Experimental testing of Timoshenko predictions of supercritical natural frequencies and mode shapes for free-free beams

Rapid deployment of marine structures is of growing importance to U.S. naval forces. Surface-based inflatable structures including Rigid Inflatable Boats (RIBs), inflatable causeways and bridging, and launch and recovery systems provide unique solutions for temporary structures during sea-based missions. When performance specifications demand minimal weight and stowage, rapid deployability and temporary rigidity, solutions are limited to inflatable structures constructed of flexible materials. Driven by air pressure, today’s inflatables provide significant load-carrying capacities per unit weight (or stowed volume) utilizing technical textiles, elastomers or “soft” composites. Overloading of inflatable structures produces unique fail-safe behaviors (reversible wrinkling) that allow the structures to assume rigidity and load-carrying capacity upon load removal. Design standards are virtually nonexistent for inflatable structures involving shapes constructed of spheres, beams, arches and most recently flat panels using 3D woven drop-stitch panels. Predictive performance tools (analytical and numerical) for static applications lag significantly behind those for conventional structures. Nonlinear system behaviors (material and geometric), thermo-mechanical coupling and fluid-structure interactions (FSI’s) pose significant challenges when applying existing design tools to inflatable structures. This gap is further exacerbated for dynamic applications as inflatable structures exhibit pressure-dependent natural frequencies and mode shapes. Surface-based structures must be designed with consideration given to operational sea state frequencies and wave periods so that the onset of structural instabilities (wrinkling, buckling) and loss of load-carrying capacities can be prevented. The present research establishes the validity of physics based models using the Ideal Gas Law as an equation of state (EOS) to predict the natural frequencies and corresponding mode shapes of air-inflated drop-stitch fabric panels as functions of inflation pressure. Particular concern is given to the breathing modes for inflation pressures ranging from 5.0 to 30.0 psig. The presence of breathing modes can negatively impact the riding performance of RIBs vessels constructed with drop-stitch fabric hulls by amplification of the panel’s skin separation displacements and vertical accelerations, and are not seen in this material system for the pressures considered. Both numerical and experimental methods are pursued; the results of laboratory modal experiments are used to validate the numerical models. Predicted and experimental natural frequencies and mode shapes are compared and excellent correlation was observed. Increasing inflation pressures produced increasing in-plane and through-thickness normal stresses and modal frequencies of the drop-stitch fabric panels.

Download Full-text

Tire Vibrations

Tire Science and Technology ◽

10.2346/1.2167240 ◽

1977 ◽

Vol 5 (4) ◽

pp. 202-225 ◽

Cited By ~ 35

Author(s):

G. R. Potts ◽

C. A. Bell ◽

L. T. Charek ◽

T. K. Roy

Keyword(s):

Natural Frequencies ◽

Standing Waves ◽

Resonant Mode ◽

Mode Shapes ◽

Resonant Vibrations ◽

Resonant Frequencies ◽

Radial Tire ◽

Analysis Techniques ◽

Thin Ring ◽

Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Download Full-text

Dynamic model for high-speed rotors based on their experimental characterization

Application and Theory of Computer Technology ◽

10.22496/atct.v2i4.108 ◽

2017 ◽

Vol 2 (4) ◽

pp. 25

Author(s):

L. A. Montoya ◽

E. E. Rodríguez ◽

H. J. Zúñiga ◽

I. Mejía

Keyword(s):

Dynamic Model ◽

High Speed ◽

Natural Frequencies ◽

Mode Shapes ◽

Experimental Characterization ◽

Rotating Systems ◽

Computing Performance ◽

The Impact ◽

Stiffness Distribution ◽

Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

Download Full-text

Spatially Resolved Experimental Modal Analysis on High-Speed Composite Rotors Using a Non-Contact, Non-Rotating Sensor

Sensors ◽

10.3390/s21144705 ◽

2021 ◽

Vol 21 (14) ◽

pp. 4705

Author(s):

Julian Lich ◽

Tino Wollmann ◽

Angelos Filippatos ◽

Maik Gude ◽

Juergen Czarske ◽

...

Keyword(s):

High Speed ◽

Natural Frequencies ◽

Mode Shapes ◽

Fiber Reinforced ◽

Structural Dynamic ◽

Spatially Resolved ◽

Glass Fiber Reinforced ◽

Vibration Responses ◽

And Performance

Due to their lightweight properties, fiber-reinforced composites are well suited for large and fast rotating structures, such as fan blades in turbomachines. To investigate rotor safety and performance, in situ measurements of the structural dynamic behaviour must be performed during rotating conditions. An approach to measuring spatially resolved vibration responses of a rotating structure with a non-contact, non-rotating sensor is investigated here. The resulting spectra can be assigned to specific locations on the structure and have similar properties to the spectra measured with co-rotating sensors, such as strain gauges. The sampling frequency is increased by performing consecutive measurements with a constant excitation function and varying time delays. The method allows for a paradigm shift to unambiguous identification of natural frequencies and mode shapes with arbitrary rotor shapes and excitation functions without the need for co-rotating sensors. Deflection measurements on a glass fiber-reinforced polymer disk were performed with a diffraction grating-based sensor system at 40 measurement points with an uncertainty below 15 μrad and a commercial triangulation sensor at 200 measurement points at surface speeds up to 300 m/s. A rotation-induced increase of two natural frequencies was measured, and their mode shapes were derived at the corresponding rotational speeds. A strain gauge was used for validation.

