Nonlinear Vibrations and Stability of Shells and Plates: Vibrations of Circular Cylindrical Panels with Different Boundary Conditions
Citations
38 citations
Cites methods from "Nonlinear Vibrations and Stability ..."
...18 A different form for the equation of motion can be found in [13], using Donnels shell theory applied to a circular cylindrical shell one can find a set of three coupled PDE's describing the displacement:...
[...]
30 citations
Cites background or methods from "Nonlinear Vibrations and Stability ..."
...The basic theory backing the present investigation can be found in Paı̈doussis [22] and Amabili [23]....
[...]
...Following previous studies and using the method of separation of variables [22,23,31], the perturbation pressure on the shell wall is found to be Ph 1⁄4 rF L mp fw @(2)w @t2 þ2U @ (2)w @t@x þU(2) @ (2)w @x2 ! , ð19Þ with fw 1⁄4 1 Inðn 1,mpR=LÞ I 0 nðn,mpR=LÞ n mpR=L , ð20Þ where rF is the fluid density, In the nth order modified Bessel function and I 0 n is its derivative with respect to its argument....
[...]
...On the other hand, excepting Case 5, the resonant branch becomes unstable, as the forcing frequency decreases due to a pitchfork bifurcation [23] and simultaneously the companion mode is excited and participates in the oscillations with nonzero value in the main resonance region around j/O01⁄41....
[...]
...Expansion (13) has been thoroughly tested by Amabili and co-workers [23,25]....
[...]
17 citations
Cites background or methods from "Nonlinear Vibrations and Stability ..."
...This model includes the basic vibration (driven) mode, its companion mode, four axisymmetric modes and the gyroscopic modes (driven and companion) with twice the number of waves in the axial direction as the basic vibration mode, which becomes important at high flow velocities [3,12]....
[...]
...These topics are also present in detail in the books by Paı̈doussis on fluid–structure interactions [3] and Amabili on nonlinear vibrations and stability of shells and plates [12]....
[...]
...However, more refined modal solutions can be found in the literature [12]....
[...]
12 citations
Cites background or methods or result from "Nonlinear Vibrations and Stability ..."
...A detailed review of this subject was p ublished in 2003 by Amabili and Païdoussis (2003)....
[...]
...Finally, experimental results of dynamic buckling loads of slender structures are rather scarce in literature (Virgin, 2000; Amabili, 2008)....
[...]
...These values are bas d on the experimental results by Amabili and co-workers (Amabili, 2008)....
[...]
8 citations
Cites background or methods from "Nonlinear Vibrations and Stability ..."
...This is a good approximation for thin shells, say R/h>20 (see, for example, Amabili, 2008)....
[...]
...Amabili (2008) focused on nonlinear vibrations and stability aspects. Interest in previous studies is mainly motivated by structures of planes, cars, submarines and military applications. But engineering problems for which considerations of blast loads are required are not limited to those areas. A new field of interest involving the nonlinear dynamics of cylindrical shells emerged during the last ten years as a consequence of damage and destruction of oil storage tanks caused by explosions for both, vertical and horizontal tanks. Although most cases of explosions on tanks reported in the literature are caused by accidents, some recent events show that vulnerability with respect to intentional acts should also be of great concern to designers and forensic engineers. The mechanics of the problem and the variables involved in the phenomenon of an explosion can be seen for instance in Glasstone and Dolan (1977) for nuclear explosions and with more detail in UFC-3-340-02 (2008), with the aim of improving structural designs to resist the effects of explosions. The spatial distribution of a blast pressure around cylindrical tanks is described in a limited number of publications. In recently reported work, a group of researchers in France performed experiments on small-scale cantilever cylindrical shells having a scale factor of 1:48 to obtain time dependent pressure distributions (Duong et al., 2012a; Duong et al., 2012b; Noret et al., 2012). The goal of such testing program was to establish a probabilistic analysis about threshold values causing different damage levels. Analytical studies based on Donnell’s approximation were performed using static response to establish performance limits based on plasticity. Testing has been recently performed at University of North Carolina at Charlotte by Weggel and Whelan (2013) for small scale rigid models.. An alternative to blast testing is to employ computational Fluid Dynamics or Fluid-Structure interaction to simulate the process, such as in the work of Trajkovski et al. (2014). The analysis of nonlinear elastic behavior of thin-walled structures subjected to short duration pressures were shown by Ruiz et al....
[...]
...Amabili (2008) focused on nonlinear vibrations and stability aspects....
[...]
...Amabili (2008) focused on nonlinear vibrations and stability aspects. Interest in previous studies is mainly motivated by structures of planes, cars, submarines and military applications. But engineering problems for which considerations of blast loads are required are not limited to those areas. A new field of interest involving the nonlinear dynamics of cylindrical shells emerged during the last ten years as a consequence of damage and destruction of oil storage tanks caused by explosions for both, vertical and horizontal tanks. Although most cases of explosions on tanks reported in the literature are caused by accidents, some recent events show that vulnerability with respect to intentional acts should also be of great concern to designers and forensic engineers. The mechanics of the problem and the variables involved in the phenomenon of an explosion can be seen for instance in Glasstone and Dolan (1977) for nuclear explosions and with more detail in UFC-3-340-02 (2008), with the aim of improving structural designs to resist the effects of explosions. The spatial distribution of a blast pressure around cylindrical tanks is described in a limited number of publications. In recently reported work, a group of researchers in France performed experiments on small-scale cantilever cylindrical shells having a scale factor of 1:48 to obtain time dependent pressure distributions (Duong et al., 2012a; Duong et al., 2012b; Noret et al., 2012). The goal of such testing program was to establish a probabilistic analysis about threshold values causing different damage levels. Analytical studies based on Donnell’s approximation were performed using static response to establish performance limits based on plasticity. Testing has been recently performed at University of North Carolina at Charlotte by Weggel and Whelan (2013) for small scale rigid models.. An alternative to blast testing is to employ computational Fluid Dynamics or Fluid-Structure interaction to simulate the process, such as in the work of Trajkovski et al. (2014). The analysis of nonlinear elastic behavior of thin-walled structures subjected to short duration pressures were shown by Ruiz et al. (1989) and Hoo-Fatt and Pothula (2010) for cylindrical shells, Kowal-Michalska et al. (2011) for conical and spherical shells, Gao and Hoo-Fatt (2012) for a cylindrical sector, Goel et al....
[...]
...Use of these equations has been illustrated, for example in the texts by Brush and Almroth (1975) for buckling problems and by Amabili (2008) for vibrations of shells....
[...]
References
1,532 citations
1,166 citations
133 citations
89 citations