Prediction of Vertical Tail Buffet Using CFD/CSD Coupling Method

The vertical tail buffet induced by the vortex breakdown flow is numerically investigated. The unsteady flow is calculated by solving the RANS equations. The structural dynamic equations are decoupled in the modal coordinates. The radial basis functions (RBFs) are employed to generate the deformation mesh. The buffet response of the flexible tail is predicted by coupling the three sets of equations. The results show that the presence of asymmetry flow on the inner and outer surface of the tail forced the structural deflection offsetting the outboard. The frequency of the 2nd bending mode of the tail structure meets the peak frequency of the pressure fluctuation upon the tail surface, and the resonance phenomenon was observed. Therefore, the 2nd bending responses govern the flow field surrounding the vertical tail. Finally, the displacement of the vertical tail is small, while the acceleration with a large quantitation forces the vertical tail undergoing severe addition inertial loads.

Advances In The Modeling And Dynamic Simulation of Reeving Systems Using The Arbitrary Lagrangian-Eulerian Modal Method

This paper presents new advances in the arbitrary Lagrangian-Eulerian modal method (ALEM) recently developed for the systematic simulation of the dynamics of general reeving systems. These advances are related to a more convenient model of the sheaves dynamics and the use of axial deformation modes to account for non-constant axial forces within the finite elements. Regarding the sheaves dynamics, the original formulation uses kinematic constraints to account for the torque transmission at the sheaves by neglecting the rotary inertia. One of the advances described in this paper is the use of the rotation angles of the sheaves as generalized coordinates together with the rope-to-sheave no-slip assumption as linear constraint equations. This modeling option guarantees the exact torque balance the sheave without including any non-linear kinematic constraint. Numerical results show the influence in the system dynamics of the sheave rotary inertia. Regarding the axial forces within the finite elements, the original formulation uses a combination of absolute position coordinates and transverse local modal coordinates to account for the rope absolute position and deformation shape. The axial force, which only depends on the absolute position coordinates, is constant along the element because linear shape functions are assumed to describe the axial displacements. For reeving systems with very long rope spans, as the elevators of high buildings, the constant axial force is inaccurate because the weight of the ropes becomes important and the axial force varies approximately linearly within the rope free span. To account for space-varying axial forces, this paper also introduces modal coordinates in the axial direction. Numerical results show that a set of three modal coordinates in the axial direction is enough to simulate linearly varying axial forces.

Modal Analysis to Interpret Localization Phenomena in Two Nonlinear Tuned Mass Dampers

This study investigates localization phenomena in two identical nonlinear tuned mass dampers (TMDs) installed on an elastic structure, which is subjected to external, harmonic excitation. In the theoretical analysis, the mode shapes of the system are determined, and the modal equations of motion are derived using modal analysis. These equations are demonstrated as forming an autoparametric system in which external excitation directly acts on the first and third vibration modes, whereas the second vibration mode is indirectly excited due to the nonlinear coupling with the other modes. Van der Pol’s method is employed to obtain the frequency response curves for both physical and modal coordinates. The two TMDs vibrate in phase for the first and third modes, but vibrate out of phase for the second mode. Consequently, when all modes appear, the two TMDs may vibrate at different amplitudes, i.e., localization phenomena may occur because the TMD motions are expressed by the summation of motions for all modes. The numerical calculations clarify that the localization phenomena may occur in the two TMDs when all three modes appear simultaneously. Moreover, there are two steady-state solutions of the harmonic oscillations for the second mode with identical amplitudes; however, their phases differ by π. Hence, which TMD vibrates at higher amplitudes depends on which of these two steady-state solutions for the phase.

Dynamic Simulation of Reeving Systems With the Extension of the Modal Approach in the Axial Direction

In this work, the simulation of reeving systems has been studied by including axial modes using the Arbitrary Lagrangian-Eulerian (ALE) description. The reeving system is considered as a deformable multibody system in which the rigid bodies are connected by the elastic wire ropes through sheaves and reels. A set of absolute nodal coordinates and modal coordinates is employed to describe the motion and deformation in the axial direction. This new method allows the analysis of elements with non-constant axial strain along its length. In addition, modal coordinates are employed to describe the dynamic motion in the transverse direction. The non-constant axial displacement within the wire rope is computed in terms of the absolute position coordinates, longitudinal material coordinates, and modal deformation coordinates. To derive the governing equations of motion, Lagrange’s equation is employed. The formulation is validated for a simple pendulumlike motion actuated by an initial velocity. The simulation results are provided to trace the movements of the payload. It can be seen that by adding modal coordinates, the axial force within the element changes. Moreover, the effects of modal coordinates in the axial direction are presented for a different number of nodes, and the resulting axial forces are compared with reference solution.

