Determination Of Rigid Body Characteristics From Time Domain Modal Test Data

A theoretical analysis of free dry and wet vibration of a trapezoidal, 2-way tapered, marine spade rudder, is presented. The rudder is considered as a hollow Kirchhoff’s plate, with the chord section as a NACA profile. The chord length and the thickness taper from the top to the bottom, over the vertical span. The rudder is pivoted at the top, with the pivot behind the leading edge. The pivot is modeled as a combination of a translational and a rotational spring, in order to include the rigid body modes of the rudder vibration. The span-wise and chord-wise non-uniform beam vibration is first analyzed by the Rayleigh-Ritz method, in order to establish the non-uniform beam mode shapes. The span-wise beam is a linearly tapered vertical cantilever, with non-classical edge at the top and free at the bottom. The chord-wise section is a 2-span beam with the ends free, and four continuity conditions at the pivot. The non-uniform mode shapes, in either direction, are a weighted summation of the uniform beam mode shapes, which also satisfy the boundary/continuity conditions. They now act as admissible spatial functions to the plate vibration, which is analyzed by the Galerkin’s method. Eigenvalue analysis generates the plate natural frequencies. A weighted superposition, of the product of the beam mode shapes, in either direction, generates the plate mode shapes. Alternately, uniform beam mode shapes are used as admissible functions into the Galerkin’s method for the plate natural frequencies and mode shapes. The natural frequencies are generated for various positions of the rudder stock along the chord length. The pivot conditions (in both translational and rotational rigid body degree of freedom) influence the prominence of the rigid body mode shapes. The natural frequencies are analyzed for various pivot fixities, taper ratios, and aspect ratios of the plate. This is followed by the wet vibration analysis of the rudder. First, 2D strip theory is used to generate the added mass of each chord section. Constant strength source distribution technique is used to generate the added mass in sway and yaw of a 2D aerofoil. Each flexural and torsional mode is associated with its own added mass. Various empirical corrections are done to account for the 3D flow. Finally, 3D panel method is used to generate the modal added masses, and hence the wet natural frequencies. The added mass coefficient is generated for various aerofoil fineness ratios, pivot fixities, taper ratios, and aspect ratios of the plate.

Adequate design of tree harvesting equipment requires reliable estimates of centers of gravity and moments of inertia for full trees and tree-length stems. Several prediction models were developed for both centers of gravity and moments of inertia based on the theory of geometric solids. These models were fitted to center of gravity and moment of inertia estimates that were derived from stem dimension and weight measurements on loblolly pine (Pinus taeda L.) trees. The models were compared, and the best prediction equations for center of gravity and moment of inertia of tree-length stems were identified. Application of standard multiple regression methods resulted in a moment of inertia prediction model with a slope parameter estimate that had a sign opposite to that indicated by a theoretical model. Ridge regression and nonlinear regression were used to fit moment of inertia prediction models having coefficient signs consistent with those predicted by the theoretical model. The parameter estimates obtained by nonlinear regression were selected since they conformed more closely to properties of the theoretical moment of inertia model. FOR. SCI 39(2):260-274.

