Minimization of the Vibration Energy of Thin-Plate Structures

1992 ◽  
Author(s):  
Katsumi Inoue ◽  
Dennis P. Townsend ◽  
John J. Coy
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Thin Plate ◽  
Optimization Method ◽  
Optimum Shape ◽  
Vibration Energy ◽  
Plate Structures ◽  
Constant Weight ◽  
Exciting Frequency ◽  
The Given

Abstract An optimization method is proposed to reduce the vibration of thin-plate structures. The method is based on a finite-element shell analysis, a modal analysis, and a structural optimization method. In the finite-element analysis, a triangular shell element with 18 degrees of freedom is used. In the optimization, the overall vibration energy of the structure is adopted as the objective function, and it is minimized at the given exciting frequency by varying the thickness of the elements. The technique of modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variables. The sensitivity is represented by the sensitivities of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. A computer code, based on the proposed method, is developed and is applied to design problems using a beam and a plate as test cases. It is confirmed that the vibration energy is reduced at the given exciting frequency. For the beam excited by a frequency slightly less than the fundamental natural frequency, the optimized shape is close to the beam of uniform strength. For the plate, the optimum shape is obtained such that the changes in thickness have the effect of adding a stiffener or a mass.

scholarly journals Optimum Design of a Gearbox for Low Vibration

1993 ◽  
Vol 115 (4) ◽  
pp. 1002-1007 ◽  
Author(s):  
K. Inoue ◽  
D. P. Townsend ◽  
J. J. Coy
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Shell Element ◽  
Optimization Method ◽  
Vibration Energy ◽  
Nasa Lewis Research ◽  
Element Analysis ◽  
Constant Weight ◽  
Triangular Shell Element ◽  
Exciting Frequency

A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that even the optimization of the top plate alone is effective in reducing total gearbox vibration.

scholarly journals Optimum Design of a Gearbox for Low Vibration

1992 ◽  
Author(s):  
Katsumi Inoue ◽  
Dennis P. Townsend ◽  
John J. Coy
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Optimization Method ◽  
Vibration Energy ◽  
Nasa Lewis Research ◽  
Analysis Method ◽  
Element Analysis ◽  
Constant Weight ◽  
Triangular Shell Element ◽  
Exciting Frequency

Abstract A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis method, a modal analysis method, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that optimization of the top plate alone is effective in reducing total gearbox vibration.

Modal Analysis of Automotive Steering System Based on Finite Element Method

2011 ◽  
Vol 121-126 ◽  
pp. 2085-2090 ◽  
Author(s):  
Shu Ming Chen ◽  
Deng Feng Wang ◽  
Gang Ping Tan ◽  
Jian Ming Zan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Modal Analysis ◽  
Excitation Frequency ◽  
Steering System ◽  
Point Of View ◽  
Steering Wheel ◽  
Exciting Frequency ◽  
Wheel Vibration ◽  
Element Method

In order to understand the vibration characteristics of the steering system and provide suggestions for improvement, a model of the steering system was created based on finite element method (FEM). Also, the modal analysis of the steering system was presented, and the first twenty step modes were calculated and analyzed. The steering system was also evaluated from the resonance point of view. The result shows that the frequency of the first step mode is 31.578 Hz which is higher than the exciting frequency of the engine; also, the road roughness excitation frequency has a minor influence on steering wheel vibration.

scholarly journals Numerical Simulation for the Treatment of Nonlinear Predator–Prey Equations by Using the Finite Element Optimization Method

2021 ◽  
Vol 5 (2) ◽  
pp. 56
Author(s):  
H. M. Srivastava ◽  
M. M. Khader
Keyword(s):  
Finite Element ◽  
Error Function ◽  
Optimization Method ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Predator Prey ◽  
Efficient Simulation ◽  
Runge Kutta Method ◽  
Proposed Model ◽  
The Given

This article aims to introduce an efficient simulation to obtain the solution for a dynamical–biological system, which is called the Lotka–Volterra system, involving predator–prey equations. The finite element method (FEM) is employed to solve this problem. This technique is based mainly upon the appropriate conversion of the proposed model to a system of algebraic equations. The resulting system is then constructed as a constrained optimization problem and optimized in order to get the unknown coefficients and, consequently, the solution itself. We call this combination of the two well-known methods the finite element optimization method (FEOM). We compare the obtained results with the solutions obtained by using the fourth-order Runge–Kutta method (RK4 method). The residual error function is evaluated, which supports the efficiency and the accuracy of the presented procedure. From the given results, we can say that the presented procedure provides an easy and efficient tool to investigate the solution for such models as those investigated in this paper.

Modal Analysis Using Implicit Boundary Finite Element Methods

2014 ◽  
Author(s):  
Zhiyuan Zhang ◽  
Ashok V. Kumar
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
B Spline ◽  
Boundary Method ◽  
Mass Matrices ◽  
Background Mesh ◽  
The Given

Modal analysis is widely used for linear dynamic analysis of structures. The finite element method is used to numerically compute stiffness and mass matrices and the corresponding eigenvalue problem is solved to determine the natural frequencies and mode shapes of vibration. Implicit boundary method was developed to use equations of the boundary to apply boundary conditions and loads so that a background mesh can be used for analysis. A background mesh is easier to generate because the elements do not have to conform to the given geometry and therefore uniform regular shaped elements can be used. In this paper, we show that this approach is suitable for modal analysis and modal superposition techniques as well. Furthermore, the implicit boundary method also allows higher order elements that use B-spline approximations. Several test examples are studied for verification.

Design and modal analysis of a Quadcopter propeller through finite element analysis

2021 ◽  
Author(s):  
Faraz Ahmad ◽  
Pushpendra Kumar ◽  
P. Pravin Patil ◽  
Vijay Kumar
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Modal Analysis ◽  
Element Analysis
Sign in / Sign up

Export Citation Format

Share Document