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Abstract Prediction of a ship's roll motion in parametric roll and dead ship condition using CFD and experiments is time consuming and expensive, while a reliable equation based method can drastically decrease the computation time. The commonly used roll motion equation contains roll mass and added mass moment of inertia, damping and restoring terms and associated coefficients. Improving the prediction of these coefficients increases the accuracy of the method. There is a lack of precise calculation for the roll added mass moment of inertia, which is commonly estimated using semi-empirical techniques and as a percentage of the roll mass moment of inertia coefficient. This paper presents a new method to determine the roll added mass moment of inertia using CFD simulations based on a harmonic excitation roll motion technique and the results are compared against Bhattacharyya's method. The influences of excitation frequency, Froude number, roll angle and appendages on the roll motion characteristics and the roll added mass moment of inertia coefficient are investigated. In addition, the roll added mass moment of inertia coefficients on the model scale and full scale ship are computed to investigate the scale effect. [ABSTRACT FROM AUTHOR]

Highlights • Propose a novel isolation structure with flexible joints. • Introduce Origami mechanism in vibration isolation/protection structure. • Utilize asymmetrical nonlinearity to extend the effective isolation bandwidth. • Determine the optimal structural parameter of folds for isolation effectiveness improvement. • Carry out the experimental prototype with remarkable isolation/protection property. Abstract This paper proposes a novel isolation/protection structure inspired by structure and forcing method of leg parts of bipeds, the Origami-Joint Flexible (OJF) isolation structure. The vibration performances are studied under impact and ultralow-frequency excitations. According to the mechanical features of the legs of bipeds, the restoring force is considered mainly at the joints. Simulating the structure of bipeds, the flexibility of the proposed structure is realized by using an Origami structure with resilience at its folds. Based on the analysis of potential energy, the restoring and damping forces are nonlinear and symmetrical, depending on both magnitude and direction of motions. Then, solutions for transient and steady states are obtained for different high-energy excitations. Due to the large displacement and strong nonlinearity, the Method of Multiple Scales (MMS) with high-order approximation is utilized for theoretical study. The main theoretical results are verified by experiments. The relevant prototype displays remarkable isolation/protection effectiveness for impact and ultralow-frequency excitations. This study not only shows the advantages of strong asymmetrical nonlinearity of the novel isolation structure with flexible joints but also theoretically explains its control mechanism. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

A nonlinear oscillator, using a cubic-spring restoring function with high-deformation stiffening, is introduced and studied experimentally to improve passively the harnessed marine hydrokinetic power using Flow Induced Vibrations (FIVs) of a cylinder. In this research, the FIV of a single, rigid, circular cylinder on elastic end-supports is tested for Reynolds number 30,000 ≤  Re  ≤ 120,000. Damping, cubic stiffness, and flow-velocity are used as parameters. Selective roughness is applied to enhance FIV and increase the hydrokinetic energy converted by the oscillator. The second generation of the digital, virtual spring-damping system Vck, developed in the Marine Renewable Energy Laboratory (MRELab), enables embedded computer-controlled change of the functions and values of viscous damping and spring stiffness. Cubic modeling of the oscillator stiffness in parametric form is thus realized and tested. Experimental results for amplitude response, frequency response, energy harvesting, efficiency and instantaneous energy of the converter are presented and discussed. All experiments are conducted in the Low Turbulence Free Surface Water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are: (1) The cubic stiffness function is an effective way to raise the harnessed efficiency over a wider range of flow velocities. (2) At lower flow speed (upper and lower VIV branches), the harnessed power increases as the nonlinearity increases. A strongly nonlinear system exhibits a 100% increase in harnessed energy in this region. (3) At a higher flow speed (galloping), the cubic nonlinearity benefits the harnessed power in two ways because the natural frequency of the oscillator in water ( f n,water ) depends on the amplitude of oscillation. At low harness damping, the amplitude increases resulting in higher f n,water thus enhancing the harnessed power. At high harness damping, the harnessed power increases regardless of f n,water . [ABSTRACT FROM AUTHOR]

This study deals with analysis of stochastic crosswind response of tall buildings with bilinear hysteretic restoring force character at the vicinity of vortex lock-in speed where nonlinear negative aerodynamic damping is significant. The nonlinear aerodynamic damping at a given wind speed and the hysteretic damping resulted from hysteretic restoring force are modelled as polynomial functions of amplitude of narrow-band building response. It permits analytical estimations of response statistics by using equivalent nonlinear equation (ENEL) approach, which include root-mean-square value, kurtosis, extreme value distribution and fatigue damage. Response history analysis is also performed to prove the accuracy of this analytical framework. A comprehensive parameter study is carried out to shed insights on the characteristics of inelastic crosswind response. This study also illustrates the advantage of the ENLE approach over the statistical linearization approach with assumption of Gaussian response distribution when applied to estimate inelastic crosswind response at wind speed region with negligible aerodynamic damping. This study not only presents an effective analytical approach but also sheds new insights towards improved understanding of inelastic crosswind response of tall buildings, contributing to a safer and more economical design of tall buildings against strong winds. [ABSTRACT FROM AUTHOR]

