On the motion of thin plates and shells subject to Stokes damping

The motion of a homogeneous, thin rigid plate or shell subject to Stokes damping over its entire surface and to any additional system of workless forces, including those that are equipollent to zero, is studied. It is shown that the equation for the single-degree of freedom motion of every thin body having the same mass density per unit area is universal; the result, except for sufficient mathematical smoothness essential to integration over the body, is independent of any other physical features or dimensions of the body. A few examples illustrate the general problem and the universal nature of the equation of motion for thin plates and shells.     

On beams membranes and plates vibration backbone curves in cases of internal resonance

The amplitude — frequency relations of beams, membranes and plates in free vibration with moderately large amplitude are of interest. A two harmonics solution of motion equation and the reciprocal interaction of two modes of vibration are taken into account. The resulting backbone curves with loops, additional branches and bifurcation points are determined and discussed. The physical meaning of the considered curves is also explained.

---

Sommario Si studiano le vibrazioni libere di ampiezza moderatamente grande di travi, membrane e piastre. Si sviluppano soluzioni approssimate con due armoniche delle relative equazioni di moto in due diversi casi di risonanza interna, e si analizza l'effetto dell'interazione di due modi di vibrazione. Vengono determinate e discusse le curve frequenza-ampiezza con l'associata ricchezza di rami addizionali e punti di biforcazione. Il significato fisico di tali curve viene altresì evidenziato.

     

Experiments on damping at contacts of a sphere with flat plates

An apparatus for studying slip damping at rounded contacts for three different systems of forces is described. Experimental results for the constant normal force/varying tangential force problem when a Type 316 stainless-steel sphere is driven between two flat Type 316 stainless-steel plates are presented. They are in fair agreement with theoretical predictions by R. D. Mindlin,et al.     

On the effect of non-smooth Coulomb damping on flutter-type self-excitation in a non-gyroscopic circulatory 2-DoF-system

This article deals with self-excited vibrations, attractivity of stationary solutions, and the corresponding bifurcation behavior of two-dimensional differential inclusions of the type $\mathbf{M}\mathbf{q}'' + \mathbf{D}\mathbf{q}' + (\mathbf{K} + \bar{\mu}\mathbf{N})\mathbf{q} \in-\mathbf{R}\operatorname{Sign}(\mathbf{q}')$ . For the smooth case R=0, the equilibrium may become unstable due to non-conservative positional forces stemming from the circulatory matrix N. This type of instability is usually referred to as flutter instability and the loss of stability is related to a Hopf bifurcation of the steady state, which occurs for a critical parameter $\bar{\mu}= \bar{\mu}_{\mathrm{crit}}$ . For R≠0, the steady state is a set of equilibria, which turns out to be attractive for all values of the bifurcation parameter $\bar{\mu}$ . Depending on $\bar{\mu}$ , the basin of attraction of the equilibrium set can be infinite or finite. The transition from an infinite to a finite basin of attraction occurs at the stability threshold $\bar{\mu}_{\mathrm{crit}}$ of the underlying smooth problem. For the finite basin of attraction, its size is proportional to the Coulomb friction and inverse-proportional to $(\bar{\mu}- \bar{\mu}_{\mathrm{crit}})$ . By adding Coulomb damping the notion of steady state stability for the smooth problem is replaced by the question whether the basin of attraction of the steady state is infinite or finite. Simultaneously, the local Hopf-bifurcation is replaced by a global bifurcation. This implies that in the presence of Coulomb damping the occurrence of self-excited vibrations can only be investigated with regard to the perturbation level.     

Low-frequency dispersion of fundamental waves in anisotropic piezoelectric plates

Low-frequency onset of the fundamental branches in piezoplates is studied with a view to identify the impact of piezoelectric coupling. General analytical expressions for the zero- and leading-order terms of the velocity versus wavenumber expansion in an anisotropic homogeneous piezoplate are obtained. On this ground, it is shown what types of anisotropy and electric boundary conditions enable the onset parameters of fundamental branches to be piezoactive. Particular attention is given to the linear dispersion at the origin of two upper fundamental branches. This property is entirely caused by the piezoeffect, being ruled out for elastic plates. An invariant hierarchy is established between the zero-order velocities of the fundamental waves under different electric boundary conditions in homogeneous and functionally graded plates. It is shown that some of these velocities in a metallized plate become piezoactive specifically if the piezoplate is functionally graded.     