BModes is a finite-element code we developed to provide coupled modes for flexible blades, rotating or non-rotating, and for towers, onshore or offshore (supported either on floating platforms or on monopile foundations). Both the blade and the tower allow a tip attachment, which is modeled as a rigid body with mass, six moments of inertia, and a mass centroid that may be offset from the blade or tower axis. Examples of tip attachments are aerodynamic brakes for blades and nacelle-rotor subassemblies for towers. Allowable supports for the tower include tension wires, floating platforms, and shallow-water monopiles with elastic foundation. Coupled modes (implying coupling of flap, lag, axial, and torsion motions) have several applications. Examples are: modeling of major flexible components for modal-based aeroelastic codes such as FAST [1], validation of turbine models using experimental data, modal-based fatigue analysis, and understanding of aeroelastic-stability behavior of turbines. This paper presents verification of the blade modal analysis capability of BModes. Verification begins with simple uniform beams, rotating and non-rotating, and progresses to realistic blades. BModes-computed modes for all models are compared with analytical modes, if possible to obtain, and with modes generated by RCAS [2]. All results, presented in terms of frequencies and mode shapes, show excellent agreement. I. Introduction BModes is a finite-element code that allows high-fidelity modal analysis of a turbine blade or a tower. Both the blade, rotating or non-rotating, and the tower can have arbitrary distribution of structural properties along their length. Both allow tip attachment, which is assumed to be a rigid body with mass, six moments of inertia, and a mass centroid that may be offset from the blade or the tower axis. Examples of tip attachments are aerodynamic brakes for blades and nacelle-rotor subassemblies for towers. In addition, the blade may have precone and an arbitrary pitch-control setting. For the tower, BModes allows three configurations: a land-based tower, an offshore monopile-supported tower, or an offshore floating-platform-supported tower. The land-based tower may optionally have tension support wires. BModes yields coupled modes for both the blade and the tower. A coupled mode implies presence of flexural, axial, and torsion motions in a natural mode of vibration. For the blade, flexural motion means flap and lag bending, whereas for the tower it means fore-aft and side-to-side bending. Knowledge of coupled modes is crucial to several applications. Examples are: modeling of major flexible components for modal-based aeroelastic codes, validation of turbine models using experimental data, modal-based fatigue analysis, and in-depth interpretation of aeroelasticstability behavior of turbines, both onshore and offshore. Obtaining rotating-blade coupled modes involves solving a complex boundary-value problem, and only a few codes rigorously handle this. BModes is accurate because it uses a finite-element approach in conjunction with analytical linearization and a special finite-element assembly that properly captures Coriolis and centrifugal effects. The finite-element method (FEM) is based on a 15- degree of freedom (dof) element with three internal and two boundary nodes. Because BModes is a finite-element based, it has the capability to handle a complex range of boundary conditions. The structural properties along the blade length are specified in terms of the flap bending, lag bending, torsion, and axial stiffness; mass; section moments of inertia; and chordwise offsets of section shear center, tension center, and center-of-mass along the blade. These properties may be obtained from experimental tests, blade manufacturer, or a properties-extractor code, such as PreComp [3] or BPE [4]. Currently, BModes can handle only metallic or

Comparing the influence of Roll-Over Protective Structure type on tractor lateral stability

PrandtlPlane Joined Wing: Body freedom flutter, limit cycle oscillation and freeplay studies

State-space system identification with physically motivated residual states and throughput rank constraint

The rotor is a key element of rotating machinery that can be used in different of mechanical devices such as gas turbines, industrial compressors, motors, and aero engines. The dynamic analysis of a rotor system with active magnetic bearings is presented in this paper. This system consists of a flexible shaft with a rigid disk and flexible bearings. An sys Workbench is used to study a 3D simulation of a finite element model. Correct estimation of the rotor's natural frequencies and mode shapes is required for rotating machinery safety procedures. In order to compute the natural frequencies and mode shapes of this system, in the first case it is assumed a free-free system in which no bearings are used, and the natural frequencies and mode shapes are calculated without rigid body modes. In the second case, the natural frequencies and mode shapes are determined with bearing stiffness. The natural frequencies are also evaluated using finite elements based on matlab code. A comparison between the two methods was carried out.

It’s found that the rigid-body modes of brake pads and brake caliper have significant influence on squeal occurrence while analyzing disc brake squeal problems using close-loop coupling disc brake squeal model. The modal shapes of these rigid-body modes calculated from finite element method (FEM) are linear combination of multiple translational and rotational motions, which is unfavorable for further analysis. In this paper, method to achieve ‘pure’ rigid-body modes such as translations along and rotations on its principal axes of inertia is presented. Modal shapes derived from this method consist with those from FEM model under suitable constraints. The result is used in substructure modal composition analysis on a disc brake squeal problem, where the effects of specific rigid-body modes can be shown clearly. The method is helpful for researchers to choose right measures to suppress squeals.

