Attenuation of stress waves in single and multi-layered structures

Analytical and experimental studies were made of the attenuation of the stress waves during passage through single and multilayer structures. The investigation included studies on elastic and plastic stress wave propagation in the composites and those on shock mitigating material characteristics such as dynamic stress-strain relations and energy absorbing properties. The results of the studies are applied to methods for reducing the stresses imposed on a spacecraft during planetary or ocean landings

Acoustics of the piezo-electric pressure probe

Acoustical properties of a piezoelectric device are reported for measuring the pressure in the plasma flow from an MPD arc. A description and analysis of the acoustical behavior in a piezoelectric probe is presented for impedance matching and damping. The experimental results are presented in a set of oscillographic records

An Experimental and Theoretical Investigation fo Axially Symmetric Wave Propagation In Thick Cylindrical Waveguides

Solid circular cylinders as wavaguides for the propagation of longitudinal elastic waves are used pximarily as buffer rods in high temperature nondestructive evaluation (NDE), and are also found in the split Hopkinson pressure bar (SHPB). Experiments are typically designed so that only the nondispersive range of the first mode propagates. Design constraints sometimes require larger wavcguides and higher ficquencies that propagate multiple dispersive modes, which can add considerable con1plexity to the signal. This thesis presents an analytical modcl for multiple mode wave propagation in a finite solid cylindrical waveguide as a means of interpreting the complex signals and possibly removing the complexity. The model uses the phase velocities and normal stresses of the axially symmetric modes calculated by the Pochhammer-Chree equations to calculate atransfer hnction for each of the propagating modes. The sum of the tranxfcr functions of the propag:,ting modes is the transfer function of the waveguide, which can be used to predict the change of a signal in the waveguide. The ability of the model to accurately capture the general physics of multiple mode wave propagation is demonstrated in the time, frequency and joint time-frequency domain. In the time-reverral domain the calculated dispersed signal for a dispersive multi-mode waveguide is shown to producc a s i p a l with compact support in the time domain. A range of diameter to wavelength ratios is considered for these comparisons, which show the limitations of the model for wavelengths less than th.e raditls. The transfer functions generated by the model indicate which modes are dominant over a particular range of frequencies and which modes have a much smaller magnitude. The transfer functions further indicate that broadband signals are composed of multiple modes. It is found that observed trailing pulses contain energy from multiple propagating modes, and it is the superposition of the modes that creates the trailing pulses. The information from the transfer functions is also used to show the conditions for a sufficiently narrow band signal to excite a single higher order mode with little dispersion

Numerical Computations of Radial Vibrations of Axially Polarized Piezoelectric Circular Cylinder

Influence of the initial stresses on the frequency equation and the natural frequencies for radial vibrations of axially polarized piezoelectric circular cylinder have been taken into account. The mechanical boundary conditions correspond to those of stress free lateral surfaces while the electrical boundary conditions correspond to those of open and short circuit are considered. The satisfaction of the boundary conditions lead to the frequency equation, in the form of determinant involving Bessel functions, have been taken into consideration. The roots of the frequency equations give the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots are numerically computed and programmed for numerical evaluation by ''Bisection Method Iterations Technique (BMIT)'' and presented graphically for various thickness of the circular cylinder and for different values of the initial stress. The effect of the initial stress on the natural frequencies are illustrated graphically for a transversely isotropic piezoelectric martial PZT?4 circular cylinder. It is found that both the thickness of the circular cylinder and the initial stress have a substantial effect on the dispersion behavior. The results obtained in this paper may be applied to the vibrations of annular accelerometers operating in the radial shear mode. Also, they have theoretical basis application and have meaningful design for piezoelectric probes and electro-acoustic devices in the nondestructive evaluation. Keywords: Piezoelectricity, frequency equation, Transverse surface waves, Initial stress, Hexagonal crystals

Vibration frequencies of whirling rods and rotating annuli

Static Whirling Rods: Past researchers suggested that “static instabilities” exist at certain rotational speeds of whirling rods. This thesis shows these instabilities are an artefact of the material constitutive laws that are being used well outside their range of applicability. An alternative approach is developed where strains due to rotation are separated from the superimposed vibration. This enables the generally predicted lowering of longitudinal natural frequencies with rotational speed shown to be simply a result of the bulk changes in the geometry of whirling rods. Steady state equations of whirling rods are formulated in Lagrangian coordinates. Due to the non-linear nature of the governing equations, an original numerical method is applied to solve the problem. Numerical results are compared with analytical results obtained from the linearized uniaxial model. There is a close agreement between these two models at low angular velocities. However, at high angular velocities, discrepancies between them arise, confirming that the nonlinear strain-displacement relationship has significant effect on the results and the inferred “static instabilities”. This approach first solves the “static” problem of the deformed geometry of a highly strained whirling rod before longitudinal natural modes are determined by classical methods. Furthermore, conditions for existence and uniqueness of solutions are derived. Dynamic Rotating Annuli: In-plane modes of vibration of annular plates are investigated. Two different models of equations one from Bhuta and Jones and the other from Biezeno and Grammel that govern the rotational motions of annuli will be studied. Since Biezeno and Grammel’s model was originally derived in Eulrian coordinates, their model will be transformed to the Lagrangian coordinates for the purpose of comparison with Bhuta and Jones’ model.The solutions of the equations assume small oscillations of vibration being superimposed on the steady state of the annulus while it is in rotation. Exact and approximate solutions are obtained for the Bhuta and Jones’ model, where the approximate solutions on in-plane displacements and natural frequencies are acquired by ignoring the Coriolis effect. A proposed numerical scheme is implemented to solve the governing equations coupled with radial and circumferential displacements. Uniqueness of solutions will be mentioned although it will not be rigorously derived because it is out of the scope of this thesis. Approximate analytical results show that both radial and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing. The exact and numerical results on both models that take the Coriolis effect into account show that radial natural frequencies are increasing and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing

Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process

We rederive the equations of motion for relativistic strings, that is, one-dimensional elastic bodies whose internal energy depends only on their stretching, and use them to study circular string loops rotating in the equatorial plane of flat and black hole spacetimes. We start by obtaining the conditions for equilibrium, and find that: (i) if the string's longitudinal speed of sound does not exceed the speed of light then its radius when rotating in Minkowski's spacetime is always larger than its radius when at rest; (ii) in Minkowski's spacetime, equilibria are linearly stable for rotation speeds below a certain threshold, higher than the string's longitudinal speed of sound, and linearly unstable for some rotation speeds above it; (iii) equilibria are always linearly unstable in Schwarzschild's spacetime. Moreover, we study interactions of a rotating string loop with a Kerr black hole, namely in the context of the weak cosmic censorship conjecture and the Penrose process. We find that: (i) elastic string loops that satisfy the null energy condition cannot overspin extremal black holes; (ii) elastic string loops that satisfy the dominant energy condition cannot increase the maximum efficiency of the usual particle Penrose process; (iii) if the dominant energy condition (but not the weak energy condition) is violated then the efficiency can be increased. This last result hints at the interesting possibility that the dominant energy condition may underlie the well known upper bounds for the efficiencies of energy extraction processes (including, for example, superradiance).Comment: 32 pages, 6 figures; v2: minor improvements; v3: small changes, matches final published version; v4: typos in the references fixe

The numerical solution of certain problems in elastodynamics

The method of integral transforms can provide the solution of a differential equation satisfying prescribed boundary conditions if certain requirements involving the boundary conditions and the transforms are met. The three requirements are stated explicitly in the thesis for the differential equation L gamma = f on a finite domain R, where L is a matrix and gamma and f are columns. In general not all the requirements can be satisfied for the equations of elasticity. If one particular requirement is relaxed, then the transform procedure may be applied in such a way as to reproduce in R a formal series solution of the above differential equation without reference to the boundary conditions, and the solution is a general solution in that sense. When the solution is applied to a particular set of boundary conditions there results an infinite system of simultaneous linear equations in an infinite number of unknowns, whose solution yields a solution of the differential equation. The infinite system is given formally in chapter I for the equations of elasticity. Theoretical results pertaining to the solution of infinite systems of equations and approximate methods of solution are known, and chapter II is devoted to a statement and a discussion of those results which are relevant to the problems of the thesis. A deficiency in the existing theory is noted. The application of the above approach to the solution of some specific vibration problems in elastodynamics is given in chapters and IV, A study of the vibrating elastic parallelepiped with clamped edges provides an indication of the rate of convergence of the approximate numerical solution for different dimensions, and allows some conclusions to be drawn about the value of the method as a practical numerical procedure. The numerical results are compared with those obtained by another method due to V.V. Bolotin. The approximate solution of the infinite system of equations is justified in terms of the theory in chapter II. Two problems of the axially symmetric vibrations of elastic rods are investigated in chapter IV. The first rod has all its bounding surfaces stress-free, while the second rod has one of its plane ends clamped and the remaining- surfaces stress-free. Numerical results are presented for both problems. Those for the first case are compared with existing theoretical and experimental values, and they are shown to be the most accurate yet available. No other results for the second problem have been found in the literature. The infinite system of equations is studied in both cases, the conclusions being less satisfactory than for the parallelepiped, as certain questions remain unanswered. In chapter V consider an initial-value problem in which a stress pulse is suddenly applied to one end of an elastic rod. The solution is expressed as an infinite sum over the solutions for the free- free rod, using the method of eigenfunction expansions. The motion of the free end of the rod is computed using the finite set of eigenfunctions in Chapter IV, and the resulting solution is sufficiently accurate to show the successive reflections of the initial pulse as it traverses the rod. Some aspects of the solution are discussed by comparing it with the solution of the analogous problem for an infinite slab

Identification and analysis of factors affecting thermal shock resistance of ceramic materials in solar receivers

An analysis was conducted of the possible modes of thermal stress failure of brittle ceramics for potential use in point-focussing solar receivers. The pertinent materials properties which control thermal stress resistance were identified for conditions of steady-state and transient heat flow, convective and radiative heat transfer, thermal buckling and thermal fatigue as well as catastrophic crack propagation. Selection rules for materials with optimum thermal stress resistance for a particular thermal environment were identified. Recommendations for materials for particular components were made. The general requirements for a thermal shock testing program quantitatively meaningful for point-focussing solar receivers were outlined. Recommendations for follow-on theoretical analyses were made