scholarly journals Adaptive Polynomials for the Vibration Analysis of an L-Type Beam Structure with a Free End

2021 ◽  
Vol 9 (3) ◽  
pp. 300
Author(s):  
Duck Young Yoon ◽  
Jeong Hee Park
Keyword(s):  
Vibration Analysis ◽  
Natural Mode ◽  
Finite Model ◽  
Cantilever Beams ◽  
Design Work ◽  
Local Structures ◽  
Flexible Mode ◽  
Mode Method ◽  
Vibration Problems ◽  
Structural Engineers

Vibration analysis using the component mode method has been less popular than before, since computers are powerful enough to solve complicated structures by a single large finite model. However, many structural engineers designing local structures on a ship still need simple tools to check anticipated vibration problems during their design work. Since most of local structures on a ship are simple enough to consist of several substructures, the component mode method could be of use as long as good, natural mode functions can be provided so that reasonable natural frequencies can be yielded. In this study, since mode polynomials based on static deflection of cantilever beams fail to work to cover the various configurations of L-type beams with a free end, two alternatives are suggested. One is based on more flexible mode functions—we call them adaptive polynomials. The other is a purely mathematical approach, which makes realistic mode functions unnecessary. Suggested alternatives yield very good numerical results.

Reduction of Harmonic Response of Cylindrical Shells

1975 ◽  
Vol 97 (4) ◽  
pp. 1371-1377 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Cantilever Beams ◽  
Steady State Response ◽  
Optimum Conditions ◽  
Harmonic Force ◽  
Shell Surface ◽  
Single Degree Of Freedom ◽  
Harmonic Response ◽  
State Response ◽  
Single Degree ◽  
Mode Method

The normal mode method is used to investigate the reduction in the steady-state response of a simply supported cylindrical shell when conventional absorbers are attached to the shell. Two types of excitation are considered: (a) a single radial harmonic force, and (b) a harmonic pressure distributed over the shell surface. The effect upon response of varying the absorber parameters is studied. Optimum conditions for specific cases are obtained and compared with those required to minimize response when absorbers are added to cantilever beams and to the classical single degree of freedom system.

FREE VIBRATION ANALYSIS OF NON-UNIFORM TIMOSHENKO BEAMS USING DIFFERENTIAL TRANSFORM

1998 ◽  
Vol 22 (3) ◽  
pp. 231-250 ◽  
Author(s):  
Cha’o Kuang Chen ◽  
Shing Huei Ho
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Present Method ◽  
Series Solution ◽  
Free Vibration Analysis ◽  
Timoshenko Beams ◽  
Differential Transform ◽  
Vibration Problems ◽  
Algebraic Operations

This study introduces using differential transform to solve the free vibration problems of a general elastically end restrained non-uniform Timoshenko beam. First, differential transform is briefly introduced. Second, taking differential transform of a non-uniform Timoshenko beam vibration problem, a set of difference equations is derived. Doing some simple algebraic operations on these equations, we can determine any i-th natural frequency, the closed form series solution of any i-th normalized mode shape. Finally, three examples are given to illustrate the accuracy and efficiency of the present method.

Flapwise bending vibration analysis of rotating composite cantilever beams

2004 ◽  
Vol 18 (2) ◽  
pp. 240-245 ◽  
Author(s):  
Seung Hyun Lee ◽  
Sang Ha Shin ◽  
Hong Hee Yoo
Keyword(s):  
Vibration Analysis ◽  
Cantilever Beams ◽  
Bending Vibration

Vibration Analysis of Rotors Utilizing Implicit Directional Information of Complex Variable Descriptions

2002 ◽  
Vol 124 (3) ◽  
pp. 340-349 ◽  
Author(s):  
C. Kessler ◽  
J. Kim
Keyword(s):  
Free Vibration ◽  
Complex Variable ◽  
Vibration Analysis ◽  
Equation Of Motion ◽  
Natural Mode ◽  
Clear Understanding ◽  
Response Functions ◽  
Rigid Rotor ◽  
Directional Information ◽  
Free Vibration Response

A complex variable description of planar motion incorporates directivity as inherent information which is therefore very convenient in vibration analysis of rotors. This paper proposes to use the directional information explicitly when the equation of motion of a rotor is formulated in complex variables. It is shown that the free vibration solution to the equation of motion formulated as such can be defined as the directional natural mode because it describes not only the shape and frequency but also the direction of the free vibration response. The directional frequency response functions (dFRFs) that have been used recently are obtained as the solution to the forced vibration solution to the equation of motion. Symmetric and anti-symmetric motions of a geometrically symmetric rigid rotor are used as examples to explain these concepts and their practical significances. The proposed approach allows clear understanding and definitions of some unique characteristics of rotor vibrations, such as the forward and backward modes, and forward and backward critical speeds, which have been often used in confusing or incorrect ways.

A New General Solution for the Bending and Vibration of Orthotropic Rectangular Thin Plates with Four Free Edges

2010 ◽  
Vol 168-170 ◽  
pp. 1158-1162 ◽  
Author(s):  
Hong Zhang ◽  
Hai Qun Que ◽  
Huan Ding
Keyword(s):  
General Solution ◽  
Vibration Analysis ◽  
Thin Plates ◽  
Physical Parameters ◽  
Winkler Foundation ◽  
Vertical Force ◽  
Rectangular Plates ◽  
Cosine Series ◽  
Vibration Problems ◽  
Free Edges

This paper firstly introduces a new general solution constructed by double trigonometric cosine series with supplementary terms for the bending and vibration analysis of orthotropic rectangular plates with four free edges on the Winkler foundation subjected to arbitrary vertical force. The general solution, which is fourth-order continuously differentiable with less undetermined coefficients, can be used to solve the bending and vibration problems of orthotropic rectangular plates on the Winkler foundation with various physical parameters requiring no classification and superposition. This makes the bending and vibration analysis of orthotropic rectangular plates with four free edges on the Winkler foundation more unified, simplified and regulated. This paper also gives a Series of analytical example to prove that the method is feasible.

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