Dynamic Force Response Research Articles

Identifying Delamination in Composite Beams Using Built-In Piezoelectrics: Part I—Experiments and Analysis

An investigation was performed on using piezoelectrics built into laminated composite structures to detect a delamination and estimate its size and location. Both experiments and analysis were conducted. In experiments, piezoceramics were attached to composite beams with and without an artificial delamination. Some of the piezoceramics were used as actuators to dynamically excite specimens while others were used as sensors to measure the beam responses. Tests showed that a delamination changed the measured piezo-induced dynamic forced response of beams. A delamination identification method is proposed which consists of a structural analysis, a response comparator, and a damage selector. The structural analysis was developed for predicting the output voltages of the sensors when a delaminated beam was excited by the actuators. The experimental results as well as the structural analysis are described in Part I of the study. In Part II, a response comparator and damage selector will be presented and will be integrated with the structural analysis for identifying delamination in composite beams with built-in piezoelectrics.

Thermohydrodynamic analysis of fluid film bearings for cryogenic applications

A thermohydrodynamic analysis and computer program for prediction of the static and dynamic force response of hydrostatic journal bearings, annular seals, or damping bearings, and fixed arc-pad bearings are presented. The study includes the most important flow characteristics found in cryogenic fluid film bearings such as flow turbulence, fluid inertia, liquid compressibility, and thermal effects. Numerical results detail a comparison of the static performance and dynamic force coefficients for a six-recess hydrostatic bearing and a damping bearingseal for the Space Shuttle Main Engine high-pressure oxidizer turbopump. The calculations indicate that turbulent-flow, externally pressurized bearings support the expected loads with moderate journal center eccentricities and with force coefficients of relevant magnitude for this critical application.

Effect of a Circumferential Feeding Groove on the Dynamic Force Response of a Short Squeeze Film Damper

The effect of a circumferential feeding groove on the dynamic force response of a short length, open end squeeze film damper is studied experimentally. Damper configurations with increasing groove depths and journal orbit radii were tested for several conditions of whirl frequency and lubricant viscosity. Significant levels of dynamic pressure were measured at the circumferential groove, and relatively large tangential (damping) forces are produced at the groove which contribute considerably to the damping characteristics of the SFD test articles. Radial forces of substantial magnitude are determined at the groove and at the thin film land where the squeeze film Reynolds number is typically less than 1. The circumferential groove is thought to induce an inertia like effect into the film land. The experimental results correlate well with the predictions from a groove volume-circumferential flow model developed.

The Effect of Journal Misalignment on the Operation of a Turbulent Flow Hydrostatic Bearing

An analysis for calculation of the dynamic force and moment response in turbulent flow, orifice compensated hydrostatic journal bearings is presented. The fully developed flow of a barotropic liquid is described by variable properties, bulk-flow equations and local turbulent friction factors based on bearing surface condition. Bearing load and moments and, dynamic force and moment coefficients are calculated for perturbations in journal center displacements and misaligned journal axis rotations. Numerical results for the effect of static misalignment angles in the plane of the eccentricity vector are presented for a water lubricated hydrostatic bearing. The predictions show that journal axis misalignment causes a reduction in load capacity due to loss in film thickness, increases the flow rate and produces significant restoring moments (couples). Force and moment coefficients due to dynamic journal axis rotations are also discussed.

Dynamic Force Response of an Open-Ended Squeeze Film Damper

The effects of whirl frequency and lubricant viscosity on the experimental pressure field and film forces in an open-ended squeeze film damper test rig are presented. The measurements refer to circular centered journal motion of amplitude equal to one half the damper clearance (ε = 0.5). The whirl frequency varied between 16 Hz and 85 Hz, while the lubricant temperature increased from 25°C to 45°C. The damper operated with levels of external pressurization that supressed lubricant cavitation. The experimental results show conclusively that the radial film force is purely an inertial effect, i.e., it depends solely on the fluid density and the second power of the whirl frequency. The tangential film force shows a variation that depends on the viscous and inertial flow conditions in the squeeze film region. Correlation of experimental forces with conventional SFD models shows the radial force to be π times larger than the theoretical prediction, while the tangential force correlates well for low whirl frequencies and large lubricant viscosities.

