Non-harmonic resonance of viscoelastic structures subjected to time-dependent exponentially decreasing transverse distributed loads

In this paper,the non-harmonic resonance of Bernoulli viscoelastic beams,Kirchhoff viscoelastic plates,Timoshenko viscoelastic beams,and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing transverse distributed load is investigated for the first time.The constitutive equations are expressed utilizing Boltzmann integral law with a constant bulk modulus.The displacement vector is approximated by employing the separation of variables method.The Laplace transformation is used to transfer equations from the time domain to the Laplace domain and vice versa.The novel point of the proposed method is to express,prove and calculate the critical time in which the displacement will be several times the displacement at time zero.In addition,this new method calculates the maximum deflection at the critical time,explicitly and exactly,without any need to follow the time-displacement curve with a low computational cost.Additionally,the proposed method introduces the critical range of time so that the responses are greater than the responses at time zero.

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.

Optimal deployment schedule of an active twist rotor for performance enhancement and vibration reduction in high-speed flights

The best active twist schedules exploiting various waveform types are sought taking advantage of the global search algorithm for the reduction of hub vibration and/or power required of a rotor in high-speed conditions. The active twist schedules include two non-harmonic inputs formed based on segmented step functions as well as the simple harmonic waveform input. An advanced Particle Swarm assisted Genetic Algorithm（PSGA） is employed for the optimizer. A rotorcraft Computational Structural Dynamics（CSD） code CAMRAD II is used to perform the rotor aeromechanics analysis. A Computation Fluid Dynamics（CFD） code is coupled with CSD for verification and some physical insights. The PSGA optimization results are verified against the parameter sweep study performed using the harmonic actuation. The optimum twist schedules according to the performance and/or vibration reduction strategy are obtained and their optimization gains are compared between the actuation cases. A two-phase non-harmonic actuation schedule demonstrates the best outcome in decreasing the power required while a four-phase non-harmonic schedule results in the best vibration reduction as well as the simultaneous reductions in the power required and vibration. The mechanism of reduction to the performance gains is identified illustrating the section airloads, angle-of-attack distribution, and elastic twist deformation predicted by the present approaches.

Numerical Comparison of the LOOCV-MFS and the MS-CTMfor 2D Equations

The method of fundamental solutions(MFS)and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations.Despite many attractive features of these two methods,they also experience different aspects of difficulty.Recent advances in the selection of source location of theMFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent.In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.