Exact solutions for extensible circular curved timoshenko beams with nonhomogeneous elastic boundary conditions

1998 ◽  
Vol 130 (1-2) ◽  
pp. 67-79 ◽  
Author(s):  
S. M. Lin
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Timoshenko Beams ◽  
Elastic Boundary ◽  
Elastic Boundary Conditions

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.

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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