Effect of Shaft Misalignment on the Dynamic Force Response of Annular Pressure Seals

An analysis for calculation of the dynamic force and moment response in turbulent flow, annular pressure seals is presented. The fully developed flow of a cryogenic liquid within the annular thin film region is described by variable properties, bulk-flow equations with a turbulent friction factor based on Moody's formula. The analysis considers arbitrary shaft center eccentric displacements and rotor axis misalignment angles. Solution to zeroth-order flow field equations determines the seal leakage, film forces, and moments. Dynamic force and moment coefficients due to perturbations in shaft center displacements and axis rotations are obtained from the solution of first-order (linear) flow equations. Numerical results on the effect of large static misalignment angles on the dynamic force response of a liquid oxygen damper seal typical of a cryogenic application are discussed in detail. The predictions show that a static misalignment mode relative to the seal entrance plane causes a large magnitude stiffening effect on the seal, while the opposite effect, occurs for large misalignments about the seal exit plane. Alignment considerations are then shown to be of importance for adequate and predictable performance of annular pressure seals.

Experimental Pressures and Film Forces in a Squeeze Film Damper

The effect of whirl frequency and lubricant viscosity on the dynamic pressures and force response of an open end and a partially sealed squeeze film dampers (SFD) with a radial clearance of 0.38 mm is determined experimentally. The experiments are carried out in a damper test rig executing circular centered orbits and for whirl frequencies ranging from 33 to 83 Hz. The experimental results show that the sealed SFD configuration produces larger tangential forces than the open end SFD. The tangential (damping) force increases linearly with increasing whirl frequency. For this radial clearance fluid inertia effects in the damper are found to be negligible since the squeeze film Reynolds number is less than 1.20. Cavitation was observed in both damper configurations at high frequencies and high lubricant viscosities. This condition limited the rate of increment of the damping (tangential) force with increasing frequency and reduced the radial force when lubricant viscosity increased.

Analysis of Multi-Land High Pressure Oil Seals

An analysis for the laminar/turbulent flow in high pressure oil ring seals is presented. A fully-developed bulk-flow model for low axial Reynolds numbers is introduced to predict the static and dynamic force response of multi-land oil seals. The model includes the effects of bearing surface roughness, variable seal clearances, fluid inertia and viscous loss effects at the inlet of the first land in a multi-land oil seal. Internal groove pressures in the seals are determined via a mass conservation algorithm with Reynolds condition at the cavitation inception zone. Predictions show that the viscosity effect at the seal inlet is minimal for turbulent flow across the seal. However, for laminar oil seals, the entrance loss viscous effect can substantially increase the direct stiffness. Load capacity and rotordynamic force coefficients for one-land, two-land and three-land seal examples are discussed in detail. Presented at the 47th Annual Meeting in Philadelphia, Pennsylvania May 4–7, 1992

Analysis of Short Squeeze Film Dampers With a Central Groove

A novel analysis for the dynamic force response of a squeeze film damper with a central feeding groove considers the dynamic flow interaction between the squeeze film lands and the feeding groove. For small amplitude centered motions and based on the short bearing model, corrected values for the damping and inertia force coefficients are determined. Correlations with existing experimental evidence is excellent. Analytical results show that the grooved-damper behaves at low frequencies as a single land damper. Dynamic force coefficients are determined to be frequency dependent. Analytical predictions show that the combined action of fluid inertia and groove volume—liquid compressibility affects the force coefficients for dynamic excitation at large frequencies.

