In this paper, the effect of pre-stress condition on the resonance frequency of the transducer is studied by using numerical and analytical methods. To compare the obtained results, two sandwich-type transducers with nominal frequency of 25 kHz and 30 kHz are considered. Experimental determination of pre-stress value in transducer is described and measured. Then resonance frequency of transducers in the presence of pre-stress is determined by impedance analyser. Numerical analysis is conducted by modelling three-dimensional transducer in details at ABAQUS software. The resonance frequency is determined with and without pre-stress. The FE results show that by applying pre-stress on the transducers, the resonance frequency of transducers decreased. Furthermore, the FE results are very close to experimental results. Furthermore, a systematic analytical solution is presented based on one-dimensional wave propagation. The resultant displacement for each sub-section of the transducer is calculated and then all of them are assembled and solved by considering the continuity conditions of displacement and force components. It is found that pre-load condition that is produced by central bolt reduces resonance frequency of the transducer. The obtained analytical results provide fast and reliable model for predicting resonance frequency of transducer. پرونده مقاله

Second-order corrugated cores are one types of advanced hierarchical cores that use the common corrugated cores as constituent elements for primary core. This paper attempts to identify and optimize bending properties of composite sandwich panels with second-order corrugated cores. To this end, construction of both first- and second-order corrugated cores are explained. Based on Taguchi method, various finite element models with different geometrical parameters are modeled and reaction force and stiffness are determined. Stiffness formulas for first- and second-order corrugated cores are determined by using regression analysis. The constrained-optimization results are determined to optimize stiffness of sandwich panels with first- and second-order corrugated cores, separately. After that, global optimization problem is implemented to compare the first- and second-order configuration. It is found that when using second-order corrugated cores, the stiffness per unit mass increased more than twice compared to first-order corrugated cores. پرونده مقاله

In the present research, a unified formulation for free vibration analysis of the bidirectional functionally graded conical and cylindrical shells and annular plates on elastic foundations is developed. To cover more individual cases and optimally tailored material properties, the material properties are assumed to vary in both the meridian/radial and transverse directions. The shell/plate is assumed to be supported by a non-uniform Winkler-type elastic foundation in addition to the edge constraints. Therefore, the considered problem contains some complexities that have not been considered together in the available researches. The proposed unified formulation is derived based on the principle of minimum total potential energy and solved using a differential transform analytical method whose center is located at the outer edge of the shell or plate; so that the resulting semi-analytical solution can be employed not only for truncated conical shells and annular plates, but also for complete conical shells and circular plates. Accuracy of results of the proposed unified formulation is verified by comparing the results with those of the three-dimensional theory of elasticity extracted from the ABAQUS finite element analysis code. A variety of the edge condition combinations are considered in the results section. A comprehensive parametric study including assessment of influences of the material properties indices, thickness to radius ratio, stiffness distribution of the elastic foundation, and various boundary conditions, is accomplished. Results reveal that influence of the meridian variations of the material properties on the natural frequencies is more remarkable than that of the transverse gradation. پرونده مقاله

Due to their continuous material variation and eliminating the mismatch stress field in the thickness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for thick functionally graded plate based on three-dimensional elasticity theory. To this end, first, the characteristic equation of FG plate is derived and general closed-form is obtained analytically. Both positive and negative discriminant of characteristic equation is considered and solved. The presented method is validated with finite element results by considering isotropic thick plate. Several parametric studies are carried out to investigate the effect of geometric and material parameters. The aim of this research is to present analytical solution form for thick FG plate and work out the problem of inconsistency for corresponding displacements field. The presented solution can be used to examine accuracy of various plate theories such as first-order, third order shear deformation theories and other equivalent plate theories. پرونده مقاله

Bending analysis of multilayer graphene sheets (MLGSs) subjected to non-uniform shear and normal tractions is presented. The constitutive relations are considered to be non-classical based on nonlocal theory of elasticity. Based on the differential transformation method, numerical illustrations are carried out for circular and annular geometries. The effects of nano scale parameter, radius of circular and annular graphene sheet, number of layers as well as distance between layers in the presence of van der Waals interaction forces are investigated. In addition, the effects of different boundary conditions are also examined. The numerical results show that above mentioned parameters have significant effects on the bending behavior of MLGSs under the action of non-uniform shear and normal tractions. پرونده مقاله