Optimum Design of Vibration Absorbers for Structurally Damped Timoshenko Beams

1998 ◽  
Vol 120 (4) ◽  
pp. 833-841 ◽  
Author(s):  
E. Esmailzadeh ◽  
N. Jalili
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Beam Theory ◽  
Optimization Procedure ◽  
Vibration Absorbers ◽  
Rotatory Inertia ◽  
Cross Sectional ◽  
Beam Dynamic ◽  
Practical Applications ◽  
Optimal Dynamic

A procedure in designing optimal Dynamic Vibration Absorbers (DVA) for a structurally damped beam system subjected to an arbitrary distributed harmonic force excitation, is presented. The Timoshenko beam theory is used to assess the effects of rotatory inertia and shear deformation. The method provides flexibility of choosing the number of absorbers depending upon the number of significant modes which are to be suppressed. Uniform cross-sectional area is considered for the beam and each absorber is modeled as a spring-mass-damper system. For each absorber with a selected mass, the optimum stiffness and damping coefficients are determined in order to minimize the beam dynamic response at the resonant frequencies for which they are operated. For this purpose, absorbers each tuned to a different resonance, are used to suppress any arbitrarily number of resonances of the beam. The interaction between absorbers is also accounted for in the analysis. The optimum tuning and damping ratios of the absorbers, each tuned to the mode of concern, are determined numerically by sloving a min-max problem. The Direct Updated Method is used in optimization procedure and the results show that the optimum values of the absorber parameters depend upon various factors, namely: the position of the applied force, the location where the absorbers are attached, the position at which the beam response should be minimized, and also the beam characteristics such as boundary conditions, rotatory inertia, shear deformation, structural damping, and cross sectional geometry. Through the given examples, the feasibility of using proposed study is demonstrated to minimize the beam dynamic response over a broad frequency range. The resulting curves giving the non-dimensional absorber parameters can he used for practical applications, and some interesting conclusions can be drown from the study of them.

Dynamic Response of a Supported Beam to Oscillatory Moving Masses

2003 ◽  
Vol 9 (9) ◽  
pp. 1083-1091 ◽  
Author(s):  
Seroj Mackertich
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Beam Theory ◽  
Rotatory Inertia ◽  
Infinite Beam ◽  
The Masses ◽  
Elastically Supported

The dynamic response of an elastically supported infinite beam to oscillatory moving masses has been investigated. The moving velocity and distance between the masses was assumed to be constant. The solution is presented within the framework of a beam theory, which includes the effects of shear deformation and rotatory inertia.

scholarly journals Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

2020 ◽  
Vol 10 (15) ◽  
pp. 5245
Author(s):  
Chunfeng Wan ◽  
Huachen Jiang ◽  
Liyu Xie ◽  
Caiqian Yang ◽  
Youliang Ding ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Timoshenko Beam Theory ◽  
Rotary Inertia ◽  
Cross Sectional

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.

Effect of Shear Deformation and Rotatory Inertia on Dynamic Buckling of Elastic Plates

1988 ◽  
Vol 110 (3) ◽  
pp. 282-286
Author(s):  
V. Birman
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Plate Theory ◽  
Deformation Mode ◽  
Dynamic Buckling ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Qualitative Effect

The influence of shear deformation and rotatory inertia on dynamic response of elastic rectangular plates subject to in-plane loads increasing with time is discussed using Mindlin’s plate theory. The qualitative effect of those factors on transverse displacements is estimated. It is shown that this effect becomes essential only if the plate is thick and the number of half-waves along the plate axes in the deformation mode is large.

The Influence of Geometric and Material Design Variables on the Free Vibration of Thin-Walled Composite Material Beams

1989 ◽  
Vol 111 (3) ◽  
pp. 290-297 ◽  
Author(s):  
L. C. Bank ◽  
C. H. Kao
Keyword(s):  
Shear Deformation ◽  
Beam Theory ◽  
Material Design ◽  
Mode Shapes ◽  
Cross Sectional ◽  
Advanced Composite Materials ◽  
Design Variables ◽  
Maximum Stiffness ◽  
Thin Walled ◽  
Materials Used

The natural frequencies and mode shapes of thin-walled beams constructed of walls, or panels, of advanced composite materials depend upon both the geometry of the cross-section and the mechanical properties of the materials used in the panels. A shear deformation beam theory having the form of a Timoshenko beam theory is used to investigate the influence of these design variables. It is found that the maximum stiffness of a particular beam configuration is obtained when the contributions from the bending and shearing modes of deformation are optimized. Results show the influence of shear deformation even in the fundamental mode of vibration. Simply-supported, cantilever and free-free beams of various cross-sectional shapes and materials are analyzed.

