Membrane and Bending Strain in Cylindrical Shell Vibrations

2009 ◽  
Author(s):  
Basem Alzahabi ◽  
Henry Kowalski
Keyword(s):  
Natural Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Operating Conditions ◽  
Total Strain ◽  
Design Stage ◽  
Total Strain Energy ◽  
Scaled Model ◽  
Membrane Strain

Cylindrical Shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. Therefore, investigating the dynamic characteristics of cylindrical shells is very critical in developing a strategy for modal vibration control for specific operating conditions. Reduction of vibration amplitudes and in sound radiation is most efficiently achieved at the design stage, and the acoustic signatures may be determined by considering operational scenarios, and modal characteristics. In cylindrical shells, mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes, and unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. The ratio of membrane strain energy to total strain energy is high for modes with simple modal patterns and decrease toward zero as the number of nodal (n) lines increase, while the ratio of bending energy to total strain energy is small for simple nodal patterns and increase with increase in complexity of it. Modes associated with membrane deformation require a lot of strain energy while modes associated with bending deformation require less strain energy. The lowest natural frequency occurs where the sum of the two energies are at minimum. Moreover, the natural frequencies that are controlled by membrane strain energy are approximately independent of the shell thickness change. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then the experimental modal analysis of the scaled model utilizing strain gauges was performed to decouple the strain components. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.

Analytical and Experimental Modal Characteristics of Cylindrical Shells

2005 ◽  
Author(s):  
Basem Alzahabi
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Offshore Structures ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Design Stage ◽  
Scaled Model ◽  
Modal Characteristics ◽  
Acoustic Signature

Cylindrical Shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. The acoustic signature of submarines is very critical in such high performance structure. Submarines are not only required to sustain very high dynamic loadings at all time, but also being able maneuver and perform their functions under sea without being detected by sonar systems. Reduction of sound radiation is most efficiently achieved at the design stage, and the acoustic signatures may be determined by considering operational scenarios, and modal characteristics. The acoustic signature of submarines is generally of two categories; broadband which has a continuous spectrum; and a tonal noise which has discrete frequencies. Therefore, investigating the dynamic characteristics of cylindrical shells is very critical first step in developing a strategy for modal vibration control for specific operating conditions. Unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. Mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then experimental modal analysis of the scaled model utilizing a fixed response approach was performed to obtain the modal characteristics of the cylindrical shell between 0 and 800 Hz. The cylinder was excited at predetermined points with an impact hammer, while the response was measured using an accelerometer at specified fixed point. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. A total of ten natural frequencies were found within that range with their corresponding mode shapes. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.

Study on Bi-Stable Behaviors of Double-Layered Cylindrical Shell

2011 ◽  
Vol 243-249 ◽  
pp. 5981-5984
Author(s):  
Yao Peng Wu
Keyword(s):  
Cylindrical Shell ◽  
Shell Model ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Stable Structure ◽  
Total Strain ◽  
Total Strain Energy ◽  
Broad Application ◽  
Layered Cylindrical Shell ◽  
External Forces

Bi-stable structure can be stable in both its extended and coiled forms. As a novel deployable structure, it shows a broad application prospect in the field of aeronautics and civil engineering, etc. Considered two cylindrical shells having the same flattening configurations, they can be closely bound together by applying external forces. And the corresponding double-layered cylindrical shell model is proposed. Expressions for the bending and stretching strain energies of the cylindrical shells are presented. Calculations show that total strain energy has two local minimal values, which reveals that the double-layered cylindrical shell has its bi-stability. The corresponding rolled-up radii are thus determined.

PNEUMATIC VIBROISOLATION SYSTEM OF THE BASE DESK WITH NATURAL FREQUENCY REGULATION

2021 ◽  
Vol 113 ◽  
pp. 91-100
Author(s):  
Radka JÍROVÁ ◽  
Lubomír PEŠÍK
Keyword(s):  
Natural Frequency ◽  
Automotive Industry ◽  
Natural Frequencies ◽  
Dynamical Behaviour ◽  
Operating Conditions ◽  
Frequency Regulation ◽  
The Stability ◽  
Short Time

Vibroisolation systems of base desks for machine and testing facilities usually cannot effect efficient changing of their own frequencies according to operating conditions. Especially in the case of the automotive industry, the possibility of changing natural frequencies is very desirable. During varying operating conditions, the vibroisolation system needs to be regulated easily and quickly regarding the minimisation of dynamical forces transmitted to the ground and to ensure the stability of the testing process. This paper describes one of the options of tuning the base desk at a relatively short time and by sufficient change of own frequencies, which decides the dynamical behaviour of the whole system.

A Model to Predict Fatigue Life of Concrete Based on Total Strain Energy Density

2011 ◽  
Vol 99-100 ◽  
pp. 1018-1022
Author(s):  
Li Zhang ◽  
Si Chu Gong ◽  
Xu Dong Ma
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Fatigue Damage ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Cumulative Damage ◽  
Total Strain ◽  
Total Strain Energy ◽  
Cumulative Fatigue Damage ◽  
Total Strain Energy Density

A law on the cumulative damage is presented basing on total strain energy induced as damage parameter to calculate the cumulative damage when the specimens of concrete subjected to fatigue loading.Then the maximum of critical cumulative damage and location of production are determined basing on the equation of cumulative fatigue damage combined with experimental result through using the finite element analysis and the critical plane method in fatigue analysis.The relation equation between the standardized critical total strain energy density and stress level is obtained by considering the impact of loading level.The fatigue life of specimens can be predicted by combining the equation of cumulative fatigue damage with the relation equation of damage and stress level and the prediction results coincide with experimental results very well.

