Characteristics Of Mode Shapes Research Articles

Nondestructive determination of longitudinal rail stress from guided wave dispersion properties

The determination of the longitudinal stress in continuous welded rails is essential for the safe operation of high-speed railways. Guided wave inspections have many advantages, and can provide an effective tool for non-destructive measurements of the longitudinal stress in rails. This paper provides a new method for determining longitudinal rail stress using ultrasonic guided wave dispersion properties. First, the characteristic equations of guided waves propagating in a waveguide with existing longitudinal stress are constructed, generating the dispersion properties of the waveguide such as the wavenumber, phase velocity and group velocity. The sensitivity of the dispersion properties of propagative modes to the longitudinal rail stress is investigated, which is then used for selecting appropriate modes for guided wave inspections. On the basis of the perturbation method, the relationship between the change in longitudinal rail stress and the change in dispersion properties is developed, which can be used for determining the longitudinal rail stress from dispersion properties. Furthermore, a mode selection index considering both the stress sensitivity and mode shape characteristics is employed for selecting appropriate propagative modes for guide wave inspections. Finally, a numerical example for CHN60 rail is adopted to demonstrate the effectiveness of the proposed method. From the results, the proposed method can accurately determine the longitudinal stress in the rail by using the dispersion properties available.

Non-reciprocal piezoelectric metamaterials with tunable mode shapes

The mode shapes of piezoelectric metamaterials are tuned by manipulating spatially the electrical boundary conditions of the piezo-elements, in a desired and controlled manner, in order to tailor the wave propagation characteristics through these metamaterials. The boundary conditions of the piezo-elements are controlled by using inductive shunting networks. With appropriate tuning and optimization of the spatial distribution of these inductive boundary conditions, it would be possible to alter the mode shape characteristics of the metamaterial in order to control the magnitude and direction of wave propagation. This enables also breaking the reciprocity characteristics of the metamaterial in a controlled manner. A finite element model (FEM) is developed to model the mode shape characteristics and the wave propagation in a one-dimensional piezo-metamaterial. The effect of various shunting strategies on the spatial control of the mode shapes, energy flow, and reciprocity characteristics of the piezo-metamaterial are investigated. The presented work lays down the foundation for two and three-dimensional metamaterial with tunable mode shape characteristics.

Bandgap and mode shape tuning of piezoelectric metamaterial

The mode shape of piezoelectric metamaterials is tuned by manipulating spatially the electrical boundary conditions of the piezo-elements, in a desired and controlled manner, in order to tailor the wave propagation characteristics through these metamaterials. The proposed concept relies on the fact that open-circuit piezo-elements made of lead-zirconate-titanate (PZT4) are twice as stiff as the same piezo-elements when operating under short-circuit conditions. Appropriate switching of the boundary conditions of the different piezo-elements between open and short-circuit conditions results in any desirable spatially distribution of the stiffness over the entire metamaterial volume. With such capabilities, it would be possible to control the bandgap characteristics of the metamaterial. But, more importantly, it would also be feasible to alter the mode shape characteristics of the metamaterial in order to control the magnitude and direction of wave propagation. This in effect enables controlling or breaking the reciprocity characteristics of the metamaterial. A finite element model (FEM) is developed to model the bandgap and mode shape characteristics of one-dimensional piezo-metamaterial. The effect of various switching strategies on the location and spectral width of the bandgap characteristics is illustrated. Furthermore, the switching strategies are also shown to influence the mode shapes, energy flow, and reciprocity characteristics of the piezo-metamaterial.

Optimal design of two viscous dampers for multi-mode control of a cable covering broad frequency range

For the conventional design of viscous dampers attached to cables, only the first few modes are of interest. However, a recent cable vibration event occurred on the Sutong Bridge highlights that the higher mode vibrations of cables also need to be controlled. To this end, a novel optimal design of two viscous dampers near to a cable anchorage is explored which can broaden the control frequency range covering both the lower and higher modes. In the proposed design scheme, the one damper nearest to the cable anchorage is targeted for lower-mode control and the other damper is targeted for higher-mode control. The mode shape characteristics of a cable with two viscous dampers, which is prerequisite for optimal damper design, are investigated. Based on that, the optimal design of the two dampers in a cable is simply reduced to two individual designs of one single viscous damper, which can lower the design complexity. The control performance of the proposed design both for lower and higher vibration modes is numerically validated by a cable on the Sutong Bridge and compared with the conventional design considering only lower vibration modes. Finally, the effects of parametric variations of the two dampers in the proposed design are discussed. It is shown that the proposed design using two dampers can both increase damping ratios of cables for lower and higher vibration modes, and the acceleration response of the cable is effectively reduced to around 60% of that using the conventional design.

