Firstly, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates is deduced directly from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate is simply given. For multilayered hybrid plates, we derive the solution in terms of the propagator matrices. The techniques accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, and the transverse shear deformation and the rotary inertia of laminate are also considered in the global algebraic equation of structure. Meanwhile, there is no restriction on the thickness and the number of layers. As an application of the numerical inversion of Laplace transform presented in this paper, typical numerical examples of the harmonic vibration and transient response are proposed and discussed. Since the highly accurate numerical results, they can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems. 相似文献
In the context of human-robot and robot-robot interactions, the better cooperation can be achieved by predicting the other party’s subsequent actions based on the current action of the other party. The time duration for adjustment is not sufficient provided by short term forecasting models to robots. A longer duration can by achieved by mid-term forecasting. But the mid-term forecasting models introduce the previous errors into the follow-up forecasting and amplified gradually, eventually invalidating the forecasting. A new mid-term forecasting with error suppression based on restricted Boltzmann machine(RBM) is proposed in this paper. The proposed model can suppress the error amplification by replacing the previous inputs with their features, which are retrieved by a deep belief network(DBN). Furthermore, a new mechanism is proposed to decide whether the forecasting result is accepted or not. The model is evaluated with several datasets. The reported experiments demonstrate the superior performance of the proposed model compared to the state-of-the-art approaches.
Comparative experiments are performed in friction stir welding (FSW) of dissimilar Al/Mg alloys with and without assistance of ultrasonic vibration. Metallographic characterization of the welds at transverse cross sections reveals that ultrasonic vibration induces differences in plastic material flow in two conditions. In FSW, the plastic material in the peripheral area of shoulder-affected zone (SAZ) tends to flow downward because of the weakening of the driving force of the shoulder, and a plastic material insulation layer is formed at the SAZ edge. When ultrasonic vibration is exerted, the stirred zone is divided into the inner and outer shear layers, the downward material flow trend of the inner shear layer disappears and tends to flow upward, and the onion-ring structure caused by the swirl motion is avoided in the pin-affected zone. By improving the flow behavior of plastic materials in the stirred zone, ultrasonic vibration reduces the heat generation, accelerates the heat dissipation in nugget zone and changes the thermal cycles, thus inhibiting the formation of intermetallic compound layers.