Nonlinear vibrations and damping of fractional viscoelastic rectangular plates

Nonlinear Dynamics - A new model-free robust control scheme for payload swing angle attenuation of two-dimensional crane systems with varying rope length is introduced in this work. The proposed...     

Active damping of vibrations of plates subject to unknown pressure

An approach to the active damping of the forced resonant vibrations of orthotropic thermoviscoelastic plates with distributed sensors and actuators is proposed. The mechanical load is assumed unknown and is determined from the sensors’ indications. The problem of active damping of an isotropic thermoviscoelastic rectangular plate with hinged edges is solved as an example. A formula for the voltage to be applied to the actuator to damp the forced vibrations in the first mode is derived. The effect of the dimensions of the sensor and actuator and the dissipative properties of the materials on the effectiveness of active damping is studied     

Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates

Long-wavelength onset of the fundamental branches is described for a free anisotropic plate with arbitrary through-plate variation of material properties. Main attention is given to the flexural branch. Closed-form expressions for the leading-order dispersion coefficient of the velocity and displacement are derived for a generic case and exemplified for the various types of either continuous, or discrete, or periodic inhomogeneity and for the monoclinic symmetry. The relevance of the static averaging is examined in detail. The bounds for the slope of the flexural velocity branch are established. The upper fundamental branches are considered for the case when these are uncoupled inplane and shear horizontal ones.     

On the critical damping in multi-degree-of-freedom systems

The concept of criticality in viscously damped multi-degree-of-freedom systems is discussed. A necessary and sufficient condition for critical damping is presented. The fundamental physical basis is the same as in Beskos and Boley [ASME J. Appl. Mech. 47 (1980) 627], but numerical convenience is enhanced.     

约束阻尼层合板的稳态响应

基于Reddy分层理论推导出约束阻尼层合板的稳态振动方程,得到了约束阻尼层合板的振动频率和损耗因子;分别分析了约束阻尼层合板的粘弹性夹层厚度、模量对固有频率和损耗因子的影响;得到了稳态振动时振幅和频率曲线以及横向应力与面内应力。数值计算结果表明所采用的算法是可靠的。     

On a new “destabilization” phenomenon: effect of rotary damping

Summary In this note we consider the effect of rotary damping on the instability of Beck's column — almost entirely overlooked in the field of nonconservative problems of elastic stability.

---

Zu einem neuen Destabilisierungs-Phänomen: Der Einfluß von Drehdämpfung

Übersicht Behandelt wird der Einfluß von Drehdämpfung auf die Instabilität des Beckschen Stabes, welche bisher bei der Betrachtung nichtkonservativer Probleme der elastischen Stabilität nahezu vollständig unbeachtet blieb.

     

On the thermodynamics of fractional damping elements

Constitutive models of viscoelasticity in combination with fractional differential operators are successfully used by many authors to describe the mechanical properties of polymers. The topic of the present paper is the investigation of rheological models incorporating fractional damping elements from the point of view of thermodynamics. We take the Clausius Duhem inequality as admissibility criterion and investigate uniaxial and three-dimensional deformation processes at constant temperature. We specify sufficient conditions and show that rheological models, which consist of springs in combination with fractional dashpots, are compatible with the dissipation principle. As a new aspect of the subject, we present a systematic method for deriving the free energy functionals. With the help of two examples we demonstrate that the free energy of fractional systems can be derived as a generalisation of related discrete systems. To illustrate this method, we study in detail an isolated fractional dashpot (also known as a power-law model) and a fractional standard solid (Zener model). Finally, we propose a three-dimensional formulation of the fractional Zener model and specify the corresponding free energy functional. Received: July 3, 1996     