Dynamic Characteristic Study of Riser with Complex Pre-stress Distribution

Abstract In this study, the dynamic characteristic problem of riser structure with complex pre-stress distribution is investigated. At first, the differential equation of the riser structure with complex pre-stress distribution is derived. The analytical expression of the free vibration of a riser structure with complex pre-stress distribution is discussed by using the orthogonal property of the trigonometric series. A top-tensioned riser (TTR) for example, the influences of the amplitude and direction of complex pre-stress on natural frequency and mode shape characteristics are compared. This study provides a new method for addressing the riser structure response problem with complex loading.

Wind-induced responses and dynamics characteristics of an asymmetrical base-isolated building observed during typhoons

Responses of an asymmetrical base-isolated building during the passage of Typhoon Roke 2011, Typhoon Guchol 2012 and a bomb cyclone strong-wind event on April 3, 2012 were investigated in this paper. Wind-induced accelerations of the building were recorded by dense array permanent monitoring system and analyzed in detailed by spectra analysis, time-frequency wavelet analysis and system identification. Results of analysis revealed that wind-induced responses of the buildings were dominated by the first mode which is the fundamental flexural mode coupled with torsion of the upper stories. Building responses demonstrated non-linear characteristics of natural frequencies, damping ratio and mode-shapes. Natural frequencies of fundamental modes decreased with the increase of acceleration amplitude, with the maximum reduction of 8–10% of natural frequencies observed during the peak wind speed. Damping estimates of the fundamental modes increased with the increase of accelerations, while characteristics of mode-shapes were also found to be dependent on the wind speed. Further analysis revealed that non-linear characteristics of building responses are related to isolator deformations caused by wind-induced static force.

Wind Effects and Dynamics Characteristics of Base-Isolated Building based on Full-scale measurement during Typhoons

This paper presents analysis of wind-induced response of asymmetrical base-isolated building during the passage of Typhoon Roke 2011, Typhoon Guchol 2012 and a bomb cyclone strong-wind event on April 3, 2012. Dense array permanent monitoring system provides three-days continuous records of the building accelerations during the events. The building’s wind-induced responses reveal non-linear characteristics of natural frequencies, damping ratio and mode-shapes. Natural frequencies of fundamental modes decreased with the increase of amplitude of building’s acceleration. Frequency reductions during strong wind are shown to be related to deformation of isolators due to static wind force. Damping estimates of the fundamental modes were increased with increase of building’s accelerations, which is attributed to the increase in damping from isolators and dissipative energy devices. Shapes of the fundamental modes showed different behavior than that of earthquake-induced mode-shapes. Characteristics of the mode-shapes were also found to be depended on the wind speed.

Large Deflection Mechanical Characteristics of Graphene Films

Considering the mechanical behavior analysis of graphene film for micro-pressure sensor, the load-deflection models in graphene film are established based on the large deflection elastic theory of circular film. With regard to the typical load-deflection models, the effects of the film parameters, including elastic modulus and film layer, on deflection deformation and vibration behavior are computed numerically and simulated by using nonlinear statics analysis and mode analysis units with ANSYS software. The results show that the prestressing force has a significant impact on the deflection deformation at low load, and especially there is a linear relation between load and deflection in the pressure range from 0 to 3.6 k Pa. However, a decreasing effect on the deflection deformation is produced by the above-mentioned film parameters with the increase of pressure load. Also, the natural frequency and mode shape characteristics mainly depend on the prestressing force instead of these two film parameters. This phenomenon verifies the used validity of spherical shell theoretical model because of the average relative error less than 0.49% between the analytical solution and ANSYS simulation results in the presence of prestressing force in the aforementioned pressure range.