Effects of Lateral Limited Area and Substrate Compliance on Strain Distribution and Critical Thickness of Sige Film on Si Mesa Substrates

1995 ◽  
Vol 379 ◽  
Author(s):  
Zhang Rong ◽  
Huang Hongbin ◽  
Shi Yi ◽  
Yang Kai ◽  
Gu Shulin ◽  
...  
Keyword(s):  
Strain Distribution ◽  
Strain Energy ◽  
Critical Thickness ◽  
Total Strain ◽  
Limited Area ◽  
Lateral Size ◽  
Total Strain Energy

ABSTRACTIn this paper, we calculated theoretically the strain distribution and the critical thickness of the SiGe epilayers on Si(100) mesa structural substrates by considering the effect of the compliance of substrates, along with the effect of the limited area, and found that the compliance of substrates was relevant not only to its thickness, but also to their lateral size. The introduction of substrate compliance significantly reduced the total strain energy in the epilayers, and increased the critical thickness. That approach was realized by growth on the mesa substrates. The TEM observations confirmed the results of calculations.

The Effect of Compressive Damage on Tensile Loading Failure of Titanium 6Al-4V

2012 ◽  
Author(s):  
Onome Scott-Emuakpor ◽  
Tommy George ◽  
John Wertz ◽  
Casey Holycross
Keyword(s):  
Strain Energy ◽  
Tensile Loading ◽  
Damage Parameter ◽  
Total Strain ◽  
Tensile Fracture ◽  
Half Cycle ◽  
Physical Damage ◽  
Total Strain Energy ◽  
Tension And Compression ◽  
Compressive Damage

In order to explore the belief that total strain energy accumulation during monotonic tensile fracture is a universal damage parameter, the effect of compressive preloads on specimens failed via tensile loading is analyzed. The motivation behind this analysis is due to the theory of an energy-based life prediction model, which states that the total strain energy required for monotonic tensile fracture is defined as the physical damage quantity for the fatigue lifing model. Two things are observed in order to determine the effects of a compressive preload on tensile monotonic fracture. First, the compressive work is viewed as accumulated damage, thus adding to the total work necessary for failure. Second, tensile works of fractured specimens with and without stored compressive energy are compared to see if the damage parameter is affected. The analysis is conducted through experimental data acquisition from round stock Titanium 6Al-4V dogbone specimens. The results from this study show that compressive damage has a negligible effect on monotonic tensile work to fracture, and combined half-cycle tension and compression preloads have an unnoticeable effect on the tensile work of the final pull to fracture. These results contradict the theory and research validations of the energy-based predictions; however, they provide a platform for future efforts to understand the strain energy correlation between monotonic, low cycle and high cycle failures.

Analysis of Multi-Stable Architectures for Morphing Structures

2020 ◽  
Author(s):  
Anil Erol ◽  
Jeffery Baur
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Compressive Loading ◽  
Total Strain ◽  
Total Strain Energy ◽  
Wide Range ◽  
Unit Cells ◽  
Mechanical Logic ◽  
The Individual

Abstract The field of multi-stable structures has been steadily growing due to a wide range of potential applications including energy harvesting, MEMS, and mechanical logic. This work focuses on utilizing elastic energy trapping and snap-through phenomena of bistable unit cells to design a latticed, hierarchical multi-stable cylinder that can articulate up to 30 degrees from its center axis. The employment of bistable elements is hypothesized to reduce the total strain energy required to articulate the cylinder, and yield faster responses with the snap-through. While multi-stable cylinders exist in previous studies, there have been no previous attempts at studying different modes of deformation beyond compressive loading. Thus, the current work presents a new problem regarding the effects of bistable elements in a latticed cylinder that is carrying tensile, compressive, and shear loadings and exhibiting large displacements as the cylinder is articulated.. The total strain energy density of the articulating cylinder is investigated as a function of the heights of the unit cells, which aids in determining an ideal height for the design that minimizes the strain energy density. Results show that the strain energy of an articulating cylinder can be minimized with the use of multi-stability, and that a multi-stable cylinder can require up to three times less loads to maintain desired articulation compared to a mono-stable structure. These results will lead to future works on further optimizing the articulating cylinder by varying additional parameters like the individual heights of rows, the thicknesses of unit cell beams, the strain energy density, and the initial loading threshold for articulation. In addition, the work in this study can yield methodologies for designing arbitrarily morphing skins beyond just cylindrical geometries.

Effective properties of composite material based on total strain energy equivalence

2019 ◽  
Vol 166 ◽  
pp. 213-220 ◽  
Author(s):  
Anna Wiśniewska ◽  
Szymon Hernik ◽  
Aneta Liber-Kneć ◽  
Halina Egner
Keyword(s):  
Composite Material ◽  
Strain Energy ◽  
Effective Properties ◽  
Total Strain ◽  
Total Strain Energy ◽  
Energy Equivalence
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