We study a third-order partial differential equation in the form τuttt +αutt −cuxx −buxxt = 0, (1) that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures. In contrast with the current literature on the subject, we show that when the critical parameter γ := α − τc2 b is negative, the e...

Acoustic vibrations in tissue are often difficult to image, requiring high-speed scanning, high sensitivity and nanometer-scale axial resolution. Here we use spectrally encoded interferometry to measure the vibration pattern of two-dimensional surfaces, including the skin of a volunteer, at nanometric resolution, without the need for rapid lateral scanning and with no prior knowledge of the dri...

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to si...

The purpose of this mini-review is to outline diversity of chest wall vibrations, specify biomechanical peculiarities and point out a few problems crucial for development of diagnostic and therapeutic applications of chest wall vibrations. The review considers two types of chest wall vibrations: spontaneous, induced by breathing, and forced (or artificial), induced by external vibration forces....

A three-dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates. Suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations, which are then solved by employing the power series me...

The study of nonlinear vibrations/oscillations in mechanical and electronic systems has always been an important research area. While important progress in the development of mathematical chaos theory has been made for finite dimensional second order nonlinear ODEs arising from nonlinear springs and electronic circuits, the state of understanding of chaotic vibrations for analogous infinite dim...

In this paper, the flexural free vibrations of three dimensional micro beams are investigated based on strain gradient theory. The most general form of the strain gradient theory which contains five higher-order material constants has been applied to the micro beam to take the small-scale effects into account. Having considered the Euler-Bernoulli beam model, governing equations of motion are w...

<p style='text-indent:20px;'>A classical stability criterion for Hill's equation is extended to more general families of periodic two-dimensional linear systems. The results are motivated by the study mechanical vibrations with friction and prey-predator systems.</p>

We consider the von Kármán nonlinearity and the Casimir force to first develop a reduced-order model for a prestressed clamped elliptic electrostatically actuated microplate, and then use it to study vibrations and pull-in instability. The reduced-order model is derived by taking a family of linearly independent kinematically admissible functions as basis functions for the transverse displaceme...

The thickness stretch vibrations of piezoelectric ceramic plates are analyzed by solving the first-order Mindlin plate equations with finite element method in the twodimensional domain. The precise resonance frequency and distribution of displacements are obtained from the analysis in detail. The results based on the two-dimensional solutions are more important particularly in the evaluation of...