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.

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.

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.

Free Vibration of a Multilayered One-Dimensional Quasi-Crystal Plate

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Natalie Waksmanski ◽  
Ernian Pan ◽  
Lian-Zhi Yang ◽  
Yang Gao
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Crystal Plate ◽  
Mode Shapes ◽  
Sandwich Plates ◽  
One Dimensional ◽  
Propagator Matrix ◽  
Multilayered Plates

An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

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.

Electromechanical Modeling of the Low Frequency MEMS Energy Harvester

2009 ◽  
Author(s):  
M. Amin Karami ◽  
Daniel J. Inman
Keyword(s):  
Power Output ◽  
Natural Frequencies ◽  
Vibrational Energy ◽  
Closed Form Solution ◽  
Low Frequency ◽  
Form Solution ◽  
Mode Shapes ◽  
Energy Harvesters ◽  
Electromechanical Modeling ◽  
Deflection Voltage

An analytical electromechanical model is proposed to predict the deflection, voltage and the power output a proposed low frequency micro harvesting structure. The high natural frequencies of the existing designs of MEMS vibrational energy harvesters are serious drawbacks. A zigzag design is proposed to overcome this limitation. The mode shapes of the free vibration problem are first calculated together with the natural frequencies of the structure. The piezoelectric direct and reverse effect equations together with the electrical equations are used to relate the voltage output of the structure to the base vibrations magnitude and frequency. The closed form solution of the continuous electromechanical vibrations precisely gives the power output as a function of base acceleration spectrum. The usefulness of the design is proved by the significant increase of the power output from the same base accelerations, providing a method of designing a MEMS harvester with low natural frequency.

scholarly journals Free vibration of a single-walled carbon nanotube based on the nonlocal Timoshenko beam model

2021 ◽  
Vol 37 ◽  
pp. 616-635
Author(s):  
Yu-Chi Su ◽  
Tse-Yu Cho
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Elastic Medium ◽  
Timoshenko Beam ◽  
Slenderness Ratio ◽  
Mode Shapes ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon

Abstract Free vibration of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium is studied on the basis of the nonlocal Timoshenko beam model. Influences of the slenderness ratios, the boundary conditions, the atomic structures and the stiffness of the embedded medium on the natural frequencies and mode shapes of SWCNT are examined. The nonlocal effect is significant for the higher modes of SWCNT with a small slenderness ratio embedded in a soft elastic medium, and it softens the SWCNT except for the fundamental frequency of the clamped–free SWCNT.

scholarly journals A closed-form solution for free vibration of multiple cracked Timoshenko beam and application

2017 ◽  
Vol 39 (4) ◽  
pp. 315-328
Author(s):  
Nguyen Tien Khiem ◽  
Duong The Hung
Keyword(s):  
Free Vibration ◽  
Closed Form ◽  
Timoshenko Beam ◽  
Crack Depth ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Frequency Equation ◽  
Form Solution ◽  
Mode Shapes ◽  
Timoshenko Beams

A closed-form solution for free vibration is constructed and used for obtaining explicit frequency equation and mode shapes of  Timoshenko beams with arbitrary number of cracks. The cracks are represented by the rotational springs of stiffness calculated from the crack depth.  Using the obtained frequency equation, the sensitivity of natural frequencies to crack of the beams is examined in comparison with the  Euler-Bernoulli beams. Numerical results demonstrate that the Timoshenko beam theory is efficiently applicable not only for short or fat beams but also for the long or slender ones. Nevertheless, both the theories are equivalent in sensitivity analysis of fundamental frequency to cracks and they get to be different for higher frequencies.

Complex Modal Analysis of Non-Self-Adjoint Hybrid Serpentine Belt Drive Systems

2000 ◽  
Vol 123 (2) ◽  
pp. 150-156 ◽  
Author(s):  
Lixin Zhang ◽  
Jean W. Zu ◽  
Zhichao Hou
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mode Shapes ◽  
Belt Drive ◽  
Serpentine Belt ◽  
Complex Modal Analysis ◽  
Drive Systems ◽  
Complex Modal

A linear damped hybrid (continuous/discrete components) model is developed in this paper to characterize the dynamic behavior of serpentine belt drive systems. Both internal material damping and external tensioner arm damping are considered. The complex modal analysis method is developed to perform dynamic analysis of linear non-self-adjoint hybrid serpentine belt-drive systems. The adjoint eigenfunctions are acquired in terms of the mode shapes of an auxiliary hybrid system. The closed-form characteristic equation of eigenvalues and the exact closed-form solution for dynamic response of the non-self-adjoint hybrid model are obtained. Numerical simulations are performed to demonstrate the method of analysis. It is shown that there exists an optimum damping value for each vibration mode at which vibration decays the fastest.

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