Effect of primary system damping on the optimum design of an untuned viscous dynamic vibration absorber

Explicit criteria for the optimum design of an untuned viscous dynamic vibration absorber are developed for the case of a viscously damped single degree of freedom springmass system. It is shown that for the particular case of an undamped main system, the results reduce to the classical ones obtained by using the concept of a fixed point on the response curve.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

An Explicit Guidance Scheme For A Low-Thrust Terminal Rendezvous

An explicit near-optimal guidance scheme is developed for a terminal rendezvous of a spacecraft with a passive target in circular orbit around the earth. The thrust angle versus time profile for the continuous-thrust, constant-acceleration maneuver is derived, based on the assumption that the components of inertial acceleration due to relative position and velocity are negligible on account of the close proximity between the two spacecraft. The control law is obtained as a ''bilinear tangent law'' and an analytic solution to the state differential equations is obtained by expanding a portion of the integrand as an infinite series in time. A differential corrector method is proposed, to obtain real-time updates to the guidance parameters at regular time intervals. Simulation of the guidance scheme is carried out using the Clohessy-Wiltshire equations of relative motion as well as the inverse-square two-body equations of motion. Results for typical examples are presented.

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.

Bi-criteria single machine scheduling problem with a learning effect: Aneja-Nair method to obtain the set of optimal sequences

In this paper, we consider the bi-criteria single machine scheduling problem of n jobs with a learning effect. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). The objective is to find a sequence that performs well with respect to both the objectives: the total completion time and the total absolute differences in completion times. In an earlier study, a method of solving bi-criteria transportation problem is presented. In this paper, we use the methodology of solvin bi-criteria transportation problem, to our bi-criteria single machine scheduling problem with a learning effect, and obtain the set of optimal sequences,. Numerical examples are presented for illustrating the applicability and ease of understanding.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Stability criteria for single pulse solutions of cw passive mode-locked lasers

The stability of the steady-state solutions of mode-locking of cw lasers by a fast saturable absorber is imvestigated. It is shown that the solutions are stable if the condition (Ps/Pa) = (2/3) (P0Pa) is satisfied, where (Ps/Pa) is the steady-state la ser power, (P0/Pa) is the power at mode-locking threshold, and Pa is the saturated power of the absorber.

Optimum design of a Lanchester damper for a viscously damped single degree of freedom system subjected to inertial excitation

The problem of designing an optimum Lanchester damper for a viscously damped single degree of freedom system subjected to inertial harmonic excitation is investigated. Two criteria are used for optimizing the performance of the damper: (i) minimum motion transmissibility; (ii) minimum force transmissibility. Explicit expressions are developed for determining the absorber parameters.

L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Studies On Hydrogen Bonds: Part IV. Proposed Working Criteria for Assessing Qualitative Strength of Hydrogen Bonds

The data obtained in the earlier parts of this series for the donor and acceptor end parameters of N-H. O and O-H. O hydrogen bonds have been utilised to obtain a qualitative working criterion to classify the hydrogen bonds into three categories: "very good" (VG), "moderately good" (MG) and weak (W). The general distribution curves for all the four parameters are found to be nearly of the Gaussian type. Assuming that the VG hydrogen bonds lie between 0 and ± la, MG hydrogen bonds between ± 1 and ± 2, W hydrogen bonds beyond ± 2 (where is the standard deviation), suitable cut-off limits for classifying the hydrogen bonds in the three categories have been derived. These limits are used to get VG and MG ranges for the four parameters 1 and θ (at the donor end) and ± and ± (at the acceptor end). The qualitative strength of a hydrogen bond is decided by the cumulative application of the criteria to all the four parameters. The criterion has been further applied to some practical examples in conformational studies such as α-helix and can be used for obtaining suitable location of hydrogen atoms to form good hydrogen bonds. An empirical approach to the energy of hydrogen bonds in the three categories has also been presented.

