Theoretical analyses are presented for free nonlinear vibrations of stiffened rectangular plates with an initial curvature. Clamped boundary conditions with movable or immovable in-plane edges and the initial deflections with single or double curvatures are assumed. The dynamic analog of the Marguerre equations extended to orthotropic stiffened rectangular plates is used and the solutions for fundamental vibration are obtained by applying the Galerkin procedure and the method of succesive approximation. Numerical results illustrate the influence of stiffening parameters, initial deflections, amplitude and in-plane edge conditions on the fundamental frequencies.
A new method is developed to calculate the dynamic response of a finite Bernoulli-Euler beam supporting a moving body. The equations of motion of a beam and a moving body are transformed into a system of Volterra integral equations of the second kind. The functions to be found are boundary values of beam, displacement of moving body and reaction force acting on beam. The system of integral equations is solved numerically by using the product integration method.
Vibrational characteristics are obtained for a rotating ring with equi-spaced elastic supports by using the wave approach. Especially, the variation of the natural frequencies with the rotating speed and the number of elastic supports is investigated. Each elastic support is idealized as a combination of concentrated tangential, rotational and radial stiffnesses acting at the mid-plane of the ring. In the wave approach, state variables at the support A; UA are related to the adjacent support B; UB as UB=eμUA where the complex μ(=μR+iμI) is the so-called propagation constant. The real part (μR) and the imaginary part (μI) of the constant μ are the measures of the rate of decay and the change of phase over the distance between the adjacent supports for travelling wave, respectively. It should be noted that, if the real part: μR is not equal to zero, the travelling wave is attenuated and the energy flow does not exist. The frequency reigions where μR≠0 are called stopping bands while the frequency reigions where μR=0 are called passing bands. And the natural frequency is determinied by the condition that, for the propagation of wave once around the whole ring through N supports, the propagation constant satisfies an equality μN=2πj(j an integer). Numerical results show the effects of rotational speed and the number of elastic supports on the propagation constants which characterize the frequency reigions as either a stopping band or a passing band. And the relation of the natural frequencies with the propagation constants is discussed.
Correlation is discussed between airplane velocities and natural frequencies of short-period and Dutch-roll modes. It is pointed out that those frequencies multiplied by √W/l (W: weight, l: airplane length) are fairly well collected with n/α (ratio of load factor change to angle of attack change) in short-period as well as in Dutch-roll mode. n/α is a parameter strongly correlated with dynamic pressure of the aircraft or the airplane velocity.
A homing missile guided by the proportional navigation guidance law has a target tracker to detect the line-of-sight rate, which is essentially needed for the guidance law. It is well known that there are two types of model uncertainties in this target tracker, and they are apt to decrease the performance of a missile guidance system. In this paper, Popov's hyperstability theory is used to analyze the stability of a guidance system with target tracker model uncertainties. As a result, the relations between the target tracker model uncertainties and the stability of a missile guidance system are shown. Moreover hyperstable minimum range is defined and the relations between the target tracker model uncertainties and the hyperstable minimum range are also given.
Electron energy distribution of the discharge plasma in a cusped ion thruster plays an important role for its discharge chamber performance. Accurate electron energy distribution measurement, particularly in the energy range above the ionization potential, is required to estimate the discharge performance correctly. This Note presents measurement system that is composed of a low-noise detector circuit with a logarithmic amplifier, digital data acquisition and computer system for data analysis. This system enables us to accurately measure the energy distribution even when the measurement is done in noisy environments. The accuracy of the experimental technique and measurement system is discussed. Using the discharge plasma in a cusped thruster, an example demonstrating the measurement system is given.
In many papers for computational aerodynamics, we often find techniques which derive higher-order-accurate finite difference operators through modification of the corresponding lower-order ones. The following two are representative; a) to shift and superpose, b) to make fractional form. This paper presents a discussion concerning the questions; how these modifications should be made? and how these accuracy should be evaluated? These modifications make derivation of higher order operators substantially easier.