Solution of a class of vibration problems by flowgraph methods

A 4-degree-of-freedom single-input system and a 3-degree-of-freedom multi-input system are solved by the Coates', modified Coates' and Chan-Mai flowgraph methods. It is concluded that the Chan-Mai flowgraph method is superior to other flowgraph methods in such cases.

Response of Circular Footings to Vertical Vibrations

In this paper, analog solutions are presented for the response of a circular footing resting on an elastic half-space with uniform and parabolic contact pressure distributions and subjected to frequency dependent and frequency independent excitations. In addition, an analog solution to a rigid circular footing subjected to frequency dependent excitation is also presented. The results have been compared with the rigorous solution of Sung and the agreement is found to be good.

Gust Response of Rotor and Propeller Systems

The influence of nonstationary turbulence on rotor and propeller systems is discussed. The review is made from a common analytical basis of nonstationary approach, with emphasis on concepts rather than on details. The necessity of such an approach and its feasibility for predicting a complete set of gust and response statistics together with correlations with somewhat limited test data are appraised.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Radiation induced depinning of a charge density wave system

The frequency-dependent response of a pinned charge density wave is considered in terms of forced vibration of an oscillator held in an anharmonic well. It is shown that the effective pinning-frequency can be reduced by applying a d.c. field. If a strong a.c. field, superposed on a d.c. field is applied on such a system “jumps” can be observed in the frequency dependent response of the system. The conditions at which these “jumps” occur are investigated with reference to NbSe3. The possibility of observing such phenomena in other systems like superionic conductors, non-linear dielectrics like ferroelectrics is pointed out. The characteristics are expressed in terms of some “scaled variables” — in terms of which the characteristics show a universal behaviour

Effect of the antitumor antibiotic chromomycin A3 on the humoral immune response in rats

Chromomycin A3 (250 mug/kg) suppressed the humoral immune response in rats against sheep erythrocytes when administered 48 h or later after antigenic stimulus. The antibiotic at this dose enhanced immunity when given along with or before antigen administration. The natural heterohemagglutinin levels in rabbits and guinea pigs were not affected by the antibiotic (10 mug/kg per day x 7).

Varied Immune Response to FVIII: Presence of Proteolytic Antibodies Directed to Factor VIII in Different Human Pathologies

The versatility of antibodies is demonstrated by the various functions that they mediate such as neutralization, agglutination, fixation of the complement and its activation, and activation of effector cells. In addition to this plethora of functions, antibodies are capable of expressing enzymatic activity. Antibodies with catalytic function are a result of the productive interplay between the highly evolved machinery of the immune system and the chemical framework used to induce them (antigens). Catalytic antibodies are immunoglobulins with an ability to catalyze the reactions involving the antigen for which they are specific. Catalytic immunoglobulins of the IgM and IgG isotypes have been detected in the serum of healthy donors. In addition, catalytic immunoglobulins of the IgA isotype have been detected in the milk of healthy mothers. Conversely, antigen-specific hydrolytic antibodies have been reported in a number of inflammatory, autoimmune, and neoplastic disorders. The pathophysiological occurrence and relevance of catalytic antibodies remains a debated issue. Through the description of the hydrolysis of coagulation factor VIII as model target antigen, we propose that catalytic antibodies directed to the coagulation factor VIII may play a beneficial or a deleterious role depending on the immuno-inflammatory condition under which they occur.

Vibration of generally orthotropic skew plates

Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free-edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as "crossings" and "quasi-degeneracies" of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.

Vibration of skew plates

The vibration problems of skew plates with different edge conditions involving simple support and clamping have been considered by using the variational method of Ritz, a double series of beam characteristic functions being employed appropriate to the combination of the edge conditions. Natural frequencies and modes of vibration have been obtained for different combinations of side ratio and skew angle. These detailed studies reveal several interesting features concerning the frequency curves and nodal patterns. The results presented should, in addition, be of considerable value and practical significance in design applications.

Waves in branched hydraulic pipes

The paper deals with the classical problem of axi-symmetric transmission of low amplitude waves through a circular pipe containing a viscous liquid. Exact governing equations are identified and solved, the radial as well as the axial component of the velocity being considered. Attention is drawn to certain fallacies underlying the conventional approach. The parameters required in the formulation of the transfer matrix for a pipe have been evaluated. In order to evaluate the response at the terminal point of a branched system for a sinusoidal input at one of the ends, a general algorithm has been developed.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Vibration of Non-Uniform Thin-Walled Beams of Arbitrary Shape

A generalised theory for the natural vibration of non-uniform thin-walled beams of arbitrary cross-sectional geometry is proposed. The governing equations are obtained as four partial, linear integro-differential equations. The corresponding boundary conditions are also obtained in an integro-differential form. The formulation takes into account the effect of longitudinal inertia and shear flexibility. A method of solution is presented. Some numerical illustrations and an exact solution are included.

A rational synthesis of vibration isolators

The paper deals with a rational approach to the development of general design criteria for non-dissipative vibration isolation systems. The study covers straight-through springmass systems as well as branched ones with dynamic absorbers. Various design options, such as the addition of another spring-mass pair, replacement of an existing system by one with more spring-mass pairs for the same space and material requirements, provision of one or more dynamic absorbers for the desired frequency range, etc., are investigated quantitatively by means of an algebraic algorithm which enables one to write down straightaway the velocity ratio and hence transmissibility of a linear dynamical system in terms of the constituent parameters.