Flow Induced Motions (FIMs) of a single, rigid, circular cylinder with piecewise continuous restoring force are investigated for Reynolds number 24,000≤ Re ≤120,000 with damping, and different piecewise functions as parameters. Selective roughness is applied to enhance FIM and increase the hydrokinetic energy captured by the VIVACE (Vortex Induced Vibration for Aquatic Clean Energy) Converter at higher Reynolds numbers. The second generation of virtual spring-damping system Vck, developed in the Marine Renewable Energy Laboratory (MRELab), enables embedded computer-controlled change of viscous-damping and spring-stiffness for fast and precise oscillator modeling. Experimental results for amplitude response, frequency response, energy harvesting, and efficiency are presented and discussed. All experiments were conducted in the Low Turbulence Free Surface Water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are: (1) The nonlinear piecewise spring Converter can harness energy from flows as slow as 0.275 m/s with no upper limit. (2) In galloping, the nonlinear spring Converter has up to 76% better performance than its linear spring counterpart. (3) The FIM response is predominantly periodic for all nonlinear spring functions used. (4) Optimal power harnessing is achieved by changing the nonlinear piecewise spring function and the linear viscous damping. (5) VIVACE exhibits local maxima in power conversion at the end of the upper branch in VIV and the highest velocity reached in galloping. (6) The efficiency optima though are at the beginning of the VIV initial branch and at the beginning of galloping. [ABSTRACT FROM AUTHOR]

A strongly nonlinear pendulum mechanism is considered in which the restoring force is approximately a cubic function of the displacement variable. Its free oscillation frequency is approximately proportional to the amplitude of oscillation and distinctly lower than that of a simple pendulum. The mechanism has therefore been named infra-pendulum. The forced undamped oscillation response of the mechanism to non-harmonic periodic loading is studied under the assumption of small displacements. The loading function is derived from the free oscillation response whose time course follows a Jacobi elliptic function. It is chosen such that exact analytical solutions are obtained for the steady-state response and the amplitude–frequency relation. The equation describing the amplitude–frequency relation is a cubic polynomial equation. Its solutions are presented. The general approach of using non-harmonic periodic loading functions is transferable to other types of nonlinear oscillators. [ABSTRACT FROM AUTHOR]

A semi-analytical approach to the simulation of the parametric roll motions of container ships in head seas is presented. In the proposed 1.5-degree of freedom model, the nonlinear change in the transverse stability induced by the vertical motions and wave elevation is approximated by investigating the relationship between the restoring lever ( GZ ) and the metacentric height ( GM ) in waves. In particular, the variations in the GM in irregular waves are modeled by the transfer functions of the mean value and first harmonic component on the basis of the assumption of superposition. Using the derived formula, the quantitative prediction of parametric roll motion as well as the susceptibility to such motion in regular and irregular waves is conducted. A comparison with the results of a weakly nonlinear time-domain method, namely, the impulse response function method based on the hydrodynamic coefficients of strip theory, is carried out to validate the proposed model. Not only the accuracy and efficiency of the present approach but also the stochastic properties of parametric roll in random seas are examined considering the sensitivities and uncertainties in the computations. [ABSTRACT FROM AUTHOR]

Pitching motion is one of the most important characteristics in the longitudinal plane for the maneuvering supercavitating vehicle. In this case, supercavity is unsteady to dramatically change hydrodynamic distribution of its vehicle because of some factors such as changes of ambient pressure and control surfaces, gravity, inertial force, and so on. More importantly, planing force is usually produced to provide restoring force and moment for motion stability. The maneuvering supercavity model is applied to model supercavitating vehicle with planing force in the longitudinal plane. The corresponding numerical algorithm is developed to simulate uncontrolled vehicle making a diving motion in the longitudinal plane and calculate planing force based on the model. The algorithm includes two intercoupling sub-algorithms: the self-developed cavitation number embedded coefficient correction algorithm for unsteady supercavity and Runge–Kutta algorithm for vehicle’s trajectory. The model and numerical algorithm are validated to some extent by comparing numerical results with ones of the empirical supercavity model applied widely. [ABSTRACT FROM AUTHOR]

