Dynamic Analysis of Non-Uniform Beams With Time Dependent Elastic Boundary Conditions

1995 ◽  
Author(s):  
Sen Yung Lee ◽  
Shueei Muh Lin
Keyword(s):  
Boundary Conditions ◽  
Time Dependent ◽  
Polynomial Functions ◽  
Third Order ◽  
The Third ◽  
Elastic Boundary ◽  
Order Degree ◽  
Elastically Restrained ◽  
Fifth Order ◽  
Elastic Boundary Conditions

Abstract The dynamic response of a non-uniform beam with time dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. The time dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third order degree, instead of the fifth order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.

Dynamic Analysis of Nonuniform Beams With Time-Dependent Elastic Boundary Conditions

1996 ◽  
Vol 63 (2) ◽  
pp. 474-478 ◽  
Author(s):  
Sen Yung Lee ◽  
Shueei Muh Lin
Keyword(s):  
Boundary Conditions ◽  
Time Dependent ◽  
Polynomial Functions ◽  
Third Order ◽  
Elastic Boundary ◽  
Order Degree ◽  
Elastically Restrained ◽  
Fifth Order ◽  
Nonuniform Beam ◽  
Elastic Boundary Conditions

The dynamic response of a nonuniform beam with time-dependent elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained nonuniform beams given by Lee and Kuo. The time-dependent elastic boundary conditions for the beam are formulated. A general form of change of dependent variable is introduced and the shifting polynomials of the third-order degree, instead of the fifth-order degree polynomials taken by Mindlin-Goodman, are selected. The physical meaning of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and several examples are given to illustrate the analysis.

A General Approach on the Mechanical Analysis of Nonuniform Beams With Nonhomogeneous Elastic Boundary Conditions

1998 ◽  
Vol 120 (1) ◽  
pp. 164-169 ◽  
Author(s):  
Sen Yung Lee ◽  
Wen Rong Wang ◽  
Terry Yuan-Fang Chen
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Fundamental Solutions ◽  
Mechanical Analysis ◽  
Polynomial Functions ◽  
Static Response ◽  
Elastic Boundary ◽  
Elastically Restrained ◽  
Nonuniform Beam ◽  
Elastic Boundary Conditions

The dynamic and static response of a nonuniform beam with nonhomogeneous elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. A general form of change of dependent variable is introduced and the shifting functions expressed in terms of the four fundamental solutions of the system, instead of the fifth degree polynomials taken by Mindlin-Goodman, are selected. The physical meanings of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and examples are given to illustrate the analysis.

Study on high volumetric efficiency of the Roots rotor profile with variable trochoid ratio

2006 ◽  
Vol 220 (9) ◽  
pp. 1375-1384 ◽  
Author(s):  
Y-W Hwang ◽  
C-F Hsieh
Keyword(s):  
Boundary Conditions ◽  
Volumetric Efficiency ◽  
Design Flow ◽  
Vacuum System ◽  
Third Order ◽  
Pump Performance ◽  
The Third ◽  
Rotor Profile ◽  
Vacuum Systems ◽  
Fifth Order

Vacuum pumps play an important role in vacuum systems. The method proposed in this article, which uses the extended cycloid curve with a variable trochoid ratio, can be utilized to improve pump performance. The third-order and the fifth-order polynomials are used, and their boundary conditions are designed to generate a smooth trochoid ratio function. Hence, a regular addendum curve for the Roots rotor is generated. The tooth profile for the complete Roots rotor is derived from the addendum curve. Undercutting and carryover analyses are used to verify the feasibility of the designed method. Finally, a design flow on how to achieve high volumetric efficiency for a vacuum system is presented.

scholarly journals A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Guohua Gao ◽  
Ningze Sun ◽  
Dong Shao ◽  
Yongqiang Tao ◽  
Wei Wu
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Thermal Environment ◽  
Search Algorithm ◽  
Golden Section ◽  
Shear Deformation Theory ◽  
Simulation Software ◽  
Elastic Boundary ◽  
Piezoelectric Beam ◽  
Elastic Boundary Conditions

This article mainly analyzes the free vibration characteristic of the sandwich piezoelectric beam under elastic boundary conditions and thermal environment. According to the first-order shear deformation theory and Hamilton’s principle, the thermo-electro-elastic coupling equations of the sandwich piezoelectric beam are obtained. Meanwhile, elastic boundary conditions composed of an array of springs are introduced, and the displacement variables and external potential energy of the beam are expressed as wave functions. By using the method of reverberation-ray matrix to integrate and solve the governing equations, a search algorithm based on golden-section search is introduced to calculate the required frequency parameters. A series of numerical results are compared with those reported in literature studies and obtained by simulation software to verify the correctness and versatility of the search algorithm. In addition, three parametric research cases are proposed to investigate the frequency parameters of sandwich piezoelectric beams with elastic restraint conditions, material parameters, thickness ratio, different temperature rises, and external electric potential.

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