Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method

The free vibration of orthotropic rectangular thin plates with four free edges on two-parameter elastic foundations is studied by the symplectic superposition method. Firstly, by analyzing the boundary conditions, the original vibration problem is converted into two sub-vibration problems of the plates slidingly clamped at two opposite edges. Based on slidingly clamped at two opposite edges, the fundamental solutions of these two sub-vibration problems are respectively derived by the separation variable method of the corresponding Hamiltonian system, and then the symplectic superposition solution of the original vibration problem is obtained by superimposing the fundamental solutions of the two sub-problems. Finally, the symplectic superposition solution obtained in this study is verified by calculating the frequencies and mode functions of several concrete rectangular thin plates with four free edges.

Analytical solutions of citrate–phosphate coupled model of rice (Oryza sativa L.) roots

The citrate secreted by the rice (Oryza sativa L.) roots will promote the absorption of phosphate, and this process is described by the Kirk model. In our work, the Kirk model is divided into citrate sub-model and phosphate sub-model. In the citrate sub-model, we obtain the analytical solution of citrate with the Laplace transform, inverse Laplace transform and convolution theorem. The citrate solution is substituted into the phosphate sub-model, and the analytical solution of phosphate is obtained by the separation variable method. The existence of the solutions can be proved by the comparison test, the Weierstrass M-test and the Abel discriminating method.

Electromechanical impact analysis of 2–2 cement-based piezoelectric sensor considering resistor

The model of the 2–2 type cement-based piezoelectric sensor, which is connected with a resistor while under the impact mechanical load, is established in this article. The dynamic theoretical expressions are acquired by utilizing the separation variable method and the matrix coefficient method and then used to analyze and discuss the electrical properties and the influence of the resistance value, which is verified correctly by numerical analysis. Also, the effect of resistor value and different material parameters on dynamic properties of such sensor is further investigated. And a reverse voltage is proposed to balance the displacement of the free-end and the stress of the fixed-end to enhance the safety. At last, the acoustic impedance ratio associated with the compatibility of the composite is discussed. The conclusions discussed in this work could provide some theoretical references for optimizing the design of the 2–2 cement-based piezoelectric sensor connected to electrical components in practical application.

Vehicle weight identification for a bridge with multi-T-girders based on load transverse distribution coefficient

It is still an issue to identify the vehicle weight for bridges with multi-T-girders which is essential in bridge operation management. In this study, a vehicle weight identification method is proposed for bridges with multi-T-girders. To consider the load transverse distribution effect, first the separation variable method is adopted to separate the spatial influence surface function of vehicle load into the product of two single-valued functions. Then the procedures of the vehicle weight identification method are proposed using the measured strain responses of the T-girders caused by the passing vehicle accordingly. A numerical example of a bridge with five T-girders and an experimental example of a bridge with two T-girders are conducted to verify the feasibility and effectiveness of the proposed method. Furthermore, the performance of the proposed method is compared with the typical existing method in which the load transverse distribution effect is not considered.

A Damage Mechanics Based Cohesive Zone Model with Damage Gradient Extension for Creep-Fatigue-Interaction

In this paper a novel Cohesive Zone Model (CZM) is derived within the framework of continuum thermodynamics to describe cracking and delamination behaviour of coatings at high-temperatures. The separation variable in the Traction-Separation-Law (TSL) is decomposed into elastic and inelastic part. For evolution of inelastic separation, a power-law in combination with a damage evolution law is used to consider the tertiary stage of inelastic separation of the interface, additionally. Thereby, damage evolution is related to the corresponding thermodynamic driving force and the inelastic opening rate. For reasons of simplicity the resulting thermo-mechanical problem only considers heat conduction through the interface. Due to the fact that standard Newton-Raphson procedure gets unstable (e.g. snap-back) when softening occurs which is the case by using a CZM, this model is enhanced with the damage gradient, similar to approaches in phase field modelling. Further on, this extension is done to investigate if it is possible to overcome the size dependence of CZMs. Finally, the model is reduced to pure Mode I opening and an example for a Double Cantilever Beam (DCB) is analysed by the finite difference method.

Study for Dynamic Stability Behavior of I-Section Cantilever Beam under Axis Compressive Load

By mean of the energy functional variational principle and considering shear lag effect of flange, the dynamic governing differential equation for the I-section cantilever beam in the action of compressive loadPat the member end is obtained. The equation is solved by the separation variable method. According to the weigh residual method, the relation between natural frequency coefficient and critical load coefficient as well as the flutter critical load coefficient are made, the influence of shear lag effect on natural frequency coefficient and critical load coefficient is discussed.