Inelastic impact dynamics of ships with one-sided barriers. Part II: experimental validation

Grace, Ihab M.; Ibrahim, R. A.; Pilipchuk, Valery N.

doi:10.1007/s11071-010-9934-9

Cited by 6 publications

(4 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation (9) describes the ship roll dynamics with one-sided inelastic barrier on the entire time interval, where conditions of reflection from the barrier and impact energy loss are already included through transformation (8). The results generated using the two transformations are compared based on the study conducted by Grace et al [7].…”

Section: Ivanov Non-smooth Coordinate Transformationmentioning

confidence: 99%

See 1 more Smart Citation

Modeling of Dynamic Systems With Vibro-Impact Interaction and Discontinuity Mapping

Ibrahim

2014

The International Conference on Applied Mechanics and Mechanica

View full text Add to dashboard Cite

This paper presents an overview of selected modeling techniques of vibro-impact dynamics. Vibro-impact dynamics has occupied a wide spectrum of studies by dynamicists, physicists, and mathematicians. These studies may be classified into three main categories: modeling, mapping and applications. The main techniques used in modeling of vibro-impact systems include phenomenological modeling, Hertzian models, and non-smooth coordinate transformations developed by Zhuravlev and Ivanov. One of the most critical situations impeded in vibro-impact systems is the grazing bifurcation. Grazing bifurcation is usually studied through discontinuity mapping techniques, which are useful to uncover the rich dynamics in the process of impact interaction. Complex dynamic phenomena of vibro-impact systems such as sub-harmonic oscillations, chaotic motion, and coexistence of different attractors for the same excitation and system parameters but under different initial conditions will be discussed.

show abstract

Section: Ivanov Non-smooth Coordinate Transformationmentioning

confidence: 99%

“…The coefficient of restitution was measured from impact tests of small ship wood model against rigid steel barrier [8] using the basic definition e /…”

Section: Uncertainty Of Restitution Coefficientmentioning

confidence: 99%

Modeling of Dynamic Systems With Vibro-Impact Interaction and Discontinuity Mapping

Ibrahim

2014

The International Conference on Applied Mechanics and Mechanica

View full text Add to dashboard Cite

show abstract

“…Ivanov proposed this method to study the vibroimpacting motion of a multi-degree-of-freedom (MDOF) system, where the displacement of a single mass is constrained. Ivanov's transformation was successfully used to study the nonlinear dynamics of a single-degree-of-freedom (SDOF) vibro-impacting ship motion (Grace et al, 2011a(Grace et al, , 2011b. In this work, we adopt Ivanov's transformation to account for the multiple unilateral constraints in a MDOF system.…”

Section: Introductionmentioning

confidence: 99%

Galerkin–Ivanov transformation for nonsmooth modeling of vibro-impacts in continuous structures

Samukham

Khaderi

Vyasarayani

2020

Journal of Vibration and Control

View full text Add to dashboard Cite

This work deals with the modeling of nonsmooth vibro-impact motion of a continuous structure against a rigid distributed obstacle. Galerkin’s approach is used to approximate the solutions of the governing partial differential equations of the structure, which results in a system of ordinary differential equations. When these ordinary differential equations are subjected to unilateral constraints and velocity jump conditions, one must use an event detection algorithm to calculate the time of impact accurately. Event detection in the presence of multiple simultaneous impacts is a computationally demanding task. Ivanov (Ivanov A 1993 “Analytical methods in the theory of vibro-impact systems”. Journal of Applied Mathematics and Mechanics 57(2): pp. 221–236.) proposed a nonsmooth transformation for a vibro-impacting multi-degree-of-freedom system subjected to a single unilateral constraint. This transformation eliminates the unilateral constraints from the problem and, therefore, no event detection is required during numerical integration. This nonsmooth transformation leads to sign function nonlinearities in the equations of motion. However, they can be easily accounted for during numerical integration. Ivanov used his transformation to make analytical calculations for the stability and bifurcations of vibro-impacting motions; however, he did not explore its application for simulating distributed collisions in spatially continuous structures. We adopt Ivanov’s transformation to deal with multiple unilateral constraints in spatially continuous structures. Also, imposing the velocity jump conditions exactly in the modal coordinates is nontrivial and challenging. Therefore, in this work, we use a modal-physical transformation to convert the system from modal to physical coordinates on a spatially discretized grid. We then apply Ivanov’s transformation on the physical system to simulate the vibro-impact motion of the structure. The developed method is demonstrated by modeling the distributed collision of a nonlinear string against a rigid distributed surface. For validation, we compare our results with the well-known penalty approach.

show abstract

“…For example, the stability and bifurcation of the vibrations of vibroimpact systems under deterministic excitation were studied by many researchers, e.g., [4][5][6][7]. Several nonsmooth coordinate transformation techniques were also developed and studied for vibro-impact vibration [8][9][10][11][12]. In particular, the stochastic response of vibroimpact systems has received more and more attention in the past decades [13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Stochastic response of a vibro-impact Duffing system under external Poisson impulses

Zhu

2015

Nonlinear Dyn

View full text Add to dashboard Cite

This paper studies the stationary probability density function (PDF) of a vibro-impact Duffing system under external Poisson impulses. A one-sided constraint is located at the equilibrium position of the system, and the system collides with the constraint by instantaneous repetitive impacts. A recently proposed solution procedure is extended to the case of Poisson impulses including three steps. First, the Zhuravlev non-smooth coordinate transformation is utilized to make the original Duffing system and impact condition be integrated into one equation. An additional impulsive damping term is introduced in the new equation. Second, the PDF of the new system is obtained with the exponential-polynomial closure method by solving the generalized Fokker-Planck-Kolmogorov equation. Last, the PDF of the original system is established following the methodology on seeking the PDF of a function of random variables. In numerical analysis, different levels of nonlinearity degree and excitation intensity are considered in four illustrative examples to show the effectiveness of the proposed solution procedure. The numerical results show that when the polynomial order is taken as six in the proposed solution procedure, it can present a satisfactory PDF solution compared with the simulated result. The tail region of the PDF solution is also approximated well for both displacement and velocity.

show abstract

Inelastic impact dynamics of ships with one-sided barriers. Part II: experimental validation

Cited by 6 publications

References 12 publications

Modeling of Dynamic Systems With Vibro-Impact Interaction and Discontinuity Mapping

Modeling of Dynamic Systems With Vibro-Impact Interaction and Discontinuity Mapping

Galerkin–Ivanov transformation for nonsmooth modeling of vibro-impacts in continuous structures

Stochastic response of a vibro-impact Duffing system under external Poisson impulses

Contact Info

Product

Resources

About