Analytical and Experimental Natural Frequencies of Transverse Vibration of Sandwich Beams Interconnected by Winkler Elastic Foundation

Aerospace ◽  
2006 ◽  
Author(s):  
Mohamed Gaith ◽  
James Masters ◽  
Sinan Muftu
Keyword(s):  
Elastic Foundation ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Theoretical Models ◽  
Asynchronous Mode ◽  
Single Beam ◽  
Beam System ◽  
Winkler Elastic Foundation ◽  
Double Beam ◽  
End Conditions

The free transverse vibration of an elastically connected axially loaded double beam system for different materials and geometry were measured experimentally and analyzed theoretically. The theory predicts that natural frequencies of the system are composed of two infinite sets, describing in-phase and out-of-phase vibrations. It is observed, for the case of identical beams, that the in-phase frequencies are independent of the elastic foundation stiffness and its frequencies are identical to a single beam with the same boundary conditions. To compare and verify the accuracy and reliability of theoretical models, experimental measurements of natural frequencies of free vibration of axially tensioned, double beams interconnected by a silicone rubber foundation with fixed-fixed supported conditions are conducted. The first four synchronous natural frequencies were measured, and they were found to increase with increasing tension. The experiments showed that the synchronous natural frequencies of axially tensioned double beam system with fixed-fixed end conditions are in excellent agreement with those for a tensioned single beam with the same end conditions. The asynchronous mode frequencies are not observed, and believed to be due to the existence of damping properties in the elastic foundation, which suppressed the out-of-phase (asynchronous) mode frequencies.

Transverse Vibration of Two Axially Moving Beams Connected by an Elastic Foundation

2005 ◽  
Author(s):  
Mohamed Gaith ◽  
Sinan Mu¨ftu¨
Keyword(s):  
Elastic Foundation ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Beam Theory ◽  
Mode Shapes ◽  
Winkler Elastic Foundation ◽  
Canonical State ◽  
Axially Moving Beams ◽  
Axially Moving

Transverse vibration of two axially moving beams connected by a Winkler elastic foundation is analyzed analytically. The system is a model of paper and paper-cloth (wire-screen) used in paper making. The two beams are tensioned, translating axially with a common constant velocity, simply supported at their ends, and of different materials and geometry. Due to the effect of translation, the dynamics of the system displays gyroscopic motion. The Euler-Bernoulli beam theory is used to model the deflections, and the governing equations are expressed in the canonical state form. The natural frequencies and associated mode shapes are obtained. It is found that the natural frequencies of the system are composed of two infinite sets describing in-phase and out-of-phase vibrations. In case the beams are identical, these modes become synchronous and asynchronous, respectively. Divergence instability occurs at the critical velocity; and, the frequency-velocity relationship is similar to that of a single traveling beam. The effects of the mass, flexural rigidity, and axial tension ratios of the two beams, as well as the effects of the elastic foundation stiffness are investigated.

The Effect of Joints on the Transverse Vibration of a Simple Structure

1990 ◽  
Vol 204 (1) ◽  
pp. 37-42 ◽  
Author(s):  
F P E Dunne ◽  
M Heppenstall
Keyword(s):  
Mild Steel ◽  
Compressive Stress ◽  
Transverse Vibration ◽  
Reasonable Agreement ◽  
Simple Structure ◽  
Natural Frequencies ◽  
Theoretical Models ◽  
Experimental Results ◽  
Predicted Values ◽  
Vibration Tests

Transverse vibration tests were carried out on a cold-drawn mild steel tubular beam containing annular metal-to-metal joints. The tests were also carried out on an unjointed beam of the same dimensions. An axial compressive preload was applied giving a compressive stress in the range of 0–80 N/mm2. Joints between rough turned surfaces, between ground surfaces and mixed joints between both types of surface were used. Dynamic bending stiffnesses of the joints over the range of compressive stress were determined. Stiffness of the turned and mixed joints was found to be proportional to preload. Stiffness of ground joints increased with preload, but not proportionally. Theoretical models were developed to determine joint bending siffness and natural frequencies of transverse vibration of the jointed beams. Predicted values of joint bending stiffness for ground and turned joints were in reasonable agreement with the experimental results.

Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation

2013 ◽  
Vol 20 (4) ◽  
pp. 359-370 ◽  
Author(s):  
Ersin Demir ◽  
Hasan Çallioğlu ◽  
Metin Sayer
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Sandwich Beam ◽  
Variable Cross Section ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Variable Cross ◽  
Winkler Elastic Foundation

AbstractIn this study, free vibration behavior of a multilayered symmetric sandwich beam made of functionally graded materials (FGMs) with variable cross section resting on variable Winkler elastic foundation are investigated. The elasticity and density of the functionally graded (FG) sandwich beam vary through the thickness according to the power law. This law is related to mixture rules and laminate theory. In order to provide this, a 50-layered beam is considered. Each layer is isotropic and homogeneous, although the volume fractions of the constituents of each layer are different. Furthermore, the width of the beam varies exponentially along the length of the beam, and also the beam is resting on an elastic foundation whose coefficient is variable along the length of the beam. The natural frequencies are computed for conventional boundary conditions of the FG sandwich beam using a theoretical procedure. The effects of material, geometric, elastic foundation indexes and slenderness ratio on natural frequencies and mode shapes of the beam are also computed and discussed. Finally, the results obtained are compared with a finite-element-based commercial program, ANSYS®, and found to be consistent with each other.

Dynamic Characteristics of a Double-Layer Sheathing Cable System Based on Dynamic Stiffness Theory

2018 ◽  
Vol 18 (07) ◽  
pp. 1850096 ◽  
Author(s):  
Fei Han ◽  
Dan-Hui Dan ◽  
Xing-Fei Yan
Keyword(s):  
Double Layer ◽  
Dynamic Characteristics ◽  
Dynamic Equilibrium ◽  
Dynamic Stiffness ◽  
Cable System ◽  
Beam Dynamic ◽  
Single Beam ◽  
Beam System ◽  
Distribution Rule ◽  
Double Beam

Based on the theory of double-beam dynamic stiffness, a dynamic equilibrium equation for an inclined beam segment was established for the analysis of the dynamic characteristics of a double-layer sheathing cable system. The closed-form transverse dynamic stiffness matrix of the system considering the bending stiffness, inclination angle, boundary condition, and the sag of the beam was obtained simultaneously. The distribution rule of its elements and determinant, defined as dynamic stiffness coefficients and the characteristic function separately, were analyzed in the space and frequency domain. By using a numerical case study, the vibration characteristics of the double-beam system were investigated. It shows that in a given frequency range, the modal frequencies of the double-beam system are affected by both beams, and the beam with smaller stiffness contributes more to the system frequency. The contributions of each single beam to the system frequencies may be further determined by the distribution rule obtained. Based on these results, a method was proposed for quick evaluation of the contribution of each single beam to the modal frequency of the system. This will help to identify the frequency and cable force of double-layer sheathing cables.

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