Download Full-text

Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons

Infrastructures ◽

10.3390/infrastructures6060083 ◽

2021 ◽

Vol 6 (6) ◽

pp. 83

Author(s):

Angelo Aloisio

Keyword(s):

Elastic Modulus ◽

Structural Reliability ◽

Natural Frequencies ◽

Concrete Beams ◽

Experimental Testing ◽

Hybrid Approach ◽

Reliable Estimate ◽

Axial Deformation ◽

Dynamic Identification ◽

Concrete Girders

The estimate of internal prestressing in concrete beams is essential for the assessment of their structural reliability. Many scholars have tackled multiple and diverse methods to estimate the measurable effects of prestressing. Among them, many experimented with dynamics-based techniques; however, these clash with the theoretical independence of the natural frequencies of the forces of internally prestressed beams. This paper examines the feasibility of a hybrid approach based on dynamic identification and the knowledge of the elastic modulus. Specifically, the author considered the effect of the axial deformation on the beam length and the weight per unit of volume. It is questioned whether the uncertainties related to the estimate of the elastic modulus and the first natural frequency yield reasonable estimates of the internal prestressing. The experimental testing of a set of full-scale concrete girders with known design prestressing supports a discussion about its practicability. The author found that the uncertainty in estimating the natural frequencies and elastic modulus significantly undermines a reliable estimate of the prestressing state.

Download Full-text

Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique

Materials ◽

10.3390/ma14030567 ◽

2021 ◽

Vol 14 (3) ◽

pp. 567

Author(s):

Łukasz Żmuda-Trzebiatowski ◽

Piotr Iwicki

Keyword(s):

Natural Frequencies ◽

Vibration Mode ◽

Mode Shapes ◽

Correlation Technique ◽

Limit Loads ◽

Linear Buckling ◽

Geometrical Imperfections ◽

Linear Problems ◽

Formed Channel ◽

Corrugated Wall

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

Download Full-text

Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

Science and Engineering of Composite Materials ◽

10.1515/secm-2020-0021 ◽

2020 ◽

Vol 27 (1) ◽

pp. 216-225

Author(s):

Buntheng Chhorn ◽

WooYoung Jung

Keyword(s):

Free Vibration ◽

Natural Frequency ◽

Natural Frequencies ◽

Basalt Fiber ◽

Orientation Angle ◽

Elliptical Hole ◽

Composite Plates ◽

Buckling Load ◽

Mode Shapes ◽

Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Download Full-text

Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

Mathematical and Computational Applications ◽

10.3390/mca25020029 ◽

2020 ◽

Vol 25 (2) ◽

pp. 29

Author(s):

Desmond Adair ◽

Aigul Nagimova ◽

Martin Jaeger

Keyword(s):

Natural Frequencies ◽

Equations Of Motion ◽

Approximate Solutions ◽

Mode Shapes ◽

Algebraic Equations ◽

Structural Vibrations ◽

Unknown Parameters ◽

One Dimensional ◽

Vibration Problems ◽

Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Download Full-text

Vibration of Beams with a Single Delamination under Axial Loading

Materials Science Forum ◽

10.4028/www.scientific.net/msf.675-677.477 ◽

2011 ◽

Vol 675-677 ◽

pp. 477-480

Author(s):

Dong Wei Shu

Keyword(s):

Free Vibration ◽

Natural Frequency ◽

Analytical Solutions ◽

Axial Load ◽

Natural Frequencies ◽

Axial Loading ◽

Composite Beams ◽

Mode Shapes ◽

Equilibrium Conditions ◽

Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Download Full-text

Using Pade´ Approximants and Curve-fitting to Approximate Eigenvalues and Eigenvectors for Large Design Changes

Journal of Mechanical Design ◽

10.1115/1.2826847 ◽

1996 ◽

Vol 118 (1) ◽

pp. 151-153 ◽

Cited By ~ 1

Author(s):

J. M. Vance ◽

J. E. Bernard

Keyword(s):

Finite Element ◽

Natural Frequencies ◽

Solution Process ◽

Mode Shapes ◽

Eigenvalues And Eigenvectors ◽

Computational Burden ◽

Design Change ◽

Design Changes ◽

Develop Software ◽

Unique Method

Our overall goal is to develop software that facilitates the interactive participation of the designer in the optimization process. We are focusing this research on problems which use finite element solutions as part of the objective function. One challenge to implementing interactive participation in these types of problems is the high computational burden of computing a finite element solution for each design change. The research presented here focuses on a unique method to develop fast approximations for natural frequencies and mode shapes which can be used to avoid the time-consuming re-solution process and which will facilitate interactive design for systems with even large design changes.

Download Full-text