scholarly journals Torsional vibration of suspension bridge with a variable cross section

1981 ◽  
Vol 3 (2) ◽  
pp. 22-26
Author(s):  
Nguyen Van Tinh

The transfer matrix method to torsion’ al vibrations of a suspension bridge with variable cross sections is reported. The method described above is particularly suitable for implementing an efficient computer program. A numerical example is also givens.

2021 ◽  
pp. 107754632110128
Author(s):  
Yunxing Du ◽  
Peng Cheng ◽  
Fen Zhou

A transfer matrix method is used to study free vibration characteristics of an axial-loaded Euler–Bernoulli beam with variable cross sections and multiple concentrated elements in the article. The differential equation for bending vibrations of the beam element is solved by the Frobenius method, and the solution is in power series form. Then, the transfer matrix method is applied to establish the state vector equation for both ends of the beam. Combined with boundary conditions, the frequency equation is obtained and expressed in a two-order determinant. The numerical results in this article are compared with those of the finite element method, which illustrates the accuracy of the method we proposed. The influence of the size of each concentrated elements and axial force on the natural frequency coefficients and the influence of the concentrated elements on the first critical buckling load are discussed.


Author(s):  
Qingna Zeng ◽  
Fenggang Zang ◽  
Yixiong Zhang ◽  
Donghui Wang

Abstract In this paper, theoretical solutions of free transverse vibration for tapering pipe considering variable cross section have been investigated using Bessel function in low frequency domain. Natural frequency was calculated by transfer matrix method (TMM) based on an accurate theoretical model. The effectiveness and validity of TMM with Bessel function was confirmed in comparison with TMM of discrete uniform pipe and Finite Element Method. Furthermore, dimensionless model was proposed to avoid the singularity, instability and overflow in calculation. The geometry effect, such as tapering ratio, thickness-radius and length-radius ratio influence on the nature frequency was explored. The present study was envisaged to provide useful insights for dynamic analysis of pipeline systems.


Author(s):  
Zhi Zhang ◽  
Dongmei Du ◽  
Qing He

Due to the disturbance of electric power system or other shock load, the torsional vibration of turbine-generator shafts occurs. It is significant to calculate the response of torsional vibration excited by the disturbance of electric power system in order to analyze and prevent catastrophic accident. The multi-mass lumped model of turbine-generator shafts is used. A new method of response calculation of torsional vibration of turbine-generator shafts, the Increment Transfer Matrix method (ITM), which combines the Riccati transfer matrix method with the Newmark-β step-by-step integral method, is presented. By the ITM method, the transient response of torsional vibration of turbine-generator shafts, especially at the dangerous cross-sections, can be calculated. The responses of torsional vibration of 200MW turbine-generator shafts due to the generator at non-all-phase operation are calculated and analyzed. The cause of bolt broken of the coupling of intermediate-pressure rotor and low-pressure rotor and the coupling of generator and exciter are discussed. The results are identical with the data recorded in field.


2021 ◽  
Author(s):  
Shengrong Xie ◽  
Yiyi Wu ◽  
Dongdong Chen ◽  
Ruipeng Liu ◽  
Xintao Han ◽  
...  

Abstract In deep underground mining, achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge. Owing to the coupling action of multiple factors such as deep high stress, adjacent faults, cross-layer design, weak lithology, broken surrounding rock, variable cross-sections, wide sections up to 9.9 m, and clusters of nearby chambers, there was severe deformation and breakdown in the No. 10 intersection of the roadway of large-scale variable cross-section at the − 760 m level in the Nanfeng working area of the Wuyang Coal Mine. As there are insufficient examples in engineering methods pertaining to the geological environment described above, the numerical calculation model was oversimplified and support theory underdeveloped; therefore, it is imperative to develop an effective support system for the stability and sustenance of deep roadways. In this study, a quantitative analysis of the geological environment of the roadway through field observations, borehole peeking, and ground stress testing is carried out to establish the FLAC 3D variable cross-section crossing roadway model. This model is combined with the strain softening constitutive (surrounding rock) and Mohr-Coulomb constitutive (other deep rock formations) models to construct a compression arch mechanical model for deep soft rock, based on the quadratic parabolic Mohr criterion. An integrated control technology of bolting and grouting that is mainly composed of a high-strength hollow grouting cable bolt equipped with modified cement grouting materials and a high-elongation cable bolt is developed by analyzing the strengthening properties of the surrounding rock before and after bolting, based on the Heok-Brown criterion. As a result of on-site practice, the following conclusions are drawn: (1) The plastic zone of the roof of the cross roadway is approximately 6 m deep in this environment, the tectonic stress is nearly 30 MPa, and the surrounding rock is severely fractured. (2) The deformation of the roadway progressively increases from small to large cross-sections, almost doubling at the largest cross-section. The plastic zone is concentrated at the top plate and shoulder and decreases progressively from the two sides to the bottom corner. The range of stress concentration at the sides of the intersection roadway close to the passageway is wider and higher. (3) The 7 m-thick reinforced compression arch constructed under the strengthening support scheme has a bearing capacity enhanced by 1.8 to 2.3 times and increase in thickness of the bearing structure by 1.76 times as compared to the original scheme. (4) The increase in the mechanical parameters c and φ of the surrounding rock after anchoring causes a significant increase in σc and σt; the pulling force of the cable bolt beneath the new grouting material is more than twice that of ordinary cement grout, and according to the test, the supporting stress field shows that the 7.24 m surrounding rock is compacted and strengthened in addition to providing a strong foundation for the bolt (cable). On-site monitoring shows that the 60-day convergence is less than 30 mm, indicating that the stability control of the roadway is successful.


