):  
Mutual Information ◽  
High Precision ◽  
Satisfactory Result ◽  
Fast Algorithm ◽  
Delay Time ◽  
Traditional Method ◽  
Chaotic Systems ◽  
Phase State ◽  
State Reconstruction ◽  
Simulation Results

According to pseudo-periodicity and ergodicity of chaotic systems, we put forward a fast algorithm to determine delay time in phase state reconstruction. The traditional method to calculate mutual information is time-consuming and complicated to realize, which greatly restricts its application. In our algorithm we gradually reduce the feasible computing interval and adjust the calculating step until satisfactory result is gotten. This method overcomes the tedious calculation of mutual information and meanwhile guarantees high precision. Finally the simulation results of Rössler and Lorenz systems verify the feasibility of our algorithm.

Determination of Vibration Source Locations in Laminated Composite Plates Using Lamb Wave Analysis

2010 ◽  
Vol 123-125 ◽  
pp. 899-902
Author(s):  
Chao Du ◽  
Qing Qing Ni ◽  
Toshiaki Natsuki
Keyword(s):  
Lamb Wave ◽  
Guided Waves ◽  
Lamb Waves ◽  
Laminated Composite ◽  
Composite Plates ◽  
Wave Dispersion ◽  
Laminated Plates ◽  
Vibration Source ◽  
Arrival Times ◽  
Wave Velocities

Signals propagate on plate-like structures as ultrasonic guided waves, and analysis of Lamb waves has been widely used for on-line monitoring. In this study, the wave velocities of symmetric and anti-symmetric modes in various directions of propagation were investigated. Since the wave velocities of these two modes are different, it is possible to compute the difference in their arrival times when these waves propagated the distance from the vibration source to sensor. This paper presents an evaluation formulation of wave velocity and describes a generalized algorithm for locating a vibration source on a thin, laminated plate. With the different velocities of two modes based on Lamb wave dispersion, the method uses two sensors to locate the source on a semi-infinite interval of a plate. The experimental procedure supporting this method employs pencil lead breaks to simulate vibration sources on quasi-isotropic and unidirectional laminated plates. The transient signals generated in this way are transformed using a wavelet transform. The vibration source locations are then detected by utilizing the distinct wave velocities and arrival times of the symmetric and anti-symmetric wave modes. The method is an effective technique for identifying impact locations on plate-like structures.

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