Effect of Stud for Plasterboard Partition on Sound Insulation Performance and Vibration Mode Shape

A plasterboard partition consists of plasterboard, stud, runner and insulation; each components influence sound insulation performance of partition. Especially the stud is very important to determine insulation performance along with other components such as plasterboard, runner and insulation. In this study, the mode shape characteristics of studs were investigated. The results show that web shape of stud influences vibration mode shape. The sound insulation of plasterboard partitions with various stud thickness and spacing was investigated. Two 12.5 mm layered plasterboard on each side, single frame of 50 mm stud and 24 kg/m3 50 mm glasswool. The stud spacing varies from 450 to 900 mm and the thickness of stud varies 0.5 and 0.8 mm. The results show that the sound insulation of plasterboard partition improves by increasing stud spacing and decreasing stud thickness.

Dynamic Response of a Pressurized Frame-Membrane Lunar Structure with Regolith Cover Subjected to Impact Load

A three-dimensional internally pressurized frame-membrane structure covered with regolith shielding has been proposed as a possible lunar habitat. This paper presents results from the static, frequency, and dynamic impact analysis of the structure using a nonlinear (large deformation) finite-element technique. The results are presented, taking into account the effects of the added mass of the regolith and stress stiffening because of the applied internal pressurization load. The impact loading is analytically derived by considering the impact of a moving object/debris/projectile hitting the midpoint of one of the frame members at the crest of the structure. For the frequency analysis, the results show that both pressurization and added regolith mass affect the frequency and mode-shape characteristics, where the effects of the added mass of the regolith are observed to be substantially larger than the effects of pressurization. For the static and dynamic analyses, the midspan impact results show that both pressurization and added regolith mass affect the displacement and stress of the structure. The internal pressurization (prestressing) causes the structure to statically expand and stresses it, but has little effect on the dynamic amplitude of the oscillation of the displacement and stress. The added mass of the regolith also influences the static displacement and stress by slightly contracting and stressing the structure. However, it has a much larger impact on the transient analysis, reducing the oscillation amplitude and increasing the period.

Modal Comparison and Bridge-Type Optimization of Light-Rail Box Girder Bridges

Top 10 natural frequencies and mode shape characteristics of four types of light-rail box girder bridges were summarized by FE modeling. And the mode analysis results were horizontal, vertical contrasted. Furthermore, the relationships between the natural frequency and structural stiffness were studied. Finally, the bridge-types of four types of light-rail box girder bridges were optimized. The results show that the torsional stiffness of the box girder with side walls and diaphragms is much greater than that of the box girder without side walls and diaphragms, the torsional stiffness of the single-box-double-cell box girder with eccentric-hole diaphragms is greater than that of the single-box-double-cell box girder with center-hole diaphragms, and the single-box –double-cell box girder with side walls and eccentric-hole diaphragms is the optimal bridge type of all light-rail box girders.

Finite Element Analysis of Heavy-Duty Dump Truck Subframe Based on ANSYS

Dump truck subframe is an important bearing components which is used for connecting the chassis frame and the cargo compartment, and the rationality of its design has an extremely important influence on performance of the entire vehicle, moreover, the use of CAE technology can optimize the design of the subframe. In this paper, using solid element as basic element, the finite element analysis model of dump truck frame is built up with the software ANSYS, the static characteristics of the subframe under bending mode, twisting mode, braking mode and lifting mode are studied. The dynamic characteristics of the subframe are also analyzed, the stress parameters under static characteristics, the natural frequency and the corresponding mode shape characteristics of the subframe under dynamic characteristics are obtained, the improved advice of structural design for the subframe is proposed.

Finite element analysis to predict the dynamic characteristics of human trunk-neck-head for whole body vibration

Finite element analysis is a powerful tool in the biomechanical study to analyse whole body vibration. The objective of this work is to develop a biomechanical model of human trunk-neck-head (above the pelvis level) and analyse its mode shape characteristics using finite element analysis (FEA). A parametric finite element model is developed using solid-works and analysed using ANSYS software. The natural frequencies were obtained for the developed human trunk-neck-head model using free vibration modal analysis, and compared with the results obtained in the past literatures. Mode shapes and deflection due to whole body vibration in all resonance frequency ranges are numerically obtained and interpreted. A total of ten vibration modes were obtained from the finite element model. The principal resonance at 5.11 Hz consisted of a half body mode, in which the head and spinal column move almost rigidly, with axial and shear deformation lower than L5 occurring in the fourth mode at 18.35 Hz. A bending mode of the entire spine was found in the eighth mode at 33 Hz, which was making a minor contribution to the principal resonance. As in the experimental results, a neck rotation was found in both the ninth mode at 35.26 Hz and in the tenth mode 43.24 Hz.

Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory

Here, the free vibration characteristics of functionally graded elliptical cylindrical shells are analyzed using finite element formulated based on the theory with higher-order through the thickness approximations of both in-plane and transverse displacements. The power law variation of properties is assumed in the thickness direction. The finite element employed in the study is based on field-consistency approach and free from shear and membrane locking problems. The strain–displacement relations are accurately introduced in the formulation without making any approximation in the thickness co-ordinate to radius ratio terms. The detailed parametric studies are carried out to study the influences of non-circularity, radius-to-thickness ratio, material composition and material profile index on the free vibration frequencies and mode shape characteristics of functionally graded elliptical shells. The significance of thickness stretch/contraction terms is highlighted through the mode shape study.

Mode-dependence of structural damping in cable-stayed bridges

The field measured data of damping, available in the literature on vibration studies of cable-stayed bridges in Japan, is examined in detail, in order to investigate the characteristics of modal damping. Mode dependency of structural damping is focused in the present investigations. An analytical method for the estimation of modal damping is also introduced and some analytical discussions on the mode dependency of damping are added based on the energy considerations. It is concluded through this study that the modal damping of cable-stayed bridges is highly dependent on the coupling characteristics of mode shapes, and that this could be caused by the modal strain energy distribution which is different for different modes.

The finite element analysis of the vibration characteristics of piezoelectric discs

Finite element methods and modal analysis techniques have been used to predict the vibration characteristics of piezoelectric discs with finite diameter to thickness ( D/T) ratios. The finite element method for piezoelectric materials is formulated in generalized variables and co-ordinates, and the eigenvalue problem is solved directly by treating the electrical term effectively as an extra mechanical degree of freedom. This not only avoids the fully populated stiffness matrix likely to be caused by the condensation technique, but also enables the problem to be solved by a standard finite element package. The mechanical response function for constant voltage excitation and the electrical impedance characteristic functions are also formed. Numerical results are presented for piezoelectric discs with D/T ratios of 20 and 10. Five types of mode are identified according to their mode shape characteristics; these are radial, edge, thickness shear, thickness extensional and high frequency radial modes. However, no mode has been predicted having the piston-like motion assumed in one dimensional theory. The most strongly excited modes of the disc are the thickness extensional modes which are in the frequency range of the first through thickness mode predicted by a one-dimensional model. The finite element results have been checked experimentally, excellent agreement being obtained.

Mode shape analysis of angle‐ply‐laminated composite shallow shells

This work represents the first known comprehensive study concerned with the natural mode shapes of angle‐ply‐laminated composite shallow shells having rectangular planform and various boundary conditions. The Ritz method with algebraic polynomial displacement functions is used. Convergence studies are made which demonstrate that reasonably accurate results are obtainable before ill conditioning starts to cause problems. Shallow shells with spherical, circular cylindrical, and hyperbolic paraboloidal curvatures and completely free, cantilevered, and doubly cantilevered (i.e., two adjacent edges clamped and the others free) boundary conditions are considered. The effects of the fiber orientation, curvature, and boundary conditions upon the mode shapes are studied. Nodal line crossing in the mode shapes, which exists for most of the cross‐ply shells, is replaced by curve veering for angle‐ply ones. A gradual change in the mode shapes is observed as the lamination angle increases. Lamination, curvature, and boundary condition change the mode shape characteristics drastically. The information presented in this paper should be useful for engineers and researchers who are interested in the acoustical characteristics of these structural elements.

Dynamic analysis of a deployable space structure

A mathematical model and a corresponding simulation code have been developed for investigating the freevibration and forced-response behavior of a deployable space structure. Specifically, the structure considered was the NASA Solar Array Flight Experiment configuration (that has undergone testing on a recent Shuttle flight) where the mast was modeled as an Euler beam column and the solar array was modeled as a membrane. The resulting partial differential equations of motion were transformed such that the boundary conditions were time-invariant. Subsequent use of the Galerkin method resulted in an infinite set of second-order differential equations that were truncated and solved for the frequency and forced-response behavior of the coupled structural components. It is demonstrated that accurate results for frequency and mode-shape characteristics can be obtained with only a small number of generalized coordinates and, thus, appears to be a more computationally efficient algorithm than the finite element method for this type of structure. Similarly, the truncated set of equations was numerically integrated to obtain response histories of certain pertinent variables from a packaged structure, through full deployment, to complete retraction.