An Experimental Study on the Performance of Fixed-End Supported PFRP Channel Beams under Flexure

2013 ◽  
Vol 702 ◽  
pp. 31-36 ◽  
Author(s):  
Jaksada Thumrongvut ◽  
Sittichai Seangatith
Keyword(s):  
Shear Deformation ◽  
Beam Theory ◽  
Beam Equation ◽  
Vertical Deflection ◽  
Cross Sectional ◽  
Modes Of Failure ◽  
Theory Equation ◽  
Flexural Torsional Buckling ◽  
Fixed End ◽  
Structural Behaviors

The experimental investigation on the fixed-end supported PFRP channel beams subjected to three-point loading is presented. The objectives of this study are to evaluate the effects of the span on the structural behaviors, the critical buckling loads and the modes of failure of the PFRP beams, and to compare the obtained deflections with those obtained from the Timoshenko’s shear deformation beam theory equation in order to check the adequacy of the equation. The beam specimens have the cross-sectional dimensions of 152 43 10 mm with span-to-depth ratio ranging from 16 to 33. A total of twenty-two specimens were performed. Based on the experimental results, it was found that the loads versus mid-span vertical deflection relationships of the beam specimens are linear up to the failure, but the load versus mid-span lateral deflection relationships are geometrically nonlinear. The general modes of failure are the flexural-torsional buckling. Finally, the Timoshenko’s shear deformation beam equation can satisfactorily predict the vertical deflection of the beams within acceptable engineering error.

The Effects of Geometric Asymmetry on the Dynamic Response of Silicon Nanowires

2011 ◽  
Author(s):  
Molly R. Nelis ◽  
Jeffrey F. Rhoads ◽  
Saeed Mohammadi
Keyword(s):  
Dynamic Response ◽  
Frequency Response ◽  
Silicon Nanowires ◽  
Electrostatic Force ◽  
Resonant Response ◽  
Cross Sectional ◽  
Practical Applications ◽  
Electrostatically Actuated ◽  
Predictive Design ◽  
The Impact

This work investigates the impact of asymmetric cross-sectional geometry on the near-resonant response of electrostatically-actuated silicon nanowires. The work demonstrates that dimensional variances of less than 2% qualitatively alter the near-resonant response of these nanosystems, rendering a non-Lorentzian frequency response structure. Theoretical and experimental results demonstrate that this effect is independent of material properties and device boundary conditions and can be easily modeled using a two-degree-of-freedom system. Proper understanding of this phenomenon is believed to be essential in the characterization of the dynamic response of resonant nanotube and nanowire systems and thus the predictive design and development of such devices. Practical applications of the devices of interest include electrostatic force gradients and mass sensing, both of which can advantageously leverage the unique frequency response structure attendant to these systems.

In-Plane Bending and Shear Deformation of Belt Contributions on Tire Cornering Stiffness Characteristics

2020 ◽  
Author(s):  
Gibin Gil ◽  
Sujin Lee
Keyword(s):  
Mathematical Model ◽  
Shear Deformation ◽  
Beam Theory ◽  
Slip Angle ◽  
Wear Properties ◽  
Angle Change ◽  
Foundation Model ◽  
Plane Bending ◽  
Stiffness Characteristics ◽  
Brush Model

ABSTRACT In radial tires, belt structure plays a role of minimizing the lateral deflection of carcass, which has a significant influence on the cornering and wear properties of a tire. The deflection of carcass affects the magnitude of tread block deformation when the tire is under the slip angle. As a result, it can change the cornering stiffness characteristics of the tire, especially when the vertical load is high. During tire development, a tire design engineer tries to find the optimal belt ply angle that satisfies the various performance requirements simultaneously, but it is not an easy task because the effect of belt angle change is different depending on the size of the tire. There have been many attempts to construct a mathematical model that represents the structural properties of the belt package, including the string-based model and the beam on elastic foundation model. But, in many cases, only the in-plane bending of belt is considered and the shear deformation is not taken into consideration. In this study, the effect of belt angle change on belt stiffness is analyzed using a mathematical model based on the Timoshenko beam theory. This model can account for the in-plane bending and shear deformation of the belt structure at the same time. The results of the analysis show how the contribution of bending and shear is changed depending on a tire design parameter, herein the belt cord angle. The effect of belt ply angle change on cornering stiffness is investigated by means of the brush model including belt flexibility. The prediction by the brush model is compared with the measurement using a Flat-trac machine, and the validity of the model is discussed.

Diagnostics of metal samples using the results of experimental and theoretical study of positively charged microparticles formed upon sample destruction

2018 ◽  
Vol 84 (10) ◽  
pp. 23-28
Author(s):  
D. A. Golentsov ◽  
A. G. Gulin ◽  
Vladimir A. Likhter ◽  
K. E. Ulybyshev
Keyword(s):  
Experimental Data ◽  
Early Stage ◽  
Experimental Studies ◽  
Material Model ◽  
Total Charge ◽  
Cross Sectional ◽  
Practical Applications ◽  
Mechanical And Electrical Properties ◽  
Order Of Magnitude ◽  
Using Data

Destruction of bodies is accompanied by formation of both large and microscopic fragments. Numerous experiments on the rupture of different samples show that those fragments carry a positive electric charge. his phenomenon is of interest from the viewpoint of its potential application to contactless diagnostics of the early stage of destruction of the elements in various technical devices. However, the lack of understanding the nature of this phenomenon restricts the possibility of its practical applications. Experimental studies were carried out using an apparatus that allowed direct measurements of the total charge of the microparticles formed upon sample rupture and determination of their size and quantity. The results of rupture tests of duralumin and electrical steel showed that the size of microparticles is several tens of microns, the particle charge per particle is on the order of 10–14 C, and their amount can be estimated as the ratio of the cross-sectional area of the sample at the point of discontinuity to the square of the microparticle size. A model of charge formation on the microparticles is developed proceeding from the experimental data and current concept of the electron gas in metals. The model makes it possible to determine the charge of the microparticle using data on the particle size and mechanical and electrical properties of the material. Model estimates of the total charge of particles show order-of-magnitude agreement with the experimental data.

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