A Sample Generation of Scenario Earthquake Shaking Maps via a Combination of Modal Decomposition and Empirical Copula toward Seismic Hazard Assessment

ABSTRACT To quantify variations in seismic hazard assessment, a large number of scenario earthquake shaking maps (hereafter referred to as s-EQ maps for short) are required. In this article, we propose a method to easily generate a large number of s-EQ maps by combining modal decomposition and empirical copula. First, by applying modal decomposition to a set of existing s-EQ maps, we identify a scenario set with a parameter space to reduce the dimensionality of models. Next, we model a probability distribution of the modal coordinates, which we regard as random variables to allow us to induce a probability measure on the parameter space. By applying an empirical copula for modeling the probability distributions, the dependence structure between modal coordinates and the probability distribution of an individual modal coordinate can be discussed independently. Some simulations show that the dependence structure between modal coordinates is important to not distort the seismic hazard assessment. The proposed method can be applied to actual existing s-EQ maps to easily generate a large number of new s-EQ maps that follow the original probability distribution. We also show that variations can be added to the newly generated s-EQ maps by adjusting the empirical copula. Furthermore, we give a generalization of the proposed method to cases with nonequal probabilities of occurrence of existing scenarios.

Absolute Displacement-Based Formulation for Peak Inter-Story Drift Identification of Shear Structures Using Only One Accelerometer

Only one accelerometer is used in this paper for estimating the maximum inter-story drifts and time histories of the relative displacements of all stories of multi-degree-of-freedom (MDOF) shear structures under seismic excitation. The calculation based on the data of one sensor using a conventional method is unstable, and when modal coordinates are used, higher modes should be included, which is different from the estimation based on the responses recorded by many accelerometers. However, the parameters of the higher modes of structures are difficult to obtain from structures under small excitations. To overcome this difficulty, the recorded absolute acceleration is converted into the absolute displacement, and a state-space equation is formulated. Numerical simulations of a nine-story structure were conducted to check the applicability, robustness against environmental noise, and optimal installation location of the accelerometer of the proposed approach. In addition, the effects of the higher modes were analyzed in terms of the number of accelerometers and type of response. Finally, the proposed approach was validated in a simple experiment. The results indicate that it can accurately estimate the time histories of the relative displacements and maximum inter-story drifts of all floors when one accelerometer is used and just the first two modal parameters are incorporated in the model. Furthermore, the approach is robust against environmental noise.

Estimation of Maximum Drift of MDOF Shear Structures Using Only One Accelerometer

This paper presents a new method to estimate maximum drifts, relative displacements between adjacent floors, of all stories of multi-degree-of-freedom (MDOF) shear structures using only one floor’s absolute acceleration time history response under the ground excitation. The absolute acceleration and relative displacement are formulated in modal coordinates and the state-space expression is derived. Then the numerical simulation for a three-story structure was conducted to verify the performance of the state-space equation. The comparison of the estimated state and input with actual values is made and shows the good agreement. In addition, the relative displacement time histories of all floors were obtained, and the errors of maximum displacements and inter-story drifts were analyzed. The robustness against environmental noise was also investigated by numerical simulations as well. The results of simulations indicate the estimation is satisfactory, and very robust against the environmental disturbance.

Frame setters and microvariation of subject-initial Verb Second

The chapter focuses on V3 patterns in West Flemish in which a subject-initial non-inverted V2 clause is preceded by an adverbial adjunct which modifies temporal or modal coordinates of the associated clause, in apparent violation of the V2 constraint. The pattern is not available in many other varieties of Dutch, including Standard Dutch. The chapter summarizes the main distributional and interpretive properties of the initial constituent, focusing on, among other things, the fact that for its interpretation, the initial adjunct cannot be reconstructed to a clause-internal position. On the basis of the distributional and interpretive properties of the initial constituent, it is argued that these V3 patterns are in line with V2 syntax because the initial constituent is extrasentential. The chapter develops the discourse syntax for main clause external constituents and argues that the micro-variation observed can be captured by the hypothesis that there is micro-variation between Standard Dutch and West Flemish in terms of the derivation of subject-initial V2 root clauses.