Vibration Equations for a Structure

1970 ◽  
Vol 14 (03) ◽  
pp. 168-180
Author(s):  
H. M. Mott-Smith
Keyword(s):  
Dynamical System ◽  
Variational Equation ◽  
Structural Parameters ◽  
New Method ◽  
Lumped Mass ◽  
Wave Solutions

The exact equations of vibrations of a dynamical system consisting of both continuous members and isolated masses are obtained by a new method employing Hamilton's variational equation. The method is quite general, and replaces the treatments by lumped-mass models in current use. It makes possible the calculation of wave solutions, which reveal new features of the nature of the motion. Comparison with the results from lumped-mass models shows the scope and limitations of these results. In some cases it makes possible the deduction of formulas for the stresses in structure members expressed directly in terms of the structural parameters, dispensing with all dynamical calculations. These statements are illustrated by examples.

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

A New Method for Computing Eigenpairs of a Finite Element Structure

2014 ◽  
Vol 590 ◽  
pp. 672-676
Author(s):  
Ping Liang ◽  
Yu Hang Zhang ◽  
Jun Wei ◽  
Bing Yu
Keyword(s):  
Dynamical System ◽  
Finite Element ◽  
New Method ◽  
Stability And Convergence ◽  
Power Method ◽  
Value Iteration ◽  
Eigenvalues And Eigenvectors ◽  
Simpler Algorithm ◽  
Distribution Of Eigenvalues ◽  
D Value

Based on the weighted inverse topological change method and by introducing a new concept of mass submembers, a dynamical system can be transformed into a static one. Using the properties of the weighted D value, i.e. the weighted D value decreases monotonously with parameter λ increasing; a new method called the weighted D value iteration method is presented for computing the eigenpairs (eigenvalues and eigenvectors). Using this method a series of eigenpairs of a finite element structure can be obtained. It has a merit of simpler algorithm and less computation efforts. Not as the power method, its stability and convergence rate does not depend on the distribution of eigenvalues, and convergent quickly. An example is given to demonstrate the valid of this method.

scholarly journals Propagation of stochastic travelling waves of cooperative systems with noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hao Wen ◽  
Jianhua Huang ◽  
Yuhong Li
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Wave Speed ◽  
Travelling Waves ◽  
Equilibrium Points ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Cooperative System ◽  
Wave Solutions ◽  
Suitable Marker

<p style='text-indent:20px;'>We consider the cooperative system driven by a multiplicative It\^o type white noise. The existence and their approximations of the travelling wave solutions are proven. With a moderately strong noise, the travelling wave solutions are constricted by choosing a suitable marker of wavefront. Moreover, the stochastic Feynman-Kac formula, sup-solution, sub-solution and equilibrium points of the dynamical system corresponding to the stochastic cooperative system are utilized to estimate the asymptotic wave speed, which is closely related to the white noise.</p>

scholarly journals An ANN-Based Approach for Prediction of Sufficient Seismic Gap between Adjacent Buildings Prone to Earthquake-Induced Pounding

2020 ◽  
Vol 10 (10) ◽  
pp. 3591
Author(s):  
Seyed Mohammad Khatami ◽  
Hosein Naderpour ◽  
Seyed Mohammad Nazem Razavi ◽  
Rui Carneiro Barros ◽  
Barbara Sołtysik ◽  
...  
Keyword(s):  
Parametric Analysis ◽  
Structural Parameters ◽  
Seismic Gap ◽  
Minimal Distance ◽  
Lumped Mass ◽  
Seismic Excitations ◽  
Ground Acceleration ◽  
Earthquake Records ◽  
Adjacent Buildings ◽  
Structural Arrangements

Earthquake-induced structural pounding may cause major damages to structures, and therefore it should be prevented. This study is focused on using an artificial neural network (ANN) method to determine the sufficient seismic gap in order to avoid collisions between two adjacent buildings during seismic excitations. Six lumped mass models of structures with a different number of stories (from one to six) have been considered in the study. The earthquake characteristics and the parameters of buildings have been defined as inputs in the ANN analysis. The required seismic gap preventing pounding has been firstly determined for specified structural arrangements and earthquake records. In order to validate the method for other structural parameters, the study has been further extended for buildings with different values of height, mass, and stiffness of each story. Finally, the parametric analysis has been conducted for various earthquakes scaled to different values of the peak ground acceleration (PGA). The results of the verification and validation analyses indicate that the determined seismic gaps are large enough to prevent structural collisions, and they are just appropriate for all different structural arrangements, seismic excitations, and structural parameters. The results of the parametric analysis show that the increase in the PGA of earthquake records leads to a substantial, nearly uniform, increase in the required seismic gap between structures. The above conclusions clearly indicate that the ANN method can be successfully used to determine the minimal distance between two adjacent buildings preventing their collisions during different seismic excitations.

scholarly journals A New Mathematical Modeling Method for Four-Stage Helicopter Main Gearbox and Dynamic Response Optimization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yuan Chen ◽  
Rupeng Zhu ◽  
Guanghu Jin ◽  
Yeping Xiong ◽  
Jie Gao ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Sensitivity Analysis ◽  
Dynamic Response ◽  
Dynamic Model ◽  
Structural Parameters ◽  
Modeling Method ◽  
System Response ◽  
Analysis Method ◽  
Lumped Mass ◽  
Sensitivity Analysis Method

A new mathematical modeling method, namely, the finite element method and the lumped mass method (LMM-FEM) mixed modeling, is applied to establish the overall multinode dynamic model of a four-stage helicopter main gearbox. The design of structural parameters of the shaft is the critical link in the four-stage gearbox; it affects the response of multiple input and output branches; however, only the meshing pairs were frequently shown in the dynamic model in previous research. Therefore, each shaft is also treated as a single node and the shaft parameters are coupled into the dynamic equations in this method, which is more accurate for the transmission chain. The differential equations of the system are solved by the Fourier series method, and the dynamic response of each meshing element is calculated. The sensitivity analysis method and parameter optimization method are applied to obtain the key shaft parameters corresponding to each meshing element. The results show that the magnitude of dynamic response in converging meshing pair and tail output pair is higher than that of other meshing pairs, and the wall thickness has great sensitivity to a rotor shaft. In addition, the sensitivity analysis method can be used to select the corresponding shaft node efficiently and choose parameters appropriately for reducing the system response.

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