Exact, Single Equation, Closed-Form Solution of Vibrating Systems With Piecewise Linear Springs

Chicurel-Uziel, Enrique

doi:10.1006/jsvi.2001.3568

Cited by 18 publications

(5 citation statements)

References 3 publications

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“…The influence of a damper on the dynamic responses of a vehicle are investigated analytically under bump and pothole excitations [4]. A method of obtaining the closed-form displacement response of free undamped vibrations and the steady state of forced damped vibrations of systems with piecewise linear springs is presented in [5]. An effective and low-cost method to assess the condition of vehicles' shock absorbers, based on the measurement of vertical accelerations on sprung and unsprung masses for a shock input, was proposed in [6].…”

Section: Introductionmentioning

confidence: 99%

Response of Shock Isolators with Piecewise Linear Asymmetric Damping

Mitu,

Solomon,

Giuclea

et al. 2023

Symmetry

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The output of a single-degree-of-freedom (SDOF) piecewise linear system with asymmetric damping and linear stiffness excited by Dirac impulse excitation is studied. Analytical solutions of the response for piecewise linear systems are obtained by replacing the equation of motion with Dirac excitation by a homogeneous differential system with zero initial displacement and a given initial velocity. A significant improvement of the response consisting in a substantial reduction in the after-shock vibrations was obtained. The obtained results are applied to the damping optimization of a shock isolation system for forging hammers.

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Section: Introductionmentioning

confidence: 99%

Response of Shock Isolators with Piecewise Linear Asymmetric Damping

Mitu,

Solomon,

Giuclea

et al. 2023

Symmetry

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show abstract

“…During the last few decades, fruitful work has been done in studying the nonlinearity of these systems, i.e., solving the piecewise linear equations. Exact solutions (Natsiavas, 1989;Chicurel-Uziel, 2001;Ji and Leung, 2004), which are composed of a set of transcendental equations, can be obtained for the frequency responses and stability analysis of such systems. However, the instances of time at which the displacement crosses the piecewise linear boundary needs to be determined, and thus the complete response history cannot be obtained in closed form.…”

Section: Introductionmentioning

confidence: 99%

Two-step transfer function calculation method and asymmetrical piecewise-linear vibration isolator under gravity

Wang

Zheng

2014

Journal of Vibration and Control

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Piecewise-linear isolators are widely used in spacecraft for satisfying ever more stringent vibration requirements of high precision payloads. This paper focuses on ground tests of such isolators, with special consideration of gravitational asymmetry and mount flexibility. With asymmetrical equivalent isolator parameters derived with the extended equivalent linearization method, a two-step transfer function calculation method is proposed for enhancing the computation efficiency in dealing with studies where huge amount of computations are required, such as design parameter studies. The asymmetrical effect due to the gravity is presented by the movement of dynamic equilibrium positions as well as the softening and hardening characteristics of frequency responses. The effects and differences of the rigid mount and flexible mount, which respectively correspond to the shake table test and the whole spacecraft structure ground test, are studied with various design parameters. Numerical results show that the preload is an important factor in determining such effects and differences.

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“…This situation is additionally complicated if the constraints are not independent. Currently, the nonlinear dynamics study for elastic limiters is largely concentrated in the single-mode system [4][5][6][7] . The practical problems are mainly solved by the numerical algorithm.…”

Section: Introductionmentioning

confidence: 99%

Dynamic investigation on floating raft with elastic limiters

Wen

Feng

Zhang

2011

J. Shanghai Jiaotong Univ. (Sci.)

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In this paper, we consider a floating raft isolation system with elastic limiters. The limiters might be "contact" or "no contact", thus forming a unilateral system generating possible contacts. In order to avoid the large displacement of the floating raft under shock, limiters might be adopted but good limiters design requires the values of the gaps. Based on the contact dynamics, the multi-degree-freedom dynamic model of floating raft isolation system with elastic limiters is established. The artificial neural network has been developed to dingtinguish the contact state of elastic limiters at each step. The example analysis shows that the algorithm of neural network for contact can shorten the time of caclaution. From the example analysis, we get some interesting results that may be useful to the ship engineering.

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Exact, Single Equation, Closed-Form Solution of Vibrating Systems With Piecewise Linear Springs

Cited by 18 publications

References 3 publications

Response of Shock Isolators with Piecewise Linear Asymmetric Damping

Response of Shock Isolators with Piecewise Linear Asymmetric Damping

Two-step transfer function calculation method and asymmetrical piecewise-linear vibration isolator under gravity

Dynamic investigation on floating raft with elastic limiters

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