1980 ◽  
Vol 102 (1) ◽  
pp. 122-129 ◽  
Author(s):  
M. S. Darlow ◽  
B. T. Murphy ◽  
J. A. Elder ◽  
G. N. Sandor

The transfer matrix method for rotordynamic analysis (alternately known as the HMP or LMP method) has enjoyed wide popularity due to its flexibility and ease of application. A number of computer programs are generally available which use this method in various forms to perform undamped critical speed, unbalance response, damped critical speed and stability analyses. For all of these analyses, the assembly of the transfer matrices from the rotor model is essentially the same. In all cases, the rotor model must be composed entirely of cylindrical beam elements. There are two situations when this limitation is not desirable. The first situation is when the rotor being modelled has one or more sections whose cross sections vary continually in the axial direction. The most common of these sections is the conical section. Presently, a conical section must be modelled as a series of “steps” of cylindrical sections. This adversely affects both the simplicity and accuracy of the rotor model. The second situation when current transfer matrix techniques are not accurate is when the rotor being modelled has one or more sections that do not behave as beam elements. The most common example is a trunnion which behaves as a plate. This paper describes the analytical basis and the method of application for direct representation of conical sections and trunnions for a transfer matrix analysis. Analytical results are currently being generated to demonstrate the need for and advantages of these modelling procedures.


Micromachines ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 970
Author(s):  
J. Israel Martínez-López ◽  
Héctor Andrés Betancourt Cervantes ◽  
Luis Donaldo Cuevas Iturbe ◽  
Elisa Vázquez ◽  
Edisson A. Naula ◽  
...  

In this paper, we characterized an assortment of photopolymers and stereolithography processes to produce 3D-printed molds and polydimethylsiloxane (PDMS) castings of micromixing devices. Once materials and processes were screened, the validation of the soft tooling approach in microfluidic devices was carried out through a case study. An asymmetric split-and-recombine device with different cross-sections was manufactured and tested under different regime conditions (10 < Re < 70). Mixing performances between 3% and 96% were obtained depending on the flow regime and the pitch-to-depth ratio. The study shows that 3D-printed soft tooling can provide other benefits such as multiple cross-sections and other potential layouts on a single mold.


Author(s):  
Dongmei Du ◽  
Zhi Zhang ◽  
Qing He

Due to the disturbance of electric power system or other shock load, the torsional vibration of turbine-generator shafts occurs. Alternative shear stress due to torsional vibration decreases the shafts life, even results in shafts broken. It is significant to calculate and analyze natural properties and the responses of tosional vibration excited by the disturbance of electric power system in order to analyze and prevent catastrophic accident. The calculation and analysis system of torsional vibration of turbine-generator shafts is developed. With multi-mass lumped model, the model of torsional vibration of turbine-generator shafts is obtained. The system calculates the natural frequencies and the modal shapes of torsional vibration with the transfer matrix method, the response of torsional vibration of shafts with the increment transfer matrix method, such as torsional angle, angular velocity, angular acceleration, cross-section torque, and torsional stress. The response spectrum of torsional vibration can be obtained by fast Fourier transform algorithm Take an example of a 200MW turbine-generator, which is in the condition of non-all-phase operation. The responses of torsional vibration of shafts are calculated and analyzed. The bolt broken reasons of the coupling of inter-pressure rotor and low-pressure rotor and the coupling of generator and exciter are discussed. The results are identical with the data recorded in field. It is proved that the system is good precision, convenient using, friendly interfacing, and visual calculating.


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