In this study, we investigated the scaling behavior of dynamic hysteresis with frequency f and electric field E in epitaxial PbZrO 3 antiferroelectric film on (111)-oriented SrTiO 3 substrate. The scaling relation for the saturated hysteresis loops takes the form of hysteresis area ∝ f 0.03 ( E − 499) 0.20 at relatively low testing f . However, when frequency exceeds 30 Hz, the shows stronger dependence on f while remains basically unchanged relation with E , leading to a form of ∝ f 0.10 ( E − 499) 0.20 . The scaling behavior is modeled as occurring in a viscous medium where several forces, such as viscous and restoring forces, act on the phase transition process. [ABSTRACT FROM AUTHOR]

In this paper, the first-passage failure of stochastic dynamical systems with fractional derivative and power-form restoring force subjected to Gaussian white-noise excitation is investigated. With application of the stochastic averaging method of quasi-Hamiltonian system, the system energy process will converge weakly to an Itô differential equation. After that, Backward Kolmogorov (BK) equation associated with conditional reliability function and Generalized Pontryagin (GP) equation associated with statistical moments of first-passage time are constructed and solved. Particularly, the influence on reliability caused by the order of fractional derivative and the power of restoring force are also examined, respectively. Numerical results show that reliability function is decreased with respect to the time. Lower power of restoring force may lead the system to more unstable evolution and lead first passage easy to happen. Besides, more viscous material described by fractional derivative may have higher reliability. Moreover, the analytical results are all in good agreement with Monte-Carlo data. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present a nonlinear approach to identify the structural parameters of a vertical riser. To carry out this task, Kalman-like observers are proposed so that they can deal with the nonlinear behavior that is exhibited in the restoring force of a riser and the noise of the measurement signals that are used to perform the identification. The observers are designed from a spatial discretization of a nonlinear model with distributed parameters that is described by a system of quasi-linear partial differential equations. Some results from numerical simulations—showing the feasibility of the proposed approach—are presented. [ABSTRACT FROM AUTHOR]

In structural engineering, sophisticated multi-dimensional analysis techniques, such as the Restoring Force Method (RFM), have been established for complex, nonlinear hysteretic systems. The purpose of the present study was to apply the RFM to quantify nonlinear spine hysteresis responses under applied moments. First, synthetic hysteretic spine responses ( n =50) were generated based on representative results from pure moment flexion–extension loading of a human cadaveric lumbar spine segment. Then, the RFM was applied to each hysteresis response to describe the flexion–extension rotation as a function of applied moment and simulated axial displacement using a set of 16 unique coefficients. Range of motion, neutral zone, elastic zone, and stiffness were also measured. The RFM coefficient corresponding to the 1st-order linear dependence of rotation on applied moment was dominant, and paralleled changes in elastic zone. The remaining RFM coefficients were not captured from the traditional biomechanical analysis. Therefore, the RFM may potentially supplement the traditional analysis to develop a more comprehensive, quantitative description of spine hysteresis. The results suggest the potential for more thorough and specific characterization of spine kinematics, and may lead to future applications of such techniques in characterizing biological structures. [ABSTRACT FROM AUTHOR]

Abstract: In my research a 3D model was created to investigate the restoring force arising and the self-alignment occurring during reflow soldering; and simulations were performed to examine the assumptions given by the model. Besides, experiments were carried out to verify both the assumptions and the simulation predictions. Passive components with the size of 0603 (1.5×0.75mm) were placed with intended misplacements and their position was measured before and after soldering. Three cases were examined: how misplacements perpendicular to the longer sides of components affects the restoring force, how parallel misplacements affect the same, and how a sidewall metallization on the component influences that. Based on the results, it is shown that the degree of restoring force is higher in the case of misplacements perpendicular to the longer side of components (x-direction) than in the case of misplacements parallel to that (y-direction). However, in the case of y-direction misplacements, the restoring force increases when sidewall metallization on the components is present. [Copyright &y& Elsevier]

Highlights: [•] Second harmonic generation is studied in layer by layer assembled thin films. [•] Chromophore reorientation is achieved by all optical poling. [•] The photoinduced reorientation relaxes faster in polyelectrolyte thin films. [•] A restoring force model is proposed and validated. [•] Restoring force is attributed to the interlayer electrostatic field. [Copyright &y& Elsevier]

Abstract: Electrostatically actuated micro devices experience a fundamental limit on their stable travel range due to a phenomenon called as the pull-in Instability. Accurate determination of pull-in parameters (pull-in displacement and pull-in voltage) is vital in the design of electrostatic micro actuators. A systematic method of analysis of prismatic type of electrostatic beam is discussed in this paper. Using Galerkin method static analysis is carried out. Behaviour of interaction of nonlinear electrostatic force with linear restoring force of the micro cantilever beam is studied. Static analysis using COMSOL multiphysics finite element package is done to validate the results. The results are also compared with existing literature. [Copyright &y& Elsevier]