Study on Natural Vibration Characteristics Based on the Coupled Wave Theory of Spring Supported Elastic Pipes and Fluids

2020 ◽  
Author(s):  
Takeshi Tokunaga ◽  
Koji Mori ◽  
Hiroko Kadowaki ◽  
Takashi Saito
Keyword(s):  
Boundary Condition ◽  
Blood Vessel ◽  
Flow Velocity ◽  
Blood Vessels ◽  
Natural Vibration ◽  
Wave Theory ◽  
Vibration Characteristics ◽  
Elastic Pipes ◽  
Coupled Wave ◽  
Natural Vibration Characteristics

Abstract A gradient of a blood flow velocity on the surface of a blood vessel is one of the clinical medicine concerns from the view point of prevention of the arteriosclerosis. In previous study, we formulated a relationship between the pressure and a flow velocity based on the coupled wave theory of elastic pipes and Newtonian fluids [1]. In addition, a flow velocity distribution and a wall shear stress are estimated by using the blood pressure data, which are non-invasively obtained by the tonometry method. This method is quasi-analytical method to apply the coupled wave theory for industrial flow field inside steel pipes proposed by Urata [4] to blood vessel, and has the advantage of systematic estimator compared with the numerical calculation. However, the coupled wave theory has applied to the elastic pipes that were assumed to be infinitely long. In addition, a single wave was assumed to be dominant within the elastic pipes and the Newtonian fluids. Therefore, in order to apply various length vessels in clinical field, the boundary of the blood vessels that varies from site to site, and the natural vibration characteristics that depend on the boundary conditions, could not be reflected in the wall shear stress estimation. In general, in order to solve the forced vibration with the boundary condition, it is necessary to clarify natural frequency and natural mode as natural vibration characteristics of structure. In this study, we introduce the spring supported elastic pipes to the coupled wave theory and formulated a relationship between the natural vibration characteristics and the boundary conditions. In this proposed method, the spring-supported elastic pipe has a feature that can be treated as an arbitrary boundary condition of an artery by giving an appropriate spring coefficients. Therefore, it is easy to apply to various types of blood vessels clinically. By investigating the natural vibration characteristics of blood vessels that varies from site to site, it may be possible to clarify fluctuations of blood flow in response to blood pressure with some frequency-bands. In addition, natural angular frequencies and natural modes of the spring supported elastic pipes and the Newtonian fluids were estimated for general blood vessel based on the coupled wave theory. In the result, the natural angular frequencies and the natural modes that reflect the clinical vibration characteristics to some extent can be estimated. On the other hand, particular modes may not reflect boundary condition, and further examination of the relationship between natural vibration characteristics and boundary condition is needed.

scholarly journals Stochastic Natural Vibration Analyses of Free-Form Shells

2019 ◽  
Vol 9 (15) ◽  
pp. 3168
Author(s):  
Bingbing San ◽  
Yunlong Ma ◽  
Zhi Xiao ◽  
Dongming Feng ◽  
Liwei Yin
Keyword(s):  
Elastic Modulus ◽  
Shape Optimization ◽  
Shell Thickness ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Free Form ◽  
Probability Models ◽  
Geometric Imperfection ◽  
Natural Vibration Characteristics

This work investigates the natural vibration characteristics of free-form shells when considering the influence of uncertainties, including initial geometric imperfection, shell thickness deviation, and elastic modulus deviation. Herein, free-form shell models are generated while using a self-coded optimization algorithm. The Latin hypercube sampling (LHS) method is used to draw the samplings of uncertainties with respect to their stochastic probability models. ANSYS finite element (FE) software is adopted to analyze the natural vibration characteristics and compute the natural frequencies. The mean values, standard deviations, and cumulative distributions functions (CDFs) of the first three natural frequencies are obtained. The partial correlation coefficient is adopted to rank the significances of uncertainty factors. The study reveals that, for the free-form shells that were investigated in this study, the natural frequencies is a random quantity with a normal distribution; elastic modulus deviation imposes the greatest effect on natural frequencies; shell thickness ranks the second; geometrical imperfection ranks the last, with a much lower weight than the other two factors, which illustrates that the shape of the studied free-form shells is robust in term of natural vibration characteristics; when the supported edges are fixed during the shape optimization, the stochastic characteristics do not significantly change during the shape optimization process.