A dispersion force approach to modelling the effect of lift forces on fibre dispersion

Wood fibres suspended in air were studied whilst flowing through a throttle. Measurements of volume fraction and velocity were compared with results from a two-fluid model simulation. Results from earlier work have shown that the lift forces acting on the individual fibres are of importance for the dispersion of volume fraction. Since the orientation of the individual fibres cannot be determined, a dispersion force was utilised to model the dispersing effect of the lift forces. The addition of a lift dispersion model significantly improved the agreement between measurement and model data.     

The effect of damping on the dynamic stability of nonconservative systems

Summary A study of the effect of vanishing viscous damping on the stability of nonconservative linear elastic systems, with special reference to systems that lose stability statically through the emergence of new equilibrium configurations close to the principal one, i. e. by divergence. It is shown that in this case slight damping presents a wide range of effects on the stability of the system.

---

Sommario Si studia l'effetto della presenza di smorzamenti viscosi tendenti a zero sulla stabilità di sistemi elastici lineari soggetti a forze posizionali non conservative, con particolare riguardo a quei sistemi che perdono stabilità staticamente, per la comparsa di nuove configurazioni di equilibrio prossime a quella principale, od anche, come si usa dire, per « divergenza ». Si mostra come in tal caso deboli smorzamenti viscosi presentino un'ampia casistica di effetti sulla stabilità del sistema.

     

On the microdynamics of composite plates

Summary The subject of the contribution is an investigation of elastic composite plates with a microperiodic structure along the plate's midsurface. The computational models of the plates are largely based on the homogenization procedures leading to equations with constant coefficients. However, the homogenization theories neglect the microstructure length-scale effect on the plate's dynamic behaviour. The objective of this research is to formulate and investigate a refined theory of the composite plates under consideration, which would describe the microdynamic plate behaviour caused by the microstructure. The possible applications of the proposed theory are shown by an example.This research was partly supported by KBN, Warsaw, under grant 3 3310 92 03.     

Experimental and numerical investigation on the damping effect of net cages in waves

A series of laboratory experiments were conducted to investigate the damping effect of net cages in waves. The wave transmission coefficient of the net cage was investigated with different wave periods, wave heights, numbers of net cages, net solidities, measurement positions, geometrical shapes of the net cage and Reynolds numbers. The experimental results show that the net cage has noticeable influence on wave propagation and the damping effect of net cages has a close relationship with many parameters. For multiple net cages, the transmission coefficient tends to increase as the wave period increases. The transmission coefficient of net cages decreases with increasing wave height. As the number of net cages increases, the wave transmission coefficient will decrease gradually. The damping effect of net cages on wave propagation tends to increase with increasing net solidity. The measurement position has an effect on the value of wave transmission coefficient. For net cages with different geometrical shapes, the circular net cage has more noticeable damping effect than the square net cage. A numerical model is introduced to simulate the interaction between waves and net cages with the fishing net treated as the porous media fluid model. The wave transmission coefficient downstream from net cages shows good agreement between experimental and numerical results. The study will contribute to understanding of the damping effect of a large fish farm on wave propagation.     

On the elastodynamics of stiffened plates

Summary A method of determining the response of a stiffened elastic plate to a dynamic excitation is presented here. Green's function for such a combined system has been systematically derived based on the eigenfunctions of the system obtained through the application of Galerkin's method. With that Green's function a wide range of dynamic forcing functions can be considered.

---

Zur elastodynamik versteifter platten

Übersicht Vorgestellt wird eine Methode zur Ermittlung der Antwort versteifter Platten auf dynamische Erregungen. Mit Hilfe der Eigenfunktionen des Systems, die durch Anwendung der Galerkin-Methode gewonnen werden, wird die Greensche Funktion solcher kombinierten Tragwerke systematisch hergeleitet. Damit kann ein weiter Bereich dynamischer Anregungsfunktionen behandelt werden.