Time-domain criteria for theL_{2}-stability of nonstationary feedback systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

A numerical study of projectile impact on thin aluminium plates

This article deals with a simulation-based Study of the impact of projectiles on thin aluminium plates using LS-DYNA by modelling plates with shell elements and projectiles with solid elements. In order to establish the required modelling criterion in terms of element size for aluminium plates, a convergence Study of residual velocity has been carried Out by varying mesh density in the impact zone. Using the preferred material and meshing criteria arrived at here, extremely good prediction of test residual velocities and ballistic limits given by Gupta et al. (2001) for thin aluminium plates has been obtained. The simulation-based pattern of failure with localized bulging and jagged edge of perforation is similar to the perforation with petalling seen in tests. A number Of simulation-based parametric studies have been carried out and results consistent with published test data have been obtained. Despite the robust correlation achieved against published experimental results, it would be prudent to conduct one's own experiments, for a final correlation via the present modelling procedure and analysis with the explicit LS-DYNTA 970 solver. Hence, a sophisticated ballistic impact testing facility and a high-speed camera have been used to conduct additional tests on grade 1100 aluminium plates of 1 mm thickness with projectiles Of four different nose shapes. Finally, using the developed numerical simulation procedure, an excellent correlation of residual velocity and failure modes with the corresponding test results has been obtained.

Conservative Design Optimization of Laminated Composite Structures Using Genetic Algorithms and Multiple Failure Criteria

This article analyzes the effect of devising a new failure envelope by the combination of the most commonly used failure criteria for the composite laminates, on the design of composite structures. The failure criteria considered for the study are maximum stress and Tsai-Wu criteria. In addition to these popular phenomenological-based failure criteria, a micromechanics-based failure criterion called failure mechanism-based failure criterion is also considered. The failure envelopes obtained by these failure criteria are superimposed over one another and a new failure envelope is constructed based on the lowest absolute values of the strengths predicted by these failure criteria. Thus, the new failure envelope so obtained is named as most conservative failure envelope. A minimum weight design of composite laminates is performed using genetic algorithms. In addition to this, the effect of stacking sequence on the minimum weight of the laminate is also studied. Results are compared for the different failure envelopes and the conservative design is evaluated, with respect to the designs obtained by using only one failure criteria. The design approach is recommended for structures where composites are the key load-carrying members such as helicopter rotor blades.

A non-orthogonal cooperative multiple access (NCMA) protocol and low ML decoding complexity codes

A half-duplex constrained non-orthogonal cooperative multiple access (NCMA) protocol suitable for transmission of information from N users to a single destination in a wireless fading channel is proposed. Transmission in this protocol comprises of a broadcast phase and a cooperation phase. In the broadcast phase, each user takes turn broadcasting its data to all other users and the destination in an orthogonal fashion in time. In the cooperation phase, each user transmits a linear function of what it received from all other users as well as its own data. In contrast to the orthogonal extension of cooperative relay protocols to the cooperative multiple access channels wherein at any point of time, only one user is considered as a source and all the other users behave as relays and do not transmit their own data, the NCMA protocol relaxes the orthogonality built into the protocols and hence allows for a more spectrally efficient usage of resources. Code design criteria for achieving full diversity of N in the NCMA protocol is derived using pair wise error probability (PEP) analysis and it is shown that this can be achieved with a minimum total time duration of 2N - 1 channel uses. Explicit construction of full diversity codes is then provided for arbitrary number of users. Since the Maximum Likelihood decoding complexity grows exponentially with the number of users, the notion of g-group decodable codes is introduced for our setup and a set of necesary and sufficient conditions is also obtained.

Scale-up criteria of square tank surface aerator

Oxygen transfer rate and the corresponding power requirement to operate the rotor are vital for design and scale-up of surface aerators. Present study develops simulation or scale-up criterion correlating the oxygen transsimulation fer coefficient and power number along with a parameter governing theoretical power per unit volume (X, which is defined as equal to (FR1/3)-R-4/3, where F and R are impellers' Fronde and Reynolds number, respectively). Based on such scale-up criteria, design considerations are developed to save energy requirements while designing square tank surface aerators. It has been demonstrated that energy can be saved substantially if the aeration tanks are run at relatively higher input powers. It is also demonstrated that smaller sized tanks are more energy conservative and economical when compared to big sized tanks, while aerating the same volume of water, and at the same time by maintaining a constant input power in all the tanks irrespective of their size. An example illustrating how energy can be reduced while designing different sized aerators is given. The results presented have a wide application in biotechnology and bioengineering areas with a particular emphasis on the design of appropriate surface aeration systems.