Natural frequencies of shallow cylindrically curved panels

The natural frequencies of cylindrically curved panels are available in closed form for only two boundary condition sets. This paper demonstrates how Sewall's shallow shell formation can be recast in a relatively simple form to allow direct computation of the natural frequencies and mode shapes of cylindrical panels with a wide range of boundary conditions.     

Excitation fronts on a periodically modulated curved surface

The evolution of an excitation front propagating on a nonuniformly curved surface is considered within the framework of a kinematical model of its motion. For the case of a surface with a periodically modulated curvature an exact solution of the front shape is obtained under the assumption of sufficiently small surface deformation. The results of the theoretical consideration are compared with the experimental data obtained with a modified Belousov-Zhabotinsky reaction in a thin nonuniformly curved layer.     

Observation of dynamic localization in periodically curved waveguide arrays

We report on a direct experimental observation of dynamic localization (DL) of light in sinusoidally-curved lithium-niobate waveguide arrays which provides the optical analog of DL for electrons in periodic potentials subjected to ac electric fields as originally proposed by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)10.1103/PhysRevB.34.3625]. The theoretical condition for DL in a sinusoidal field is experimentally demonstrated.     

Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation

Free vibration analysis of functionally graded curved panels is carried out using a higher-order formulation. A C⁰ finite element formulation is used to carry out the analysis. The element consists of nine degrees of freedom per node with higher-order terms in the Taylor's-series expansion, which represents the higher-order transverse cross-sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effects of rotary inertia and transverse shear. A realistic parabolic distribution of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided. Material properties are assumed to be temperature independent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Heat conduction between ceramic and metal constituents is neglected. The accuracy of the formulation is validated by comparing the results with those available in the literature. Effects of panel geometry parameters and boundary conditions are studied.     

Self-imaging and modulational instability in an array of periodically curved waveguides

Linear and nonlinear light propagation in an array of waveguides with a periodically bent axis is theoretically investigated. In the linear propagation regime, it is shown that a self-imaging effect at periodic planes may occur, a phenomenon analogous to that of dynamic localization observed when an electron in a periodic potential is subjected to an ac field. In the nonlinear propagation regime, it is shown that periodic waveguide bending under the self-imaging condition inhibits the phenomenon of discrete modulational instability.     

Multiband diffraction and refraction control in binary arrays of periodically curved waveguides

The possibility of controlling discrete diffraction and refraction in a multiband waveguide array by periodic waveguide bending is theoretically demonstrated. Resonance effects, leading to the enhancement or inhibition of discrete diffraction, are found and related to the quantum analog of field-induced n-photon resonances in semiconductor superlattices. A very distinct behavior for light refraction is found for odd or even resonances. In particular, for even resonances, the two-band behavior of the straight binary array is quenched, resulting in the inhibition of double refraction.     

Integrated analysis on static/dynamic aeroelasticity of curved panels based on a modified local piston theory

A flow field modified local piston theory, which is applied to the integrated analysis on static/dynamic aeroelastic behaviors of curved panels, is proposed in this paper. The local flow field parameters used in the modification are obtained by CFD technique which has the advantage to simulate the steady flow field accurately. This flow field modified local piston theory for aerodynamic loading is applied to the analysis of static aeroelastic deformation and flutter stabilities of curved panels in hypersonic flow. In addition, comparisons are made between results obtained by using the present method and curvature modified method. It shows that when the curvature of the curved panel is relatively small, the static aeroelastic deformations and flutter stability boundaries obtained by these two methods have little difference, while for curved panels with larger curvatures, the static aeroelastic deformation obtained by the present method is larger and the flutter stability boundary is smaller compared with those obtained by the curvature modified method, and the discrepancy increases with the increasing of curvature of panels. Therefore, the existing curvature modified method is non-conservative compared to the proposed flow field modified method based on the consideration of hypersonic flight vehicle safety, and the proposed flow field modified local piston theory for curved panels enlarges the application range of piston theory.     

Smearing technique for vibration analysis of simply supported cross-stiffened and doubly curved thin rectangular shells

Plates stiffened with ribs can be modeled as equivalent homogeneous isotropic or orthotropic plates. Modeling such an equivalent smeared plate numerically, say, with the finite element method requires far less computer resources than modeling the complete stiffened plate. This may be important when a number of stiffened plates are combined in a complicated assembly composed of many plate panels. However, whereas the equivalent smeared plate technique is well established and recently improved for flat panels, there is no similar established technique for doubly curved stiffened shells. In this paper the improved smeared plate technique is combined with the equation of motion for a doubly curved thin rectangular shell, and a solution is offered for using the smearing technique for stiffened shell structures. The developed prediction technique is validated by comparing natural frequencies and mode shapes as well as forced responses from simulations based on the smeared theory with results from experiments with a doubly curved cross-stiffened shell. Moreover, natural frequencies of cross-stiffened panels determined by finite element simulations that include the exact cross-sectional geometries of panels with cross-stiffeners are compared with predictions based on the smeared theory for a range of different panel curvatures. Good agreement is found.     

