Free Vibration of Doubly Curved Thin Shells

While several numerical approaches exist for the vibration analysis of thin shells, there is a lack of analytical approaches to address this problem. This is due to complications that arise from coupling between the midsurface and normal coordinates in the transverse differential equation of motion (TDEM) of the shell. In this research, an Uncoupling Theorem for solving the TDEM of doubly curved, thin shells with equivalent radii is introduced. The use of the uncoupling theorem leads to the development of an uncoupled transverse differential of motion for the shells under consideration. Solution of the uncoupled spatial equation results in a general expression for the eigenfrequencies of these shells. The theorem is applied to four shell geometries, and numerical examples are used to demonstrate the influence of material and geometric parameters on the eigenfrequencies of these shells.

ORTOGONAL COMPACT FUNCTIONS FOR NONLINEAR SPATIAL EQUATION OF VISCOUS TRANSONIC FLOW

In the article the unique algorithm of construction of the system of orthogonal compact V.L. Leontev’s type functions for the nonlinear spatial equationof viscous transonic flow is described by the method of Galerkin. The result ofdesigning on corresponding subspaces is system of ordinary differential equationswith a diagonal matrix.

Characterization of Polymer Surfaces by the Use of Different Wetting Theories Regarding Acid-Base Properties

The existing wetting methods for the determination of acid-base properties on solid surfaces are discussed. Striving for a better understanding of the adhesive polymer interactions in adhesively joined polymers, the methods of Berger and van Oss-Chaudhury-Good were found as the most suitable methods for the investigation of wetting on solid polymer surfaces. Methods of nonlinear systems by Della Volpe and Siboni were adapted and evaluated on plastic surfaces. In the context of these investigations various data of the surface free energy as well as its components have been identified for a number of polymer surfaces by application of spatial equation solutions.

Modeling and Response Analysis of Piezoelectric Flag in Wind Flow

Within the past decade, research in the piezoelectric energy harvesting field has grown significantly concerning material selection, device configurations, and actuation methods. Oscillating cantilevered piezoelectric energy harvesters are one of the more common designs. The flag is modeled as a cantilevered Euler-Bernoulli beam with a low modulus of elasticity, and the representative equation for this is broadly accepted. The wind pressure is modeled by a method that is apparently well accepted in the aerospace field. Among other modeling assumptions, the partial differential equation is considered separable. Once separated, the spatial equation is adjusted using an auxiliary function in order to determine the mode shapes. With the mode shapes characterized, the time function is rendered, which can yield representations for either a damped or undamped system. Individually, these time functions are combined with the adjusted spatial function using the Galerkin method. Plotted results represent the periodic, two-dimensional system response over time.

Measurement Data Restoring Method of Shoe Last Based on Numerical Cutting Technology

From the perspective of Analytic Geometry, the spatial equation of milling cutter rotary surface is obtained. According to the measurement and machining of shoe last, a new measurement data restoring technology that is named Numerical Cutting is presented, and the Numerical Blade is defined. The working principle of Numerical Cutting Technology is introduced in detail, and it is used to restore the measurement data of shoe last. Then the discrete model of shoe last is gotten by shoe last CAD software. Finally, an application example of Numerical Cutting Technology is presented.