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For meeting the requirements of tactical missiles seeking miniaturized launch devices for storage, transportation, and launch, a tube-launched missile wing is adopted, which folds before launch and quickly unfolds after launch. As a structure installed on the missile body to generate the required aerodynamic force for manipulating the missile, the tube-launched missile wing can effectively stabilize the missile’s flight attitude. At present, most research on the unfolding mechanism of missile folding wings is focused on one-time folding. When the wingspan is large, multiple folding is required to meet the launch requirements of modern tube-launched missiles. Therefore, this article designs a dual-joint folding wing deployment mechanism and studies the rigid–flexible coupling dynamic modeling and related technologies of folding wings based on this structure. Based on the inertial coupling between large-scale rigid body motion and structural flexible deformation, the folding wing breaks through the element convergence of the model and achieves the applicability of the structural model through zero-order approximation model analysis and other technologies. Simulation results show that the hybrid coordinate method can fully and accurately display the vibration information of flexible folding wings. At different speeds, the first-order coupling model is more advanced than the zero-order coupling model. In addition, increasing rotational speed, increasing wing thickness, and reducing wing span length can effectively increase the fundamental frequency of wing flutter. The structural design of folding wings has shown important reference significance.
For meeting the requirements of tactical missiles seeking miniaturized launch devices for storage, transportation, and launch, a tube-launched missile wing is adopted, which folds before launch and quickly unfolds after launch. As a structure installed on the missile body to generate the required aerodynamic force for manipulating the missile, the tube-launched missile wing can effectively stabilize the missile’s flight attitude. At present, most research on the unfolding mechanism of missile folding wings is focused on one-time folding. When the wingspan is large, multiple folding is required to meet the launch requirements of modern tube-launched missiles. Therefore, this article designs a dual-joint folding wing deployment mechanism and studies the rigid–flexible coupling dynamic modeling and related technologies of folding wings based on this structure. Based on the inertial coupling between large-scale rigid body motion and structural flexible deformation, the folding wing breaks through the element convergence of the model and achieves the applicability of the structural model through zero-order approximation model analysis and other technologies. Simulation results show that the hybrid coordinate method can fully and accurately display the vibration information of flexible folding wings. At different speeds, the first-order coupling model is more advanced than the zero-order coupling model. In addition, increasing rotational speed, increasing wing thickness, and reducing wing span length can effectively increase the fundamental frequency of wing flutter. The structural design of folding wings has shown important reference significance.
The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the constructed interpolation functions. Unlike the conventional constructions, each vertex in the partition of the triangular region has been assigned a color such that the chromatic number of the partition is 3. A new method for the partitioning of the triangle is proposed with a result concerning the chromatic number of its graph. Following the construction, a formula determining the vertical scaling factor is provided such that the actual double integral coincides with the integral value calculated using fractal theory. Convergence of the proposed method to the actual integral value is proven with sufficient lemmas and theorems. Adequate examples are presented to illustrate the method of construction and to verify the value of double integration.
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