Physical properties and roll decay of David Taylor Model Basin (DTMB) Model 5720, a 23rd scale free running model of the research vessel (R/V) Melville, are documented with uncertainty estimates. Properties include mass, vertical center of gravity (VCG), longitudinal center of gravity (LCG), and transverse center of gravity (TCG), and moments of inertia (MOI) for roll and pitch, transverse metacentric height (GMT), and natural roll period, Tn. Previous analysis has been expanded with additional details and uncertainty estimates. Results are based on measurements with the latest technology. The significant results for model properties are as follows: length 3.3652 ±0.0010 m (±0.030 %), mass 233.21 ±0.46 kg (±0.20 %), LCG 1.6061 ±0.0011 m (±0.067 %) aft of bow, VCG 0.2640 ±0.0017 m (±0.63 %) above keel, GMT 47.76 ±0.61 mm (±1.3 %), roll radius of gyration 0.2329 ±0.0042 m (±1.8 %), and pitch radius of gyration 0.8434 ±0.0024 m (±0.28 %). The roll period in calm water was independent of the Froude number (Fr) and initial roll angle (a). At Fr = 0, 0.15, 0.22, the average roll period was 2.2298 ±0.0040 s (±0.18 %) for 76 runs, all Fr, and all initial roll angles. The initial roll angle variation was 3° to 25°. The natural roll period was 2.139 ±0.041 s (±1.9 %). The decay coefficient data were accurately approximated by a plane in three dimensions with Fr and initial roll amplitudes (a) as the independent variables. Examples are provided that show the average values for a single roll decay event from the logdecrement method are the same as the values by the curve fitting method within the uncertainty estimates.

The project deals with the structural design and analysis of mounting structure for assembling of electronic packages in a flight vehicle section. The flight vehicle consists of various sections assembled to form an integrated vehicle. Different types of electronic packages to meet the requirements are assembled in different flight vehicle sections based on the flight vehicle configuration. One such type of flight vehicle section needs to be assembled with different electronic packages. The packages have to be rigidly mounted on a mounting structure in the flight vehicle section. The launch of a flight vehicle can be one of the most rigorous loads environments for which to design hardware. The high random vibration loads imparted on vehicle by the electronic packages during launch create an adverse design requirement that all hardware have a natural frequency greater than that of the vehicle, in order to avoid damage and failure due to dynamic coupling. Maximizing natural frequency is generally accomplished by creating as stiff and lightweight a design as possible. However, designing for the resultant high loads also requires a high strength intermediate structure for mounting the various components and subassemblies to the vehicle structure. These two opposing design requirements drive an optimization between a lightweight and high strength structure. The project comprises of design and analysis of the mounting structure. The mounting structure has to be designed to withstand the loads generated by the electronic packages. It also includes the design of mounting plate and brackets to withstand the given loads using CAD and CAE tools. Unigraphics software is used for modeling the flight vehicle section, packages and the mounting plate with brackets. The mounting plate and brackets are imported to ANSYS software for structural analysis. The mounting plate with brackets is applied with specified loads in different flight conditions like Pitch, Yaw and Roll moments. A finite element model was created to manually iterate several aspects of the design, such as geometric characteristics like thicknesses and fillet radii, to analyze the effects on weight and stress and converge on a successful design .The project elucides in detail the methodology adopted for the analysis of mounting structures for flight vehicles. configuration. These have to be mounted to withstand aerospace loads both static and dynamic. The main parts of the anatomy of an airframe are fuselage, the wing and the empennage. Each of the is in turn composed of various structural members. The area of interest in the current project is on the fuselage or the body of the aircraft in which in which electronic subsystems are mounted. In general, flight vehicle can be a air craft or rocket or missile. Mass properties are vital for the flight vehicle to travel in desired trajectory. The mass properties of the flight vehicle are Weight, Center of gravity and Moment of Inertia. Weight is the force generated by the gravitational attraction of the earth on the model rocket. The mass (and weight) is actually distributed throughout the rocket and for some problems it is important to know the distribution. But for rocket trajectory and stability, we only need to be concerned with the total weight and the location of the center of gravity. The center of gravity is the average location of the mass of the rocket. The flight vehicle or Aerospace vehicle has three modes of motion viz. Pitch, Yaw and Roll. These terms frequently used in the flight vehicle are explained below. The below figure shows the three modes of motion. Figure 2 Three modes of motion in a flight vehicle

