Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with inte...Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.展开更多
By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between...By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of ftmdamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.展开更多
Aimed at the optimal analysis and processing technology of die cavity of special-shaped products extrusion, by numerical analysis of trigonometric interpolation and Conformal Mapping theory, on the non-circle cross-se...Aimed at the optimal analysis and processing technology of die cavity of special-shaped products extrusion, by numerical analysis of trigonometric interpolation and Conformal Mapping theory, on the non-circle cross-section of special-shaped products, the conformal mapping function can be set up to translate the cross-section region into unit dish region, over numerical finite interpolation points between even and odd. Products extrusion forming can be turned into two-dimension problem, and plastic stream function can be deduced, as well as the mathematical model of the die cavity surface is established based on deferent kinds of vertical curve. By applying Upper-bound Principle, the vertical curves and related parameters of die cavity are optimized. Combining with electrical discharge machining (EDM) process and numerical control (NC) milling machine technology, the optimal processing of die cavity can be realized. Taking ellipse-shaped products as an instance, the optimal analysis and processing of die cavity including extruding experiment are carried out.展开更多
文摘Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.
文摘By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of ftmdamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.
基金Porject(50075076) supported by the National Natural Science Foundation of ChinaPorject(2007XM036) supported by Science and Technology of Beijing Jiaotong Uniersity, China
文摘Aimed at the optimal analysis and processing technology of die cavity of special-shaped products extrusion, by numerical analysis of trigonometric interpolation and Conformal Mapping theory, on the non-circle cross-section of special-shaped products, the conformal mapping function can be set up to translate the cross-section region into unit dish region, over numerical finite interpolation points between even and odd. Products extrusion forming can be turned into two-dimension problem, and plastic stream function can be deduced, as well as the mathematical model of the die cavity surface is established based on deferent kinds of vertical curve. By applying Upper-bound Principle, the vertical curves and related parameters of die cavity are optimized. Combining with electrical discharge machining (EDM) process and numerical control (NC) milling machine technology, the optimal processing of die cavity can be realized. Taking ellipse-shaped products as an instance, the optimal analysis and processing of die cavity including extruding experiment are carried out.
