Equilibria and vibration of a heavy pinched loop

Santillan, Sophia T.; Virgin, Lawrence N.; Plaut, Raymond H.

doi:10.1016/j.jsv.2004.12.016

Cited by 34 publications

(22 citation statements)

References 10 publications

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“…(4), and if the resulting equation 0"= -p COS0 is multiplied by 0' and integrated, one obtains (0')^ = M' adh -2py after applying the transversality condition. Then, one finds that From similarity conditions for the loop (i.e., relations which involve nondimensional parameters and are independent of size) [3, 39,40], and using the transversality condition, the following relations can be derived:…”

Section: Introductionmentioning

confidence: 99%

Analysis of Carbon Nanotubes and Graphene Nanoribbons With Folded Racket Shapes

Plaut

Borum

Dillard

2012

Journal of Engineering Materials and Technology

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Eolding of carbon nanotubes and graphene nanoribbons into a shape that looks like a tennis racket is considered. An elastic continuum model is utilized in two types of analysis. The first is called an "adhesion model," in which the adjacent sides of the racket handle are assumed to be straight and bonded together with constant or no separation. The nanotube or nanoribbon is represented as an elástica. This model has been treated in the literature, but new analytical results are derived here, involving the geometry, work of adhesion, and bending and adhesion energies. Expressions are determined for (i) the length for which the total energy is the same as for the straight unstrained equilibrium configuration and (ii)for the minimum length for existence of a stable racket equilibrium shape. The second type of analysis uses the Lennard-Jones potential to model the attractive (van der Waals) and repulsive forces between the two sides of the racket. A nanoribbon is investigated, and the derivative of the interatomic potential is integrated along the length and across the width. Numerical solutions of the integro-differential equations are obtained with a new technique utilizing the finite difference method and minimization of the squares of the resulting algebraic equations. The results are presented for two cases with different flexural rigidities. The separation between the two sides of the handle decreases in the direction of the racket head (loop), and the handle experiences internal compression under the external attractive and repulsive forces. Eor the adhesion model, the dimensions of the head are proportional to the square root of the fiexural rigidity, and this relationship is approximately satisfied in the numerical results based on the Lennard-Jones model.

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Section: Introductionmentioning

confidence: 99%

Analysis of Carbon Nanotubes and Graphene Nanoribbons With Folded Racket Shapes

Plaut

Borum

Dillard

2012

Journal of Engineering Materials and Technology

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“…A roving hammer method is used to excite, in the x direction, the two sides of the band (i.e.. Points 1-6 and Points [14][15][16][17][18][19][20][21][22][23][24]. Since it is difficult to excite the band in the x and y directions, at the points on the lower loop (i.e..…”

Section: Comparison Of Results With Those From the Experiments And Femmentioning

confidence: 99%

“…Note that since the two ends of the loop coincide in Ref. [15], a characteristic length a=\EI/pg is used there.…”

Section: Equations Of Motionmentioning

confidence: 99%

See 1 more Smart Citation

A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables

Zhu¹,

Ren²,

Xiao

2011

Journal of Applied Mechanics

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A nonlinear, planar model of a slack cable with bending stiffness and arbitrarily moving ends is developed. The model uses the slope angle of the centroid line of the cable to describe the moticm of the cable, and the resulting integropartial differential equation with constraints is derived using Hamilton's principle. A new method is devehped to obtain the spatially discretized equations, and the Baumgarte stabilization procedure is used to .wive the resulting differential-algebraic equations. The model can be used to calculate the equilibria and corresponding free vibration characteristics of the cable, as well as the dynamic response of the cable under arbitrarily moving ends. The results for an equilibrium and free vibration characteristics around the equilibrium are experimentally validated on a laboratory steel band. The methodology is applied to elevator traveling and compensation cables. It is found that a vertical motion of the car can introduce a horizontal vibration of a traveling or compensation cable. The results presented are verifled by a commercial finite element software. The current method is shown to be more efficient than the finite element method as it uses a much smaller number of elements to reach the same accuracy. Some other interesting features include the condition for a traveling or compensation cable equilibrium to be closest to a natural loop and a direct proof that the catenary solution is unique.

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“…This could cause many difficulties for designing a traditional system. Currently, there are many researchers, engineers and scholars who have suggested solutions to reduce the resonance frequency such as a highly deformed elastic structure working as a nonlinear spring is used to support a static load as presented by (Chnin et al, 2005), , (Virgin et al, 2003) and (Winterflood et al, 2002) or another structure that is also based on the elastic model with extreme geometric nonlinearity is studied by (Santillan et al, 2005) and . The purpose of elastic structures is to reduce the resonance frequency.…”

Section: Introductionmentioning

confidence: 99%

Dynamic simulation of seat suspension system with virtual prototyping technology

Nguyen

2017

JAMDSM

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This paper will describe and simulate the dynamic response of an innovative suspension system for vehicle seat. In which, the isolated object is supported by a wedge mechanism which comprises a horizontal spring, a roller and a wedge. Besides, the dynamic stiffness of system is corrected by an auxiliary mechanism (AM) including a roller (follower) which always contacts the circular surface of the cam via another horizontal spring. Hence, this seat suspension prototype not only broad the excitation frequency region but also remains the load bearing capacity and is named by "model with AM". The dynamic stiffness-configurative parameter relationship is presented. Then, a virtual mechanical prototyping model of the system is created by using SOLIDWORKS software. Next, by applying dynamic analysis in COSMOSMotion module of the Solidworks product family, the real behaviour of system is tested and evaluated without using the traditional build-and-test method. With this way, it can increase the quality of product by reducing manufacturing cost and error. The simulation results show that the model with AM outperforms the linear counterpart. Besides, these results furnish a useful insight for the design and manufacture of the seat suspension system for vehicle.

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Equilibria and vibration of a heavy pinched loop

Cited by 34 publications

References 10 publications

Analysis of Carbon Nanotubes and Graphene Nanoribbons With Folded Racket Shapes

Analysis of Carbon Nanotubes and Graphene Nanoribbons With Folded Racket Shapes

A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables

Dynamic simulation of seat suspension system with virtual prototyping technology

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