THE FORCED VIBRATION AND BOUNDARY CONTROL OF PRETWISTED TIMOSHENKO BEAMS WITH GENERAL TIME DEPENDENT ELASTIC BOUNDARY CONDITIONS

2002 ◽  
Vol 254 (1) ◽  
pp. 69-90 ◽  
Author(s):  
S.M. LIN ◽  
S.Y. LEE
Keyword(s):  
Boundary Conditions ◽  
Boundary Control ◽  
Forced Vibration ◽  
Time Dependent ◽  
Timoshenko Beams ◽  
Elastic Boundary ◽  
Elastic Boundary Conditions ◽  
General Time

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.

The sensibility on dynamic characteristics of pre-pressure thin-wall pipe under elastic boundary conditions

2016 ◽  
Vol 231 (6) ◽  
pp. 995-1009 ◽  
Author(s):  
Li Chaofeng ◽  
Tang Qiansheng ◽  
Miao Boqing ◽  
Wen Bangchun
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Forced Vibration ◽  
Vibration Response ◽  
Spring Stiffness ◽  
Pressure Pipe ◽  
Elastic Boundary ◽  
Elastic Boundary Conditions ◽  
Distributed Pressure

Consideration is given to dynamic behavior of cylindrical pressure pipe with elastic boundary conditions. Based on Sanders’ shell theory and Hamilton principle, the system equations are established for integrating the uniform distributed pressure into the elastic boundary condition. In the analytical formulation, the Rayleigh–Ritz method with a set of displacement shape functions is used to deduce mass, damping, and stiffness matrices of the pipe system. The displacements in three directions are represented by the characteristic orthogonal polynomial series and trigonometric functions which are satisfied with the elastic boundary conditions, which are represented as four sets of independent springs placed at the ends including three sets of linear springs and one set of rotational spring. The pressure pipe always suffers a uniform distributed pressure in radial direction. To verify the accuracy and reliability of the present method, several numerical examples with classical boundary condition, including free and simply supported supports are listed and comparisons are made with open literature. Then the influences of boundary restraint stiffness and the distributed pressure on natural frequency and the forced vibration response are studied: The natural frequencies increase significantly as the restraint stiffness or the distributed pressure increases. Compared to the rotational spring stiffness, the stiffnesses of axial, radial, and circumferential springs have more significant effect on natural frequency. And the lower modes are more sensitive on restraint stiffness than higher modes. But the variation of natural frequency with respect to the spring stiffness decreases monotonically with the increasing distributed pressure. The forced vibration response is also affected by the restraint stiffness.

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