Dean T. Mook

Bio: Dean T. Mook is an academic researcher from Virginia Tech. The author has contributed to research in topics: Aerodynamics & Nonlinear system. The author has an hindex of 16, co-authored 49 publications receiving 1224 citations.

Nonlinear coupling of pitch and roll modes in ship motions

Abstract: An analysis is presented for the nonlinear coupling of the pitch (heave) and roll modes of ship motions in regular seas when their frequencies are in the ratio of two to one. When the frequency of encounter (excitation frequency) is near the pitch frequency, the pitch mode is excited if the encountered wave amplitude (excitation amplitude) is small. As the excitation amplitude increases, the amplitude of the pitch mode increases until it reaches a critical small value. As the excitation amplitude increases further, the pitch amplitude does not change from the critical value (i.e., the pitch mode is saturated), and all of the extra energy is transferred to the roll mode. Thus, for large excitation amplitudes, the amplitude of the roll mode is very much larger than that of the pitch mode. When the excitation frequency is near the roll frequency, there is no saturation phenomenon and at close to perfect resonance, there is no steady state response in some cases. The present results indicate that large roll amplitudes are likely in this case also.

Cargo Pendulation Reduction of Ship-Mounted Cranes

Abstract: Ship-mounted cranes are used to transfer cargo from large container ships to smaller lighters when deep-water ports are not available. The wave-induced motion of the crane ship can produce large pendulations of the cargo being hoisted and cause operations to be suspended. In this work, we show that it is possible to reduce these pendulations significantly by controlling the slew and luff angles of the boom. Such a control can be achieved with the heavy equipment that is already part of the crane so that retrofitting existing cranes would require a small effort. Moreover, the control is superimposed on the commands of the operator transparently. The successful control strategy is based on delayed feedback of the angles of the cargo-hoisting cable in and out of the plane of the boom and crane tower. Its effectiveness is demonstrated in a fully nonlinear three-dimensional computer simulation and in an experiment with a 1/24th-scale model of a T-ACS (The Auxiliary Crane Ship) crane mounted on a platform moving with three degrees of freedom. The results demonstrate that the pendulations can be significantly reduced, and therefore the range of sea conditions in which cargo-transfer operations can take place can be greatly expanded.

Nonlinear-Aerodynamics/Nonlinear-Structure Interaction Methodology for a High-Altitude Long-Endurance Wing

Abstract: Nonlinear aeroelastic analysis is essential for high-altitude long-endurance (HALE) aircraft. In the current paper, we have presented a computational aeroelastic tool for nonlinear-aerodynamics/nonlinear-structure interaction. Specifically, a consistent nonlinear time-domain aeroelastic methodology has been integrated via tightly coupling a geometrically exact nonlinear intrinsic beam model and the generalized unsteady vortex-lattice aerodynamic model with vortex roll-up and free wake. The effects of discrete gust as well as flow separation at various angles of attack from attached flow to the stall and poststall ranges are also included in the nonlinear aerodynamic model. A HALE-wing model is analyzed as a numerical example. The trim angle of attack is first found for the wing, and the results show that aeroelastic instability could occur at higher angles of attack. The HALE-wing model under the trim condition is then analyzed for various gust profiles to which it is subject. It is found that for certain gust levels, the elastic deformations of the HALE wing tend to become unstable: notably, the in-plane deflections become very significant. It is noted for the unstable solution of the HALE wing that the flow may be well beyond the stall range. An engineering approach with the use of the nonlinear sectional lift is attempted to consider such stall effects.

Numerical-Perturbation Method for the Nonlinear Analysis of Structural Vibrations

Abstract: A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections. ~ 4Y large-amplitude deflection of a beam or a plate which is restrained at its ends or along its edges results in some midplane stretching/One must account for this stretching with nonlinear strain-displacement relationships. The nonlinear equations of motion describing this situation were the basis of a number of earlier investigations and are the basis for the present paper as well. The purpose of the present paper is to present a new scheme for determining the response to a harmonic excitation. Emphasis is placed on the case when the frequency of the excitation is near a natural frequency. A convenient way to attack this nonlinear problem involves representing the deflection curve or surface with an expansion in terms of the linear, free-oscillation modes. The deflection is then determined in two steps. First, the damping, the forcing, and the nonlinear terms are deleted and the linear modes (eigenfunctions) and natural frequencies (eigenvalues) are determined. Second, the time-dependent coefficients in the expansion are obtained from a set of coupled, nonlinear, ordinary, second-order differential equations, the linear modes being used to determine the coefficients in these equations. (The procedure is described in detail in Sec. II.) Generally, one cannot obtain the linear modes analytically for structural elements having complicated boundaries and composition, and one cannot easily determine the character of the timedependent coefficients through numerical integration of the set of nonlinear equations. (The results obtained in the present numerical example are typical of the complicated manner in which the steady-state amplitudes of the various modes making up the response can vary with the amplitude and the frequency of the excitation.) Consequently, an optimal procedure involves a numerical method to determine the linear, free-oscillation modes and an analytical method to determine the time-dependent coefficients. The present procedure combines either a finiteelement or a finite-difference method with the method of multiple scales (see, for example, Ref. 1). The following brief review mentions representative examples of the work that was and is

Liquid Sloshing Dynamics

Abstract: Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

Nonlinear Vibrations and Stability of Shells and Plates

Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

Dynamics and Control of Cranes: A Review:

Abstract: We review crane models available in the literature, classify them, and discuss their applications and limitations. A generalized formulation of the most widely used crane model is analyzed using th...

Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion

Abstract: This paper is divided into two parts. The authors’ purpose in Part I is to formulate a set of mathematically consistent governing differential equations of motion describing the nonplanar, nonlinear dynamics of an inextensional beam. The beam is assumed to undergo flexure about two principal axes and torsion. The equations are developed with the objective of retaining contributions due to nonlinear curvature as well as nonlinear inertia. A priori ordering assumptions are avoided as much as possible in the process. The equations are expanded to contain nonlinearities up to order three to facilitate comparison with analogous equations in the literature, and to render them amenable to the study of moderately large amplitude flexural-torsional oscillations by perturbation techniques. The utilization of the order-three equations in the analysis of nonlinear beam oscillations is the subject of Part II.

What is the ‘social construction of nature’? A typology and sympathetic critique

Abstract: This paper seeks to clarify what is meant by the ‘social construction of nature’, which has become a crude but common term used to describe very different understandings of nature, knowledge and the world. I distinguish two broad varieties of construction talk in the social sciences: construction-as-refutation and construction-as-philosophical-critique. The first uses the construction metaphor to refute false beliefs about the world and is consistent with orthodox philosophical stances, such as positivism and realism. By contrast, I identify four other, more radical sorts of construction-as-philosophical-critique that use the construction metaphor to question the culture/nature, subject/object and representation/reality dualisms that provide the conventional philosophical foundation for distinguishing true conceptions of nature from false ones. Another source of confusion has been the question of precisely what is meant by the term ‘nature’. Making distinctions among different senses of that term can prov...