For balanced cars, to achieve high-speed and stable operation, two efforts should be made. The first is to make the center of gravity of the car model as low as possible, which is conducive to upright stability. The second is to make the quality as concentrated as possible. Make the vehicle's steering more flexible and reduce the vehicle's moment of inertia. At the same time, the approach angle and departure angle of the car are very important considerations, because the running speed of the car model requires the car model to maintain a certain forward inclination to obtain acceleration. When the car model goes uphill, it also needs to consider the impact of the slope. Hanging the chassis requires a certain distance from the ground while lowering the center of gravity. The battery is the heaviest piece in the entire car. The location of the battery almost determines the height of the center of gravity, the size of the moment of inertia, and the departure angle of the approach angle. In order to reduce the noise of the car to the accelerometer and gyroscope, the sensor should be installed as low as possible.

Mass properties—weight, centers of gravity, and inertias—are critical performance parameters for any vehicle such as an aircraft, spacecraft, land vehicle, or ship as well as any subsystem or component, where precise mass properties measurement and management is necessary to meet strict engineering and performance requirements. This chapter deals with the techniques, methods, tools, and approaches for the measurement of mass properties of vehicles, and vehicle subsystems, rather than production line or bulk items. This chapter covers mass and weight measurement systems; measurement methodology; choosing measuring equipment; mass and weight measurement; centers of gravity; moments of inertia; products of inertia; measuring large vehicles; and uncertainty in mass properties measurements.

The authors propose a method of direct identification of design parameters (mass, location of the center of gravity, the moment of inertia, spring constant, damping constant and the location of the support of elastic mounts) of a damped vibration system of rigid and elastic mounts. In this method, modal parameters are repeatedly modified by changing the design parameters based on the sensitivity analysis of the complex eigen value in order to correspond to the objective values (damped natural frequency, modal damping ratio, mode shape coefficients). A calculation model and a rigid body model are examined to verify the usefulness of the method.

The purpose of this study is to identify modal parameters of an elevator car by operational modal analysis, and to estimate the stiffness parameters of the elevator car based on the obtained modal parameters. It is assumed that the inertia properties such as mass, the center of gravity and the moment of inertia are well predicted based on the design condition. However, it is difficult to predict the stiffness parameters of an elevator car especially in the operating condition. Therefore, the stiffness coefficients are estimated based on the operational modal analysis in this study. The frequency range of interest is up to 4 Hz, where the assumption that the car behaves rigidly is satisfied. In order to check the assumption the Rigidity Indicator Function (RIF) is introduced as a function of frequency. Frequency Domain Decomposition (FDD) method is used for the operational modal analysis. The stiffness parameters are estimated by minimizing the sum of the errors of natural frequencies and the errors of mode shape vectors between the experimentally identified modal model and the analytical model.

Nine low-lying ${\mathrm{O}}_{\mathit{n}}^{+}$ states of $^{20}\mathrm{Ne}$ and their possible rotational bands have been studied by employing the isomorphic shell model which is a hybrid between conventional shell model and the liquid drop model in conjunction with the nucleon finite size and which in addition uses no adjustable parameters. The configurations of six out of these nine ${\mathrm{O}}_{\mathit{n}}^{+}$ states have an \ensuremath{\alpha}-planar structure when, for each set of four closeby nucleon average positions (two protons and two neutrons), possessing the same principal quantum number n and forming an instant \ensuremath{\alpha}-like particle, the center of gravity is considered. The novelty of the present study is focused on the fact that the axis of rotation and the number of rotating nucleons inside the same rotational band may change in such a way that the relevant moment of inertia increases monotonically in steps forming for each step a new branch of the band. Up to five such branches have been found and each time the moment of inertia of the last of them approaches the rigid body limit, creating superdeformed bands. The coexistence of a superdeformed band and of lower deformation bands include several states with the same ${\mathit{I}}^{\mathrm{\ensuremath{\pi}}}$ value. Two rotational bands are introduced for the first time and the model predictions of states in all cases are very close to the experimental data. Another important feature of the present study is that two different configurations possess identical binding energy (the maximum among all possible configurations) and are assigned, by 50% each, to the g.s. of $^{20}\mathrm{Ne}$. This has been verified by successfully employing many observables and results of other models. \textcopyright{} 1996 The American Physical Society.