Shaping and switching of polychromatic light in arrays of periodically curved nonlinear waveguides

We overview our recent theoretical results on spatio-spectral control, diffraction management, and broadband all-optical switching of polychromatic light in periodically curved one and two dimensional arrays of coupled optical waveguides. In particular, we show that polychromatic light beams and patterns produced by white-light and supercontinuum sources can experience wavelength-independent normal, anomalous, or zero diffraction in specially designed structures. We also demonstrate that in the nonlinear regime, it is possible to achieve broadband all-optical switching of polychromatic light in a directional waveguide coupler with special bending of the waveguide axes. Our results suggest novel opportunities for creation of all-optical logical gates and switches which can operate in a very broad frequency region, e.g., covering the entire visible spectrum. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Wave propagation and vibration response of a periodically supported pipe conveying fluid

Propagation of free harmonic waves, in a periodically supported infinite pipe, has been studied. The presence of the Coriolis term in the equation of motion renders the phase velocity different for the positive and the negative going waves. Hence no classical normal modes (in the sense of standing modes) exist. Natural frequencies of a periodically supported finite pipe have been obtained by using the wave approach. The response of the infinite pipe to a convected harmonic pressure field has also been obtained. Owing to the difference in the phase velocities of the positive and the negative going free waves, the coincidence frequency depends on the direction of the convected loading. The static buckling or the divergence instability of such pipes has also been considered from the wave approach.     

Flutter analysis of cantilevered quadrilateral plates

In this paper, the title problem is solved by using a numerical method involving an integral equation technique and a normal mode method. Linear plate theory has been used for computing the strain energy and kinetic energy of the plate. Piston theory has been used to describe the aerodynamic pressure distribution. Numerical work has been done and convergence of the solution has been studied. Results have also been obtained for various cases and compared with those of other investigators.     

Transmission loss of periodically stiffened laminate composite panels: shear deformation and in-plane interaction effects

This paper investigates the transmission loss of symmetric and asymmetric laminate composite panels periodically reinforced by composite stiffeners. A comprehensive model based on periodic structure theory is developed. First order shear deformation theory is used and the coupling of the in-plane motion of the panel with its out-of-plane motion is taken into account. Stiffeners interact with the panel through three forces (two in-plane, one out-of-plane) and a torsion moment. Three types of cross sections are investigated for the composite stiffeners: I-shaped, C-shaped, and omega-shaped cross-sections. The model is validated numerically by comparison with the finite element/boundary element method. Experimental validations are also conducted. In both cases, excellent agreement is obtained. Numerical results show that the in-plane coupling effect is increased by increasing the panel thickness and the stiffener's eccentricity. The in-plane coupling effect is also found to increase with frequency.     

An approximate method of predicting the response of periodically supported beams subjected to random convected loading

The space-averaged response of an infinite, elastically supported, periodic beam subjected to convected random loading has been studied by using an approximate “assumed mode” method. The complex wave motion in the beam is represented by any number of suitably chosen complex modes. With a good, yet simple, choice of mode which satisfies certain boundary conditions on one periodic beam element, a “single mode approximation” can yield very accurate values of the average response. This has been verified for a wide range of the support stiffnesses and loading convection velocities. Consideration has also been given to the ratio of the maximum response in the beam to the space-averaged response. The method has been applied only to uniform beams in this paper, but it should be readily applicable to periodic systems consisting of non-uniform beam elements.     

Flutter analysis of a flag of fractional viscoelastic material

We develop a two-dimensional model to study the effects of the material viscoelasticity on the dynamics of a flag in flow. Two periodic states of an elastic flag are firstly identified with different dimensionless bending stiffness: a lower frequency state and a higher frequency state. The Scott–Blair model and the fractional Kelvin–Voigt model are further used to represent the viscoelasticity of the flag material. When the Scott–Blair model is used, with the increase of the fractional derivative order α, the flag flapping frequency of the higher frequency state decreases abruptly, and that of the lower frequency state also shows a downward trend. When the system parameters are in a certain range, an interesting phenomenon is observed, where the time needed to achieve the periodic steady state initially increases and then decreases with increasing α. The phenomenon implies that the flag has a higher energy harvesting speed when α approaches 1. When the fractional Kelvin–Voigt model is used, the increasing α also causes the transition from the higher frequency state to the lower frequency state, and quasi-periodic states are observed during the transition. The fractional Kelvin–Voigt type viscoelasticity produces complex effects on the lower frequency state.     

Dynamic response of doubly curved honeycomb sandwich panels to random acoustic excitation. Part 2: Theoretical study

In this paper a single-degree-of-freedom model is developed to predict the dynamic response of an acoustially excited doubly curved sandwich panel. Three variants of the model are investigated, based on differing assumptions regarding the spatial distribution of the applied loading. When the loading is assumed to be uniform then the model reduces to the Miles approach, and when the loading is assumed to conform to the structural mode shape then the method is very similar to the Blevins approach. The third variant involves a more detailed consideration of the travelling wave characteristics of the applied loading, and this is found to give much improved agreement with experimental results obtained in a progressive wave tube facility. In addition, an approach using the finite element method is presented in which the response to grazing incidence excitation is computed, and this is also found to yield good agreement with the experimental results.