Dynamics of Curved Beams Undergoing Large Overall Motions Using the Mode Decomposition Concept

A fully nonlinear formulation for the dynamics of initially curved and twisted beams, undergoing arbitrary spatial motions, is presented. The formulation admits finite bending, shearing and extension of the beam. The Mode decomposition method is employed to modify the strains in the finite element discretization process leading to the elimination of shear and membrane locking phenomena that arise in curved elements. The model incorporates all inertia effects and is capable of accurately capturing the phenomena of dynamic stiffening due to the coupling of the axial and membrane forces to the flexural deformation. All motion is referred to the inertial frame. The nonlinear formulation is suitable for modeling flexible multibody systems. Examples are presented to illustrate the validity of the proposed formulation.

Vibration Analysis of a Partially Covered Double Sandwich Cantilever Beam With Concentrated Mass at the Free End

The partially covered, sandwich-type cantilever with concentrated mass at the free end is studied. The equations of motion for the system modeled via Euler beam theory are derived and the resonant frequency and loss factor of the system are analyzed. The variations of resonance frequency and system loss factor for different geometrical and physical parameters are also discussed. Variation of these two parameters are found to strongly depend on the geometrical and physical properties of the constraining layers and the mass ratio.

The Origins of Engineering Design

Engineering is distinguished from craft or invention by systematic development and use of intelligence and scientific knowledge. Elements of engineering design can be found in the great Potamic civilizations but systematic engineering design activity started in the ancient Greek and Hellenistic world and matured under the Romans. The renaissance and the industrial revolution revived Engineering and modern engineering design was eventually defined during the 19th Century.

Inelastic Analysis of Reinforced Concrete Shear Wall Structures Under Seismic Excitation

During strong ground motions, members of reinforced concrete structures undergo cyclic deformations and experience permanent damage. Members may lose their initial stiffness as well as strength. Recently, Los Alamos National Laboratory has performed experiments on scale models of shear wall structures subjected to recorded earthquake signals. In general, the results indicated that the measured structural stiffness decreased with increased levels of excitation in the linear response region. Furthermore, a significant reduction in strength as well as in stiffness was also observed in the inelastic range. Since the in-structure floor response spectra, which are used to design and qualify safety equipment, have been based on calculated structural stiffness and frequencies, it is possible that certain safety equipment could experience greater seismic loads than specified for qualification due to stiffness reduction. In this research, a hysteresis model based on the concept of accumulated damage has been developed to account for this stiffness degradation both in the linear and inelastic ranges. Single and three degrees of freedom seismic Category I structures were analyzed and compared with equivalent linear stiffness degradation models in terms of maximum displacement responses, permanent displacement, and floor response spectra. The results indicate significant differences in responses between the hysteresis model and equivalent linear stiffness degradation models. The hysteresis model is recommended in the analysis of reinforced concrete shear-wall structures to obtain the in-structure floor response spectra for equipment qualification. Results of both cumulative and one shot tests are compared.

Free Vibration of Rectangular Membranes With Linearly Varying Tension and Light Flexural Rigidity

The proposal to utilize tensioned rectangular membranes as antennae in interspace communication has resulted in the focus of considerable attention on the free vibration of membranes with complicated in-plane loadings. In this paper the problem of analizing the vibration of a rectangular membrane with linear variation in tension in one direction is examined. This tension variation occurs due to gravitational forces when the membranes are tested experimentally in vibration laboratories. The Rayleigh-Ritz energy method is employed to obtain analytical results. Convergence is found to be rapid. Mode shapes are compared with those of known classical solutions when no tension variation is permitted. Generation of the eigenvalue matrix is demonstrated to be a very simple task.

The Use of Condition Number of a FRF Matrix in Mechanical Parameter Identification

A new identification algorithm is proposed in this work to identify the parameters of mechanical joints. The method considers the whole structure as two substructures which are connected by the joints to be identified. The frequency response functions of the whole structure and substructures are used to extract the joint parameters. In contrast to the traditional methods, only a FRF matrix is needed to inverse in the proposed method. Therefore, it is possible to calculate the condition number of the FRF matrix before the identification. The condition number is defined as the ratio of the maximum singular value divided by the minimum one of a matrix. The condition number of noise contaminated FRF matrix can be used to indicate the sensitivity of the FRF matrix to measurement noise. Therefore, the condition number can be used to avoid the ill-conditioned problem by eliminating the ill-conditioned FRF in some frequency ranges before identification. The simulated results show that the proposed method can significantly improve the accuracy of identification.

Forced Vibration of Thick Viscoelastic Cylinders

Harmonic forced vibration of thick viscoelastic hollow cylinders of infinite extent is considered. The cylinder is excited by stresses applied at the inner and outer boundaries. The governing equation of motion is developed by utilizing three dimensional theory of elastodynamics. The material damping is allowed using complex elastic moduli for the viscoelastic medium. Modal displacements and stresses at any point in the medium are formulated in terms of boundary stresses. Frequency responses for radial, tangential and axial displacements are computed for different circumferential and axial wave numbers. The effect of different material loss factors on the frequency responses is examined for axial and nonaxisymmetric modes. The dimensionless resonant frequencies for zero loss factor are compared with dimensionless natural frequencies available for elastic material. Comparison indicates excellent agreement between the results.

Static and Dynamic Characteristics of Spot Welded Sheet Metal Beams

Although widely used as structural components in the auto industry, spot welded sheet metal beams manifest static and dynamic behavior that is not well characterized. For the present study, sample beams of three representative cross-sections — hat, box and box with partition — were fabricated of sheet steel. The spacing between the spot welds that hold these sections together was varied from 25.4 mm (1 inch) to 203.2 mm (8 inch) using a 25.4 mm (1 inch) increment. The beams were subjected to static bending and static torsion tests, and bending and torsional stiffnesses were determined as functions of spot weld spacing. The beams were then vibrated, and significant lower natural frequencies were determined as functions of spot weld spacing. Mode shapes were also observed for these frequencies. Pains were taken throughout the testing to ensure that the results obtained were of good statistical quality. Work was also done to distinguish the effect on results of beam length and end conditions from that of spot weld spacing. As part of the study, finite element models of the beams were constructed. The results of finite element analysis (FEA) and experiment are compared and insights are offered concerning the appropriate modeling of such structures.

Measurement of Static and Dynamic Properties of a Tilting Pad Bearing and Comparison With Theory

Measurements were made of the static and dynamic properties of a seven inch diameter, four-pad, tilting pad bearing with both centrally pivoted and 60% offset pads. Data was recorded at 1500, 1800 and 3000 RPM and covered a range of Sommerfeld numbers from .055 to .625. Dynamic properties were measured by applying unbalance weights of various magnitudes to the rotor and measuring the synchronous response amplitudes and phase angles. Good agreement was obtained between measured properties and those predicted using linearized stiffness and damping coefficients obtained from isoviscous lubrication theory.

Dynamic Behavior of Vehicles Travelling on Bridges

An investigation into the dynamic behavior of a bridge with simply supported boundary conditions, carrying a moving vehicle, is performed. The vehicle has been modelled as a two degree of freedom lumped-parameter system travelling at a uniform speed. Furthermore, the bridge is assumed to obey the Euler-Bernoulli beam theory of vibration. This analysis may well be applied to a beam with different boundary conditions, but the computer simulation results given in this paper are set for only the case of freely hinged ends. Numerical solutions for the derived differential equations of motion are obtained and their close agreement, in some extreme cases, with those reported earlier by the authors are observed. Finally, the effect of speed on the maximum dynamic deflection of bridge is shown to be of much importance and hence an estimation for the critical speed of the vehicle is presented.