Analysis of Variable Fluid Properties, Turbulent Annular Seals

A computational analysis for calculation of the dynamic force response in turbulent flow annular pressure seals of arbitrary nonuniform clearance is presented. Cryogenic liquids are considered as barotropic. The fluid motion is described by a bulk flow model and Moody’s friction factor is introduced to accomodate surface roughness effects. The numerical solution scheme is computationally efficient and accurate for seal operation at arbitrary eccentricity ratios. Numerical predictions show good agreement with available experimental results. The effects of eccentricity and liquid properties on the performance of the Space Shuttle Main Engine High Pressure Fuel Turbopump interstage seal at full power level are discussed as a reference case.

Measurements of Pressure Distributions and Force Coefficients in a Squeeze Film Damper Part I: Fully Open Ended Configuration

Experimental measurements of pressure distributions and force coefficients obtained from a squeeze film damper lest rig executing a circular centered orbit are presented. The test rig has been designed to study the effect of fluid inertia on the pressure field and dynamic force response on a damper configuration with a relatively large clearance. Past measurements of the squeeze film damper force characteristics have been carried out at squeeze film Reynolds numbers not exceeding a value equal to 10. In the present paper, following contemporary applications, operations at Reynolds numbers up to fifty are tested for CCO's with an orbit radius = 0.8 (Re ≤ 10 at ε = 0.5). The results obtained from a fully open ended damper are presented in detail. The effects of fluid inertia, cavitation and the open end geometry on the pressure distributions and force coefficients are discussed.

Nonlinear dynamic response of anisotropic, arbitrarily laminated shell panels: An asymptotic analysis

An asymptotic procedure is used to derive the nonlinear equations of motion governing the forced dynamic response of an arbitrarily laminated slightly compressible composite shell panel in cylindrical bending. A combination of the Galerkin procedure and the method of multiple time scales is used to construct a uniformly valid asymptotic expansion for the dynamic response of the panel under near-resonant external excitation, and in the presence of a two-to-one internal resonance condition. A qualitative analysis shows that there is a threshold value for the amplitude of excitation, above which the panel exhibits the saturation phenomenon in which the amplitude of the directly excited mode saturates and the coupled mode starts to respond nonlinearly and eventually dominates the response. The force-response curve also exhibits the jump phenomenon.

An integrated methodology for optimizing the passive damping of composite structures

AbstractA method is presented for tailoring plate and shell composite structures for optimal forced damped dynamic response. The passive damping of specific vibration modes is optimized with respect to dynamic performance criteria including placement of natural frequencies and minimization of resonance amplitudes. The method provides the capability to tailor micromechanics, laminate and structural parameters. Application studies include the optimization of laminated composite beams and composite shells with fiber volume ratios and ply angles as design variables. The results illustrate the significance of damping tailoring to the dynamic performance of composite structures and the effectiveness of the method in optimizing the structural dynamic response.

Turbulent Hybrid Bearings With Fluid Inertia Effects

High speed hybrid bearings for cryogenic applications demand large levels of external pressurization to provide substantial load capacity. These conditions give rise to large film Reynolds numbers, and thus, cause the fluid flow within the bearing film to be turbulent and dominated by fluid inertia effects both at the recess edges and at the thin film lands. The analysis includes the effect of recess fluid compressibility and a model for the pressure rise within the recess region. Flow turbulence is simulated by friction factors dependent on the local Reynolds numbers and surface conditions. A perturbation method is used to calculate the zeroth and first flow fields and determine the bearing steady-state and dynamic force response. Comparison of results with existing experimental data shows the accuracy of the present full inertial-turbulent analysis. A roughened bearing surface is shown to improve considerably the stability characteristics of hybrid bearings operating at high speeds.

Approximate Analysis of Turbulent Hybrid Bearings. Static and Dynamic Performance for Centered Operation

An analytical study for the flow and dynamic force response in turbulent hybrid journal bearings is presented. Fluid inertia effects at the recess edges and film lands are included. For small amplitude motions about the centered position, the equations for the flow on the film lands and recesses are solved in close form by invoking the thin-land assumption. Predictions from the present simplified analytical theory agree well with full numerical predictions. The effect of recess pressure on the dynamic force response of a L02 hybrid bearing is discussed in detail.

