Timoshenko Beam Modeling for Parameter Estimation of NASA Mini-Mast Truss

1993 ◽  
Vol 115 (1) ◽  
pp. 19-24 ◽  
Author(s):  
Ji Yao Shen ◽  
Jen-Kuang Huang ◽  
L. W. Taylor
Keyword(s):  
Timoshenko Beam ◽  
Closed Form Solution ◽  
Computational Effort ◽  
Form Solution ◽  
Beam Equation ◽  
Distributed Parameter ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Modal Characteristics ◽  
Cantilevered Beam

In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss is proposed. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure and the computational effort for the estimation of modal characteristics are improved. A maximum likelihood estimator for the Timoshenko beam model is also developed. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from other approaches.

scholarly journals Simulating Building Motions Using Ratios of the Building's Natural Frequencies and a Timoshenko Beam Model

2015 ◽  
Vol 31 (1) ◽  
pp. 403-420 ◽  
Author(s):  
Ming Hei Cheng ◽  
Thomas H. Heaton
Keyword(s):  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mode Shapes ◽  
Elastic Behavior ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Linear Elastic ◽  
Modal Summation

A simple prismatic Timoshenko beam model with soil-structure interaction (SSI) is developed to approximate the dynamic linear elastic behavior of buildings. A closed-form solution with complete vibration modes is derived. It is demonstrated that building properties, including mode shapes, can be derived from knowledge of the natural frequencies of the first two translational modes in a particular direction and from the building dimensions. In many cases, the natural frequencies of a building's first two vibrational modes can be determined from data recorded by a single seismometer. The total building's vibration response can then be simulated by the appropriate modal summation. Preliminary analysis is performed on the Caltech Millikan Library, which has significant bending deformation because it is much stiffer in shear.

scholarly journals Stabilization and Observability of a Rotating Timoshenko Beam Model

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Alexander Zuyev ◽  
Oliver Sawodny
Keyword(s):  
Timoshenko Beam ◽  
Galerkin Approximation ◽  
Sufficient Conditions ◽  
Beam Equation ◽  
Distributed Parameter ◽  
Dimensional System ◽  
Beam Model ◽  
Finite Dimensional ◽  
Galerkin Approximations ◽  
Rotating Timoshenko Beam

A control system describing the dynamics of a rotating Timoshenko beam is considered. We assume that the beam is driven by a control torque at one of its ends, and the other end carries a rigid body as a load. The model considered takes into account the longitudinal, vertical, and shear motions of the beam. For this distributed parameter system, we construct a family of Galerkin approximations based on solutions of the homogeneous Timoshenko beam equation. We derive sufficient conditions for stabilizability of such finite dimensional system. In addition, the equilibrium of the Galerkin approximation considered is proved to be stabilizable by an observer-based feedback law, and an explicit control design is proposed.

FINITE ELEMENT MODELING AND STABILITY ANALYSIS OF CHATTER IN END MILLING MACHINING

2003 ◽  
Vol 27 (3) ◽  
pp. 205-221 ◽  
Author(s):  
Tong Qu ◽  
Amir Khajepour ◽  
Der Chyan Lin ◽  
Kamran Behdinan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
End Milling ◽  
Closed Form Solution ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Mass Model ◽  
Element Analysis ◽  
Stability Lobes ◽  
The Stability

In this paper, chatter in end milling machine tools is investigated using a Timoshenko beam model and finite element analysis. The model is developed for the cases where the slender machining cutters are flexible along the axial direction. A closed form solution for obtaining the stability lobes is derived assuming cutting forces as point loads applied to the end of the tool. It is shown that the stability lobes converge as the number of elements increase. The results indicate that using a single mass model used in the literature predict a more conservative chatter stability compared to the more accurate model using finite element and Timoshenko beam model.

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.

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

2020 ◽  
pp. 239779142093170
Author(s):  
M Faraji Oskouie ◽  
R Ansari ◽  
H Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Time Domain ◽  
Beam Model ◽  
Viscoelastic Foundation ◽  
Timoshenko Beam Model ◽  
Governing Equations ◽  
The Time Domain

On the basis of fractional viscoelasticity, the size-dependent free-vibration response of viscoelastic carbon nanotubes conveying fluid and resting on viscoelastic foundation is studied in this article. To this end, a nonlocal Timoshenko beam model is developed in the context of fractional calculus. Hamilton’s principle is applied in order to obtain the fractional governing equations including nanoscale effects. The Kelvin–Voigt viscoelastic model is also used for the constitutive equations. The free-vibration problem is solved using two methods. In the first method, which is limited to the simply supported boundary conditions, the Galerkin technique is employed for discretizing the spatial variables and reducing the governing equations to a set of ordinary differential equations on the time domain. Then, the Duffing-type time-dependent equations including fractional derivatives are solved via fractional integrator transfer functions. In the second method, which can be utilized for carbon nanotubes with different types of boundary conditions, the generalized differential quadrature technique is used for discretizing the governing equations on spatial grids, whereas the finite difference technique is used on the time domain. In the results, the influences of nonlocality, geometrical parameters, fractional derivative orders, viscoelastic foundation, and fluid flow velocity on the time responses of carbon nanotubes are analyzed.

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