Impact sound prediction of finite floor structures with the modal transfer matrix method

2021 ◽  
Vol 263 (6) ◽  
pp. 734-745
Author(s):  
Jasper Vastiau ◽  
Cédric Van hoorickx ◽  
Edwin Reynders
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Sound Transmission ◽  
Mode Shapes ◽  
Elastic Plates ◽  
Infinite Extent ◽  
Floor Systems ◽  
Windowing Technique ◽  
The Impact

The transfer matrix method (TMM) is commonly employed for wave propagation analysis in layered media of fluid, elastic and porous nature. Up to now it has been used extensively to analyze airborne sound transmission and sound absorption. Its use for impact sound transmission has been investigated to a limited extent, i.e. for thick homogeneous elastic plates of infinite extent and for specific receiver points. This contribution aims to broaden the scope such that the global impact sound, radiated by finite floor structures containing elastic, fluid and/or porous layers, can be analyzed in a more robust way than previously available in literature. A disadvantage of the conventional TMM is that only floors of infinite extent can be implemented. It is possible to remove this drawback using a spatial windowing technique. Furthermore, the modal behavior of the floor is approximately taken into account by projecting the impact force onto the mode shapes and only allowing for the propagation of those waves, corresponding to modal wavenumbers, in the structure. Predictions of the radiated sound power are made for various bare floors and floating floor systems of both infinite and finite extent.

Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method

1995 ◽  
Author(s):  
Siu-Tong Choi ◽  
Sheng-Yang Mau
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Transmission Error ◽  
Mode Shapes ◽  
Rotor Systems ◽  
Gear Mesh ◽  
Mass Unbalance ◽  
Rotor Bearing

Abstract In this paper, an analytical study of the dynamic characteristics of geared rotor-bearing systems by the transfer matrix method is presented. Rotating shafts are modeled as Timoshenko beam with shear deformation and gyroscopic effects taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set and a transmission-error exciter. The transfer matrix of a gear mesh is developed. The coupling motions of the lateral and torsional vibration are studied. In free vibration analysis of geared rotor systems, natural frequencies and corresponding mode shapes, and the whirl frequencies under different spin speeds are determined. Effects of bearing stiffness, isotropic and orthotropic bearings, pressure angle of the gear mesh are studied. In steady-state vibration analysis, responses due to the excitation of mass unbalance and the transmission error are studied. Parametric characteristics of geared rotor systems are discussed.

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.

Dynamic characteristics of coupling shaft system in tufting machine based on the Riccati whole transfer matrix method

2016 ◽  
Vol 231 (2) ◽  
pp. 356-371 ◽  
Author(s):  
Shuang Huang ◽  
Xinfu Chi ◽  
Yang Xu ◽  
Yize Sun
Keyword(s):  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Complex Dynamic ◽  
Rotor Systems ◽  
Machine Type ◽  
Shaft System

Focusing on tufting machine type DHUN801D-400, the complex dynamic model of coupling shaft system is built by using Riccati whole transfer matrix method, and the natural frequencies and mode shapes are analyzed. First, the components of coupling shafts system in tufting machine are introduced. Second, the structures of coupling shafts system are discretized and simplified. Third, the transfer matrix is constructed, the model is solved by using Riccati whole transfer matrix method, and then natural frequencies and mode shapes are obtained. Finally, the experimental results are quoted to demonstrate the applicability of the model. The results indicate that the Riccati whole transfer matrix method is well applicable for modeling the dynamics of complex multi-rotor systems.

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.

scholarly journals Transfer Matrix Method for Dynamic Characteristics Analysis of Missile-Canister System in Silo

2020 ◽  
Vol 319 ◽  
pp. 01001
Author(s):  
Anfeng Zhou ◽  
Daokui Li ◽  
Shiming Zhou ◽  
Da Cui ◽  
Xuan Zhou
Keyword(s):  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Discrete Distribution ◽  
Mode Shapes ◽  
Beam Model ◽  
Radial Vibration ◽  
Single Beam ◽  
Double Beam

In order to ensure the safety of the missile-canister system in silo during the earthquake, a modified transfer matrix method is provided to study the dynamic characteristics of the system. Firstly, a discrete viscoelastic connected double-beam model is developed taking account of the structural nonuniformity and the discrete distribution of the adapters. Secondly, the transfer matrix method of a single beam is modified to solve the problem of discrete connection between the two beams of the double-beam model. Then the natural circular frequencies and mode shapes are calculated by the proposed method, comparing with the finite element method (FEM). Finally, the influence of the stiffness of radial vibration isolators and adapters on the dynamic characteristics of the system is analysed. The comparison shows that the results of the proposed method are well consistent with the FEM calculations and the proposed method is validated. The variations of the first six natural circular frequencies with radial vibration isolator stiffness and adapter stiffness are obtained, which provides a basis for the seismic-relieving design.

