A closed-form solution for natural frequencies of thin-walled cylinders with clamped edges

2016 ◽  
Vol 110 ◽  
pp. 116-126 ◽  
Author(s):  
Marco Cammalleri ◽  
Antonio Costanza
Keyword(s):  
Closed Form ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Thin Walled ◽  
Clamped Edges

Wave-Induced Vibrations of an Axial-Loaded Immersed Timoshenko Beam Carrying an Eccentric Tip Mass with Rotary Inertia

2010 ◽  
Vol 54 (01) ◽  
pp. 15-33
Author(s):  
Jong-Shyong Wu ◽  
Chin-Tzu Chen
Keyword(s):  
Closed Form ◽  
Timoshenko Beam ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Mode Superposition Method ◽  
Tip Mass

Under the specified assumptions for the equation of motion, the closed-form solution for the natural frequencies and associated mode shapes of an immersed "Euler-Bernoulli" beam carrying an eccentric tip mass possessing rotary inertia has been reported in the existing literature. However, this is not true for the immersed "Timoshenko" beam, particularly for the case with effect of axial load considered. Furthermore, the information concerning the forced vibration analysis of the foregoing Timoshenko beam caused by wave excitations is also rare. Therefore, the first purpose of this paper is to present a technique to obtain the closed-form solution for the natural frequencies and associated mode shapes of an axial-loaded immersed "Timoshenko" beam carrying eccentric tip mass with rotary inertia by using the continuous-mass model. The second purpose is to determine the forced vibration responses of the latter resulting from excitations of regular waves by using the mode superposition method incorporated with the last closed-form solution for the natural frequencies and associated mode shapes of the beam. Because the determination of normal mode shapes of the axial-loaded immersed "Timoshenko" beam is one of the main tasks for achieving the second purpose and the existing literature concerned is scarce, the details about the derivation of orthogonality conditions are also presented. Good agreements between the results obtained from the presented technique and those obtained from the existing literature or conventional finite element method (FEM) confirm the reliability of the presented theories and the developed computer programs for this paper.

Closed-Form Solution of Natural Frequencies of a Cantilever Beam Under Longitudinal Rotation of the Support

2005 ◽  
Author(s):  
Mehdi Esmaeili ◽  
Mohammad Durali ◽  
Nader Jalili
Keyword(s):  
Closed Form ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Longitudinal Direction ◽  
Form Solution ◽  
Governing Equations ◽  
Well Drilling ◽  
General Base ◽  
Tip Mass

This paper presents the modeling steps towards development of frequency equations for a cantilever beam with a tip mass under general base excitations. More specifically, the beam is considered to vibrate in all the three directions, while subjected to a base rotational motion around its longitudinal direction. This is a common configuration utilized in many vibrating beam gyroscopes and well drilling systems. The governing equations are derived using Extended Hamilton’s Principle with general 6-DOF base motion. The natural frequency equations are then extracted in closed-form for the case where the base undergoes longitudinal rotation. For validation purposes, the resulting natural frequencies are compared with two example case studies; one with a beam on a stationary base and the other one with a rotor having flexible shaft.

Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams

2000 ◽  
Vol 68 (2) ◽  
pp. 176-185 ◽  
Author(s):  
S. Candan ◽  
I. Elishakoff
Keyword(s):  
Closed Form ◽  
Infinite Number ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Benchmark Solutions

An infinite number of closed-form solutions is reported for a deterministically or stochastically nonhomogeneous beam, for both natural frequencies and reliabilities, for specialized cases. These solutions may prove useful as benchmark solutions. Numerical examples are evaluated.

NEUROFUZZY MODELING OF NATURAL FREQUENCIES OF CYLINDRICAL SHELLS APPLIED TO EVOLUTIONARY BASED OPTIMAL DESIGN OF SR MOTORS

2006 ◽  
Vol 03 (03) ◽  
pp. 263-277 ◽  
Author(s):  
HOSSEIN ROUHANI ◽  
MANSOUR NIKKHAH BAHRAMI ◽  
BABAK NADJAR ARAABI ◽  
CARO LUCAS
Keyword(s):  
Finite Element ◽  
Optimal Design ◽  
Closed Form ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Problems ◽  
Special Cases ◽  
Wide Range

A thorough analysis of cylindrical shells' dynamical behavior is essential in many different industrial design problems, and particularly in electric motor design. Shell vibration equations form a set of partial differential equations of order eight, where their closed form solution is only known for few special cases with a few known boundary conditions along with many not necessarily realistic assumptions. On the other hand, finite element based numerical solutions does not yield a lumped model that can be regarded as a general solution for natural frequencies of cylindrical shells. In this paper, a neurofuzzy model for natural frequencies of cylindrical shells is developed. At first, natural frequencies are calculated for a wide range of cylindrical shells' dimensions, using either closed form solution or finite element method. Gathered data is exploited for training of a Locally Linear Neurofuzzy Network, which yields a general model for calculation of natural frequencies of cylindrical shells. While the developed neurofuzzy model may be used in different design problems that deals with cylindrical shells, as a case study, the proposed model along with an evolutionary algorithm are utilized in the optimal design of a Switched Reluctance motor.

Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag

2012 ◽  
Vol 19 (9) ◽  
pp. 2650-2655 ◽  
Author(s):  
Wang-bao Zhou ◽  
Li-zhong Jiang ◽  
Zhi-jie Liu ◽  
Xiao-jie Liu
Keyword(s):  
Closed Form ◽  
Shear Deformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Shear Lag ◽  
Box Girders ◽  
Thin Walled

A closed-form solution for composite tunnel linings in a homogeneous infinite isotropic elastic medium

2008 ◽  
Vol 45 (2) ◽  
pp. 266-287 ◽  
Author(s):  
Hany El Naggar ◽  
Sean D. Hinchberger ◽  
K. Y. Lo
Keyword(s):  
Closed Form ◽  
Elastic Medium ◽  
Closed Form Solution ◽  
Form Solution ◽  
Tunnel Lining ◽  
Linear Elastic ◽  
Isotropic Elastic Medium ◽  
Thin Walled ◽  
Walled Cylinder ◽  
Elastic Soil

This paper presents a closed-form solution for composite tunnel linings in a homogeneous infinite isotropic elastic medium. The tunnel lining is treated as an inner thin-walled shell and an outer thick-walled cylinder embedded in linear elastic soil or rock. Solutions for moment and thrust have been derived for cases involving slip and no slip at the lining–ground interface and lining–lining interface. A case involving a composite tunnel lining is studied to illustrate the usefulness of the solution.

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