Analysis of non-uniform beam vibration

In this paper a systematic development of the solution theory for the non-uniform Bernoulli-Euler beam vibration, including both forced and free vibrations, with general elastically restrained boundary conditions, is presented. The frequency equation and dynamic forced response, which is shown in closed integral form, are concisely expressed in terms of the fundamental solutions of the system. If the exact, closed form fundamental solutions are not available, then approximate fundamental solutions can be obtained through a simple and efficient numerical method. The present analysis can also be applied to the vibrational analysis of a beam with viscous and hysteretic damping.

Probabilistic vibration analysis of nearly periodic structures

A disordered structure with weakly coupled subsystems has localized modes with the vibratory energy concentrated in one part of the mode shape. The localization of modes may significantly affect the forced vibration response, increasing the maximum vibration amplitude dramatically in some cases. It is the scope of this paper to study the forced vibration of nearly periodic systems consisting of almost identical substructures and to analyze their free and forced dynamic responses probabilistically. It is shown that the sensitivity of the forced response to the degree of localization depends on a combination of the symmetry of the mode, which is excited, and the phase difference between the forces acting on each substructure. These results might explain the range of contrasting conclusions of earlier publications on the effects of forced response on mistuned structures. A probabilistic analysis of the free and forced responses of a nearly periodic structure is shown to be useful in the design of structures that are sensitive to the degree of localization. The results of the probabilistic analysis are verified using Monte Carlo simulation.

Effect of Fluid Inertia on Force Coefficients for the Long Squeeze Film Damper

The two-dimensional laminar flow in a long squeeze film damper with constant circular precession is solved numerically for increasing values of the squeeze film Reynolds number. For the full film solution and a fixed orbit radius, the calculated inertia and damping force coefficients increase as the squeeze film Reynolds number increases. The results presented show the significant effect of fluid inertia on the dynamic force response of squeeze film dampers operating with large Reynolds numbers.

Experimental Measurement of the Dynamic Force Response of a Squeeze-Film Bearing Damper

An experimental study of the hydrodynamic force response of a squeeze-film bearing damper with end seals was carried out. Measurements of the pressure distribution about a journal constrained to move in a circular orbit were made for the journal orbit centered in the annular clearance and offset from the center of the annular clearance. The effects of cyclic flow in a radial inlet were studied for the case of the journal orbit centered in the annular clearance. For the off-center case the pressure distribution around the damper was measured for four different combinations of eccentricity, radial velocity, and angular velocity of the line of centers, chosen in such a way as to allow calculation of the four bearing coefficients defined by Tondl. The experimentally determined pressure distributions were numerically integrated to determine the force components of the squeeze film. The results are compared to the “long bearing” and the “short bearing” solutions of Reynolds’ equation. For the centered case, good agreement was found with the shape of the “long bearing” solution. Higher-than-predicted pressures and forces for light viscosity oil are explained by showing that this case is operating in the Taylor vortex flow regime. Similar calculations indicate that turbine dampers can also operate with vortex or turbulent flow.

Improved Component-Mode Representation for Structural Dynamic Analysis

The new method described in this paper employs an incomplete set of free-boundary normal modes of vibration, augmented with a low-frequency account for the contribution of neglected (residual) modes. The improve the accuracy of forced dynamic response in a manner which is related to the benefit of the mode-acceleration method. The new method adds residual inertial and dissipative effects to the residual flexibility introduced by MacNeal. All effects are derived from the solution of a special statics problem, followed by removal of the contributions of the retained modes. A structural component can then be represented in a stiffness-matrix form for various applications, one of which is modal synthesis. Numerical results of modal analysis for a cantilevered rod show the new method to yield superior accuracy to several other methods (including those of Hurty, Bamford, and MacNeal). All parameters for the new representation can be derived from test; this is not true for most other methods. Required are the free-boundary normal modes and the dynamic flexibility matrix vs frequency for the boundary points. Consequently, any desired mix of analytically derived and experimentally derived parameters can be employed.