Three Dimensional Simulation of Blood Flow in the Small Arteries of a Truncated Vascular System With Three Levels of Bifurcation

2014 ◽  
Author(s):  
Kamil Kahveci ◽  
Bryan R. Becker
Keyword(s):  
Boundary Condition ◽  
Blood Flow ◽  
Blood Vessel ◽  
Velocity Profile ◽  
Flow Velocity ◽  
Blood Flow Velocity ◽  
Vascular System ◽  
Three Dimensional ◽  
Simulation Software ◽  
Small Arteries

Three dimensional blood flow in a truncated vascular system is investigated numerically using a commercially available finite element analysis and simulation software. The vascular system considered in this study has three levels of symmetric bifurcation. Geometric parameters for daughter vessels, such as their diameters and their angles of bifurcation, are specified according to Murray’s law based on the principle of minimum work. The ratio of blood vessel length to diameter is based upon experimental data found in the literature. An experimentally obtained velocity profile, available in the literature, is used as the inlet boundary condition. An outflow boundary model, consisting of a contraction tube to represent the pressure drop of the small arteries, arterioles, and capillaries that would follow the truncated vascular system, is used to specify the boundary condition at the eight outlets. The results show that although the blood flow velocity experiences a sudden decrease after the bifurcation points due to the higher total cross-sectional area of the daughter vessels as compared to the parent vessel, this decrease in velocity is partially recovered due to the tapering of the blood vessels as they approach the next bifurcation point. The results also show that the secondary flow which is typical after the bifurcation of large arteries does not develop after the bifurcation of small arteries due to the presence of laminar blood flow with very low Reynolds number in the small arteries. The numerical model yields pressure distributions and pressure drops along the vascular system that agree quite well with the physiological data found in the literature. Finally, the results show that, immediately following a bifurcation, the blood flow velocity profile is not symmetrical about the longitudinal axes of blood vessel. However, symmetry is recovered as the blood flow proceeds down the vessel.

Natural vibration characteristics of a clamped circular plate in contact with fluid

2005 ◽  
Vol 21 (2) ◽  
pp. 169-184 ◽  
Author(s):  
Myung Jo Jhung ◽  
Young Hwan Choi ◽  
Hho Jung Kim ◽  
Kyeong Hoon Jeong
Keyword(s):  
Circular Plate ◽  
Natural Vibration ◽  
Vibration Characteristics ◽  
Natural Vibration Characteristics

Study on the Natural Vibration Characteristics of Flexible Missile With Thrust by Using Riccati Transfer Matrix Method

2015 ◽  
Vol 83 (3) ◽  
Author(s):  
Gangli Chen ◽  
Xiaoting Rui ◽  
Fufeng Yang ◽  
Jianshu Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Engine Thrust ◽  
Natural Vibration Characteristics

Due to the mass consumption and engine thrust of a flexible missile during the powered phase flight, its natural vibration characteristics may be changed significantly. The calculation of natural frequencies and mode shapes plays an important role in the structural design of the missile. Aiming at calculating the natural vibration characteristics of the missile rapidly and accurately, a nonuniform beam subjected to an engine thrust is used to model the free vibration of the missile and Riccati transfer matrix method (RTMM) is adopted in this paper. Numerical results show that the natural frequencies of a typical single stage flexible missile are increased unceasingly in its powered phase, and its mode shapes are changed a lot. When the presented methodology is used to study the natural vibration characteristics of flexible missiles, not only the mass, stiffness, and axial compressive force distributions are described realistically but also numerical stability, high computation speed, and accuracy are achieved.

Vibration Analysis and Experimental Validation of Multiple Launch Rocket System Based on MSTMM

2018 ◽  
Author(s):  
Guoping Wang ◽  
Tianxiong Tu ◽  
Xue Rui ◽  
Yunfei Miao ◽  
Xiaoting Rui
Keyword(s):  
Natural Vibration ◽  
Vibration Characteristics ◽  
The Body ◽  
Dynamics Simulation ◽  
Dynamics Model ◽  
Dynamic Simulations ◽  
Dynamics Response ◽  
Rocket System ◽  
Full Loading ◽  
Natural Vibration Characteristics

Natural vibration characteristics and dynamics response of multiple launch rocket system (MLRS) are of fundamental importance from the viewpoint of vibration levels, firing dispersion, and stability. In this study, a new launch vehicle-supports-rockets coupling dynamic model for a practical MLRS is established. Rui method, namely the transfer matrix method for multibody systems (MSTMM) is a new and efficient method for multibody system dynamics (MSD) and is used to obtain the vibration characteristics and dynamics response. The dynamics model, the topology figure of dynamics model, the transfer equations of elements, the overall transfer equation, the eigenfrequency equation, the body dynamics equations, the generalized coordinate equations, and the dynamics simulation system for the MLRS are established. Based on the advantages of MSTMM in studying MSD, the vibration characteristics and dynamics response of complex MLRS are computed rapidly. Finally, the new model is validated in three ways: (1) modal experiment of MLRS, (2) launch dynamics experiment of non-full loading rockets, and (3) launch dynamics experiment of full loading rockets. The results show that the proposed model can not only simulate the natural vibration characteristics of the MLRS but also effectively perform dynamic simulations of the MLRS during launching process.

Sign in / Sign up

Export Citation Format

Share Document