Active transient elasto-acoustic response damping of a thick-walled liquid-coupled piezolaminated cylindrical vessel

The linear 3D piezoelasticity theory in conjunction with the versatile transfer matrix approach and the wave equation for the internal acoustic domain are employed for active non-stationary vibroacoustic response control of an arbitrarily thick, tri-laminate, fluid-filled, simply supported, piezocomposite cylindrical tank, excited by arbitrary (non-axisymmetric) time-dependent on-surface mechanical loads. The smart structure is composed of a supporting core layer of functionally graded orthotropic material perfectly bonded to inner and outer spatially distributed radially polarized functionally graded piezoceramic sensor and uniform force actuator (FGPM) layers. Active vibration damping is implemented by transferring the accumulated voltage on the sensor layer to the piezoelectric actuator layer in context of proportional and derivative control laws. Durbin's numerical inverse Laplace transform scheme is utilized to calculate the time response histories of the relevant interface displacement/stress components, center-point acoustic pressure, and actuator voltage, for selected loading configurations (i.e., concentrated step, impulse, and moving external loads). Numerical simulations demonstrate the effectiveness of the adopted distributed sensing/actuation configuration together with the active damping control strategy in suppressing the vibroacoustic response of a three-layered (Ba₂NaNb₅O₁₅/Al/PZT4) water-filled piezoelastic cylindrical tank. Limiting cases are considered and the validity of results is established by comparison with the available data as well as with the aid of a commercial finite element package.     

Acoustic scattering characteristics of a thick-walled orthotropic cylindrical shell at oblique incidence

The method of wave function expansion is adopted to study the scattering of a plane harmonic acoustic wave incident at an arbitrary angle upon an arbitrarily thick cylindrically orthotropic homogeneous cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach are employed to present an analytical solution based on the three-dimensional exact equations of anisotropic elasticity. The solution is used to correlate the perturbation in the material elastic constants of an air-filled and water-submerged aluminium cylindrical shell to the sensitivity of resonances associated with various modes of wave propagation appearing in the backscattered amplitude spectrum (i.e., axially guided, Lamb, Rayleigh and Whispering Gallery waves). The effects of shell wall thickness as well as inner fluid loading on the frequency response of the shell are also examined. A limiting case is considered and good agreement with the solution available in the literature is obtained.     

Free vibration analysis of an elliptical plate with eccentric elliptical cut-outs

The elaborated collocation multipole method is employed to obtain a semi-analytical solution, involving proper products of angular and radial Mathieu functions, for the free flexural vibrations of a fully clamped thin elastic plate of elliptical planform containing multiple elliptical cutouts of arbitrary size, location, and orientation. The problem boundary conditions are satisfied by uniformly collocating points on the boundaries, and exactly calculating the normal derivative of plate displacement at the collocation points through use of appropriate directional derivative in each coordinate system. The multipole expansion is truncated to yield a coupled algebraic linear system of equations that is then solved for the nontrivial eigensolutions. Extensive numerical simulations present the first three calculated natural frequencies and the associated deformed mode shapes of an elliptical plate with elliptical/circular cutouts, for a wide range of plate/cutout aspect ratios, and cutout location/orientation parameters. The accuracy of solutions is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data available in the existing literature.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Nonaxisymmetric interaction of a spherical radiator in a fluid-filled permeable borehole

The Biot theory of poroelasticity along with the proper cylindrical/spherical wave-field transformations are used to investigate general (nonaxisymmetric) harmonic radiation from a spherical surface vibrating at the center of a fluid-filled circular cylindrical cavity embedded within a fluid-saturated porous elastic formation. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole, is of practical importance with a multitude of possible applications in seismic engineering and geophysics. The analytical results are illustrated with numerical examples in which the spherical source suspended at the center of a water-filled borehole embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), is excited in vibrational modes of various orders. The basic acoustic and elastic field quantities such as the resistive/reactive components of the modal acoustic radiation impedance load as well as the radial displacement and stress components induced within the surrounding formation for a pulsating (n = 0), an oscillating (n = 1), and a quadrupole-like (n = 2) spherical source are evaluated and discussed for representative values of the parameters characterizing the system. Special attention is paid to the effects of source excitation frequency, size, surface velocity profile, and internal impedance as well as soil type on the modal impedance values and the displacement/stress amplitudes. Limiting cases are considered and fair agreements with well-known solutions are obtained.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

Acoustic wave interaction with a laminated transversely isotropic spherical shell with imperfect bonding

An exact analysis is carried out to study interaction of a time-harmonic plane-progressive sound field with a multi-layered elastic hollow sphere made of spherically isotropic materials with interlaminar bonding imperfections. A modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their spherical harmonics, ultimately leading to calculation of a global transfer matrix. A linear spring model is adopted to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. The solution is first used to correlate the perturbation in the material elastic constants of an evacuated and water submerged steel (isotropic) spherical shell to the sensitivity of resonances appearing in the backscattered amplitude spectrum. The backscattering form function, in addition to the acoustic radiation force acting on selected transversely isotropic spherical shells with distinct degrees of material anisotropy, is subsequently calculated and discussed. An illustrative numerical example is given for a multi-layered hollow sphere with two distinct interlaminar interface conditions (i.e., perfectly and imperfectly bonded layers). Limiting cases are considered and fair agreements with solutions available in the literature are established.