Search Results (5)

An analytical solution is presented for axisymmetric free vibration analysis of a functionally graded piezoelectric circular plate on the basis of the three-dimensional elastic theory of piezoelectric materials. The material properties are assumed to follow an exponential law distribution through the thickness of the circular plate. The state space equations for the free vibration behavior of the functionally graded piezoelectric circular plate are developed based on the state space method. The finite Hankel transform is utilized to obtain an ordinary differential equation with variable coefficients. By virtue of the proposed exponential law model, we have ordinary differential equations with constant coefficients. Then, the free vibration behaviors of the functionally graded piezoelectric circular plate with two kinds of boundary conditions are investigated. Some numerical examples are given to validate the accuracy and stability of the present model. The influences of the exponential factor and thickness-to-span ratio on the natural frequency of the functionally graded piezoelectric circular plate, constrained by different boundary conditions, are discussed in detail. Full article

The purpose of this paper is to study the axisymmetric vibrations of circular three-layered sandwich plates with a frequency-dependent fractional viscoelastic core and elastic face sheets. First, the equations of motion and related boundary conditions are derived using the Hamilton’s principle for the free vibrations. Then, the governing equations obtained for various boundary conditions are solved and parametric studies are carried out to examine the vibration behavior of circular sandwich plates with a viscoelastic core. The differential transform method (DTM), a well-known semi-analytical–numerical solution technique, is utilized for the eigenvalue analysis. In addition, the finite element (FE) solution obtained with the commercial code ANSYS is added to this comparison. The effect of face and core layer thicknesses and the location of the core layer and core material on the dynamic and damping characteristics of circular sandwich plates with a fractional derivative viscoelastic core is studied in detail. Full article

The applicability and limitations of simplified models of thin elastic circular cylindrical shells for linear vibrations of double-walled carbon nanotubes (DWCNTs) are considered. The simplified models, which are based on the assumptions of membrane and moment approximate thin-shell theories, are compared with the extended Sanders–Koiter shell theory. Actual discrete DWCNTs are modelled by means of couples of concentric equivalent continuous thin, circular cylindrical shells. Van der Waals interaction forces between the layers are taken into account by adopting He’s model. Simply supported and free–free boundary conditions are applied. The Rayleigh–Ritz method is considered to obtain approximate natural frequencies and mode shapes. Different aspect and thickness ratios, and numbers of waves along longitudinal and circumferential directions, are analysed. In the cases of axisymmetric and beam-like modes, it is proven that membrane shell theory, differently from moment shell theory, provides results with excellent agreement with the extended Sanders–Koiter shell theory. On the other hand, in the case of shell-like modes, it is found that both membrane and moment shell theories provide results reporting acceptable agreement with the extended Sanders–Koiter shell theory only for very limited ranges of geometries and wavenumbers. Conversely, for shell-like modes it is found that a newly developed, simplified shell model, based on the combination of membrane and semi-moment theories, provides results in satisfactory agreement with the extended Sanders–Koiter shell theory in all ranges. Full article

A free-flooded transducer that couples the vibration of a longitudinal vibration transducer and the fluid cavity of an aluminum ring was investigated. Given the transducer is based on a fluid cavity structure and has no air cavity, it can resist high hydrostatic pressure when working underwater, which is suitable for application in the deep sea. At first, the structure and working principle of the transducer were introduced. Then, the axisymmetric finite element model of the transducer was established; and the transmitting voltage response, admittance, and radiation directivity of the transducer were simulated using the finite element method. According to the size of the finite element model, a prototype of the transducer was designed and fabricated, and the electro-acoustic performance of the prototype was measured in an anechoic water tank. The experimental results were consistent with the simulation results and showed a good performance of the transducer. Finally, the improvement of the radiation directivity of the transducer by the optimal design of the free-flooded aluminum ring was obtained using the finite element method and verified by experiments. Full article

Bell-shaped vibratory angular rate gyro (abbreviated as BVG) is a new type Coriolis vibratory gyro that was inspired by Chinese traditional clocks. The resonator fuses based on a variable thickness axisymmetric multicurved surface shell. Its characteristics can directly influence the performance of BVG. The BVG structure not only has capabilities of bearing high overload, high impact and, compared with the tuning fork, vibrating beam, shell and a comb structure, but also a higher frequency to overcome the influence of the disturbance of the exterior environment than the same sized hemispherical resonator gyroscope (HRG) and the traditional cylinder vibratory gyroscope. It can be widely applied in high dynamic low precision angular rate measurement occasions. The main work is as follows: the issue mainly analyzes the structure and basic principle, and investigates the bell-shaped resonator’s mathematical model. The reasonable structural parameters are obtained from finite element analysis and an intelligent platform. Using the current solid vibration gyro theory analyzes the structural characteristics and principles of BVG. The bell-shaped resonator is simplified as a paraboloid of the revolution mechanical model, which has a fixed closed end and a free opened end. It obtains the natural frequency and vibration modes based on the theory of elasticity. The structural parameters are obtained from the orthogonal method by the research on the structural parameters of the resonator analysis. It obtains the modal analysis, stress analysis and impact analysis with the chosen parameters. Finally, using the turntable experiment verifies the gyro effect of the BVG. Full article