scholarly journals Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

2014 ◽  
Vol 6 ◽  
pp. 792478 ◽  
Author(s):  
Laith K. Abbas ◽  
Xiaoting Rui
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Coefficient Matrix ◽  
Complex Structures ◽  
Vibration Characteristic ◽  
Boundary State ◽  
Novel Algorithms

In this paper, an approach based on transfer matrix method of linear multibody systems (MS-TMM) is developed to analyze the free vibration of a multilevel beam, coupled by spring/dashpot systems attached to them in-span. The Euler-Bernoulli model is used for the transverse vibration of the beams, and the spring/dashpot system represents a simplified model of a viscoelastic material. MS-TMM reduces the dynamic problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundaries are composed of displacements, rotation angles, bending moments, and shear forces, which are partly known and partly unknown, and end up with reduced overall transfer matrix. Nontrivial solution requires the coefficient matrix to be singular to yield the required natural frequencies. This paper implements two novel algorithms based on the methodology by reducing the zero search of the reduced overall transfer matrix's determinate to a minimization problem and demonstrates a simple and robust algorithm being much more efficient than direct enumeration. The proposal method is easy to formulate, systematic to apply, and simple to code and can be extended to complex structures with any boundary conditions. Numerical results are presented to show the validity of the proposal method against the published literature.

Transfer Matrix Method for the Determination of the Free Vibration of Two Elastically Coupled Beams

2013 ◽  
Vol 372 ◽  
pp. 301-304 ◽  
Author(s):  
Laith K. Abbas ◽  
Dieter Bestle ◽  
Xiao Ting Rui
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Coefficient Matrix ◽  
The State ◽  
Discrete Elements ◽  
Numerical Result ◽  
Boundary State

The feasibility of using the transfer matrix method (TMM) to compute the free vibration characteristics of a system composed of continues and discrete elements vibrating in a plane is explored theoretically. In the approach to the problem, a general analytical method based on TMM is developed for the vibrations of two uniform Euler-Bernoulli beams coupled by a spring. The components of the transfer matrix are all functions of the systems natural frequency. The overall transfer equation only involves boundary state vectors, whereas the state vectors at all other connection points do not appear. The state vectors at the boundary are composed of displacements, rotation angles, bending moments and shear forces, which are partly known and partly unknown. Moreover, the overall transfer matrix is independent of the degrees of the freedom. A non-trivial solution of the final overall transfer equation requires the coefficient matrix to be singular. This paper reduces the zero search of its determinate to a minimization problem and demonstrates a simple, robust algorithm being much more efficient than direct enumeration. A numerical result is presented to demonstrate the proposal method.

The Application of Transfer Matrix Method for Multibody Systems in the Dynamics of Sail Mounted Hydroplanes System

2018 ◽  
Author(s):  
Dongyang Chen ◽  
Laith K. Abbas ◽  
Guoping Wang ◽  
Xiaoting Rui
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Flow Model ◽  
Main Idea ◽  
Vibration Characteristic ◽  
Software Simulation ◽  
Structure Interaction ◽  
Simulation Results

Transfer Matrix Method for Multibody Systems (MSTMM) is easy to formulate, systematic to apply, simple to code and the matrices are low order which contributes to higher computational efficiency than ordinary dynamics methods. The main idea about how to simulate the vibration characteristic and hydroelastic behavior of a submarine sail mounted hydroplanes system based on MSTMM and coupled with Theodorsen flow model is presented in this paper. The simulation results are compared with those theoretical and experimental reported in the existing literature and commercial software simulation, and good results are obtained. The main idea of this paper provides a reference for dynamics of system with fluid-structure interaction (FSI) simulation and analysis of similar problems in the field of engineering.

scholarly journals Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

2012 ◽  
Vol 19 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
A.M. Yu ◽  
Y. Hao
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Cross Sectional ◽  
Helical Springs

Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

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