A Simplified Matrix Method for the Dynamic Examination of Different Shells of Revolution

Öry, Huba; Hornung, E.; Fahlbusch, G.

doi:10.2514/6.1965-1136

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…(3) results in )'-21,* f v, y + -j »,"" (4) where A r k, z rk are the area and z coordinate of the centroid of the /cth ring cross section, respectively, and d rk is the radius of gyration of the cross-sectional area of the kih ring about the x axis.…”

Section: Methods Of Analysis Potential Energiesmentioning

confidence: 99%

An analysis of free vibration of orthogonally stiffened cylindrical shells with stiffeners treated as discrete elements.

Egle

Sewall

1968

AIAA Journal

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A free vibration analysis is developed for a ring-and-stringer-stiffened circular cylindrical shell with various types of end conditions and with the stiffeners treated as discrete elements. The number and spacing of stiffeners are arbitrary, so that there is no limitation due to averaging stiffener effects over the shell surface. The analysis shows that stringers considered as discrete elements couple circumferential modes of different wave numbers and also couple symmetric and antisymmetric circumferential modes. Moreover, the natural frequencies associated with the symmetric and antisymmetric modes may have different values, indicating the existence of "double resonances." Numerical results show that even stringers that are comparatively weak in bending may have a significant effect on both the modes of vibration and differences between the symmetric and antisymmetric frequencies. Nomenclature A = stiffener cross-sectional area D = isotropic plate flexural stiffness, Eh*/12(l -D x ,D y -orthotropic plate flexural stiffnesses due to rings and stringers, respectively E = Young's modulus (GJ) = stiffener torsional stiffness K,L = total number of rings, stringers NX™ = stringer stress resultants; see Fig. 2 N x (C \N xy^ = shell stress resultants; see Fig. 2 R = shell radius X m = axial mode functions a = length of cylindrical shell £xx, Zyy, &xy = strains in the x-y plane / = frequency drk'j dsi = radius of gyration of the kth ring, Ith stringer cross section about the x } y axis h = shell thickness i> J> k, l } m, n, P, Q = integers m*, n* -maximum number of terms used in the axial, circumferential displacement series p r k', Psi = polar radius of gyration of the kth ring, Ith stringer cross section about the y, x axis u, v, w = shell middle surface displacements in the x,y } z directions Presented as Paper 67-71 at the AIAA 5th Aerospace Sciences

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Section: Methods Of Analysis Potential Energiesmentioning

confidence: 99%

An analysis of free vibration of orthogonally stiffened cylindrical shells with stiffeners treated as discrete elements.

Egle

Sewall

1968

AIAA Journal

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“…Because of the need to Fourier transform the data to get the response spectrum in the frequency domain, the frequency domain method is usually suitable for the load identification of stationary response signals rather than transient response signals., thus reducing the recognition accuracy. Ory et al [5] converted the differential equation of motion into an uncoupled equation form of the modal space by introducing modal coordinate transformation, and thus proposed a discrete timedomain identification method for dynamic load, and expressed the relationship among system characteristics, dynamic load and structural response in the form of Duhamel equation. Miao et al [6] firstly established a load recognition equation based on Green kernel function, and then used TSVD regularization method to effectively recognize sine load and triangular wave load on a cantilever beam.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Load Identification at Natural Frequencies for Aircraft via Attention Based 1D-CNN

He,

Li,

Feng

et al. 2024

J. Phys.: Conf. Ser.

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Since the frequency response function is ill-conditioned at the natural frequency of the system, the traditional load identification method based on the system parameters is no longer applicable. Aiming at the difficulty of dynamic load identification at the natural frequency of the structural system, a dynamic load identification method at the natural frequency of the structure based on one-dimensional convolutional neural network(1D-CNN) with attention mechanism is proposed. Specifically, the high-level features in the vibration response signal are first extracted through the convolution layer. Then the weight matrix of the network is updated by backpropagation algorithm, which represents the importance of different features. The mapping relationship between response and load is established to realize the task of load identification. From the trained data, the attention module learns the contribution of features according to the different contribution of different features to load prediction. The important components in the response signal are highlighted and noise pollution is suppressed. Excitation and response signals at the natural frequency of the system were acquired using exciters and an accelerometer mounted on the GARTEUR aircraft model. Excitation and response signals at the natural frequencies of the system are obtained by an exciter and accelerometer mounted on the GARTEUR aircraft model. The responses of the model at the first three natural frequencies of 6.4Hz,35.8Hz and 48.5Hz were obtained respectively. Experimental results show that compared with the traditional TSVD load identification method, the maximum error of this method is only 3.19%. Compared with the 1D-CNN method, the proposed method has stronger robustness under 20%, 50% and 80% noise levels.

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Uhrig¹

1973

Elastostatik Und Elastokinetik in Matrizenschreibweise

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A Simplified Matrix Method for the Dynamic Examination of Different Shells of Revolution

Cited by 5 publications

References 6 publications

An analysis of free vibration of orthogonally stiffened cylindrical shells with stiffeners treated as discrete elements.

An analysis of free vibration of orthogonally stiffened cylindrical shells with stiffeners treated as discrete elements.

Dynamic Load Identification at Natural Frequencies for Aircraft via Attention Based 1D-CNN

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