An Investigation on Dynamic Characteristics of a Gas Turbine Rotor Using an Improved Transfer Matrix Method

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Cheng Meng ◽  
Ming Su ◽  
Shaobo Wang
Keyword(s):  
Gas Turbine ◽  
Dynamic Model ◽  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Mode Shapes ◽  
Correction Coefficient ◽  
Critical Speeds ◽  
Contact Effects

This paper presents an investigation on dynamic characteristics of a rod-fastened rotor. Based on the framework of a traditional Riccati transfer matrix method (TMM), an improved Riccati TMM considering contact effects brought by a face tooth is developed. A correction coefficient for equivalent stiffness imported from a three-dimensional (3D) finite element contact case analysis is defined to evaluate the contact effects, and then the dynamic model of the rod-fastened rotor including bearing support is established. A computer program is further developed to obtain the dynamic characteristics such as critical speeds of lateral vibration, mode shapes, and an unbalance response. The improved TMM is applied to investigate the dynamic characteristics of a real central tie rod rotor of the class-F gas turbine for verification of its effectiveness, and the calculated critical speeds are in good agreement with test measurement results, implying that the method is accurate and the dynamic model is reliable. This approach can also be applied to analyze other combined rotors with a homogeneous structure.

A Hybrid Method for the Vibration Analysis of Rotor-Bearing Systems

1991 ◽  
Vol 205 (2) ◽  
pp. 131-137 ◽  
Author(s):  
R Firoozian ◽  
H Zhu
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Hybrid Method ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Mode Shapes ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Rotor Bearing

The transfer matrix method together with a digital computer form the foundation of the dynamic analysis of rotor-bearing systems. The properties of each segment of the rotating shaft are expressed in simple matrix form and the overall dynamic behaviour is then obtained by successive multiplication of the element matrices. The main drawback associated with this method is the numerical instability in calculating natural frequencies for complex systems. The finite element method, on the other hand, uses the element stiffness and mass matrices to form the global equation of motion for the complete system. This avoids the numerical problems of the transfer matrix method at the expense of the computer memory requirements. The new method described in this paper combines the transfer matrix and finite element techniques to form a powerful algorithm for vibration analysis of rotor-bearing systems. It is shown that the accuracy improves significantly when the transfer matrix for each shaft segment is obtained from finite element techniques. The accuracy and efficiency of the hybrid method are compared with the transfer matrix method for a simply supported uniform rotating shaft where an analytical solution for the critical speeds and mode shapes is available. The method is then applied to a flexibly supported uniform shaft and a non-uniform shaft with a large disc to show the capability of the method for finding the critical speeds of complex rotor-bearing systems.

Dynamic Analysis of Multiple Launch Rocket System Under the Action of Jet Flow

2019 ◽  
Author(s):  
Shutian Li ◽  
Guoping Wang ◽  
Yunfei Miao ◽  
Xiaoting Rui
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody System ◽  
Calculated Data ◽  
Jet Flow ◽  
Factors Affecting ◽  
Dynamics Response ◽  
The Impact ◽  
Rocket System

Abstract Jet flow is one of the important factors affecting the vibration, initial disturbance and firing dispersion of Multiple Launch Rocket System (MLRS). In this research, based on the rocket gas jet dynamics, MLRS launch dynamics theory and transfer matrix method for multibody system, a physical model of jet flow model and a MLRS launch dynamics model considering the multiple launch rocket device and the launch of rocket are built. The launching dynamic process of rocket jet flow of MLRS is numerical simulated by using the technology of overset mesh and the Computational Fluid Dynamics (CFD) methods. The nephogram of mach number and contour map of velocity are obtained. The impact effect force on the air-facing surface of rocker launcher after the rocket slides and leaves the directional barrel is acquired. Regarding the calculated data of impact force to MLRS as external force, the MLRS launch dynamics equation is solved by using the transfer matrix method for multibody system. Finally, the dynamics response of MLRS under the effect of jet flow is analyzed.

Vibration Analysis of Linear Beam With Moving Loads Based on Riccati Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Lu Sun ◽  
Xue Rui ◽  
Dieter Bestle ◽  
Guoping Wang ◽  
Jianshu Zhang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Mode Shapes ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

The paper presents the dynamic response of an Euler-Bernoulli beam supported by an elastic foundation and subjected to a moving step load. The Riccati transfer matrix method for linear multibody systems (Riccati MSTMM) is employed to find eigenfrequencies and mode shapes of the supported beam. A comparison of results obtained with the finite element method (FEM) indicates that the Riccati MSTMM is more accurate when using the same number segments. Based on these results, the dynamic response of the beam with moving step load is investigated for different propagation velocities by mode superposition, and the effect of loads is discussed.

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