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Cantilever plate structures are widely used in civil and aerospace engineering. Here, a semi-analytical method is proposed to calculate the dynamic responses of cantilever plates subjected to moving forces. The Rayleigh–Ritz method is used to obtain the semi-analytical modal frequencies and shapes of a thin, isotropic, and rectangular cantilever plate using the assumed mode shapes that fulfill the boundary conditions of the plate. The modal superposition method is used to decouple the motion equations of the cantilever plate to obtain a series of modal equations. Then, the generalized forces are transformed into a Fourier series in terms of discrete harmonic forces. The dynamic responses of the cantilever plate are obtained by superimposing the analytical responses of a number of single-degree-of-freedom modal systems under discrete harmonic forces. The proposed semi-analytical method is verified through comparison with the numerical method. Then, the vibration of the cantilever plate under the action of moving forces is investigated based on the semi-analytical results. It is found that the contribution of the high-order modes to the dynamic responses of the plate cannot be ignored. In addition, the wavelengths of the mode shapes not only affect the magnitude of the modal forces but also the dominant frequency of the modal forces. Resonant responses of the plate are produced by the moving forces when the load interval equals the wavelength of the mode shape of a high-order mode and the exciting frequency of the moving forces equals the natural frequency of this mode.

In this study, the nonlinear vibration control of functionally graded laminated piezoelectric cylindrical shells under simultaneous parametric axial and radial external excitations is presented. The partial differential equations of shells are derived based on Hamilton’s principle, first-order shear deformation theory (FSDT), and nonlinear von Karman relations. The coupled nonlinear ordinary differential equations are obtained by Galerkin’s procedure and solved by the method of static condensation. Two piezoelectric layers are placed on the outer and inner surfaces of the cylindrical shell each as distributed sensor and actuator. Then the constant-gain negative velocity feedback strategy is employed. Regarding the nonlinear equations of motion, for the first time, the vibration analysis and active vibration control of smart FG cylindrical shells under combined parametric and external excitations are analyzed using the multiple scales approach. The effects of various parameters such as power index, external excitation’s amplitude, and control gain on the dynamic behavior of the system are investigated, using bifurcation diagrams, phase portraits, time histories, and Poincare maps. It is shown that quasi-periodic motion is the most common behavior of the system and controller gain and power index have inevitable effects on enhancing the quasi-periodic response of the system. Care should be exerted in selecting the parameters to have the desired response in the broad range of excitation frequency.

This paper proposes a three-dimensional dynamic model for high-speed railway trains moving over curved bridges considering the transition curves, circular curves, and superelevation. Key features of this study are to consider the nonlinear geometrical relationships and creep relationships between the wheels and rail, for which the interactive iterative numerical algorithms are developed based on the equations of vertical displacement and rolling of wheelset, and the torsional resonance conditions of the vehicle–bridge system are verified. The results show that the torsional vibration will cause amplification on vertical dynamic response of the beam on the outside edge of the curve. The deficient/surplus superelevation plays an important role in the lateral and torsional angular displacements of the bridge, and the peak of the torsional resonance response can be reduced by adjusting the practical superelevation of the curve. The variations of wheel–load reduction rate and derailment coefficient in the curve section are positively correlated to the deficient/surplus superelevation. The curve radius is the key factor affecting the wear and fatigue of wheel–rail, and when the curve radius is greater than 7000 m, the wear and fatigue can be significantly reduced. Running at a deficient superelevation level can also reduce the wear and fatigue.

A vibration control signal sensing method is proposed utilizing the grid electrode displacement sensitive effect of field-effect transistors. The signal sensing method is applied to nonlinear resonance delay control of a nanobeam that is used as the core component of nano–microdevices. The nonlinear vibration dynamical model of the nanobeam based on the field-effect tube sensing is established and the differential equation of motion with time delay control is presented. The amplitude frequency response equation and phase frequency response equation of the nanobeam are obtained by analyzing the first-order approximate solution of the primary and superharmonic vibration of the nonlinear equation with multi-scale method. The vibration feedback gain and time delay can affect the vibration amplitude and nonlinear behavior of the nanobeam. The nonlinear vibration of the nanobeam can be adjusted and effectively controlled by selecting appropriate feedback gains and time delays.

Dynamic vehicle–bridge interaction (VBI) plays a crucial role in the train-induced vibrations of a railway bridge for its coupling effects may reduce the bridge response and down-shift the resonant speed. The commonly used nominal theoretical resonant speed ($=f_{b}D)$ of a typical railway bridge, however, is only related to the bridge frequency ($f_b)$ and car length ($D)$, but it neglects the VBI effects of the moving trains. Such a shifted resonance phenomenon would become significant for a bridge under two trains passing by each other. This study develops a method using an equivalent modal mass to be added onto the bridge to account for the frequency shift due to the presence of multiple train cars for estimation of the shifted resonant speed. The numerical study demonstrates that the proposed method can predict the shifted resonant speed and explain the shifted-resonance phenomenon of railway bridges under train passages.

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed ($v_{\mathrm{\text{br}}}$) of the bridge, from which we can determine the sub-resonance speed as ($v_{\mathrm{\text{br}}}∕n{|}_{n=2,3}$). The primary resonance speed of a short bridge is generally much higher than the operation speeds of current high-speed trains but the corresponding sub-resonance speeds probably lie in the operation speed range. Such a resonance scenario can be observed from the vibration of a double-track bridge subjected to an eccentrically moving train, in which the deck vibration is combined by the vertical-flexural and torsional vibration modes of the bridge. Once the two modal sub-resonance speeds coincide with each other, a double sub-resonance will be developed on the bridge. In this study, an iteration-based train–bridge interaction finite element procedure will be presented to demonstrate the double resonance phenomenon. As expected, the double resonance may bring about a dramatic amplification on deck vibration. Such an excessive vibration is harmful to ballast stability and track maintenance of railway bridges.

In this paper, the internal and external cancellation phenomena for damped beams subjected to multi-moving loads are investigated in detail. To start, the theory for the vibration of a simply supported beam is revisited by including the effect of damping. For the first time, a simple expression is derived for the free vibration of the damped beam under multi-moving loads. Based on the concept of local minimum, two cancellation conditions are identified. One is the internal cancellation, which relates to the inherent property of the beam and is conventionally known. The other is the newly formulated external cancellation that relates to the number and spacing of moving loads. For comparison, both the resonant condition and the optimal criterion for span length of the bridge are also briefed. By comparing with the classical solution, the present simple expression for the free vibration of the beam is firstly validated. Then the factors affecting the cancellation are investigated against various load cases and damping levels. The results show that external cancellation occurs more frequently due to the increase in the number and spacing of the moving loads. The damping of the beam has a leaking effect on cancellation, in that nonzero vibration may occur, but it is also quickly damped out by damping itself.

The advent of railways and especially highspeed railways marks great strides in human transportation history. To guarantee exclusive right-of-way, highspeed railways are often built on equal simply supported beams resting on piers. In this paper, a historical review will be given of the resonance and cancellation phenomena observed for simply supported beams traveled by a set of moving loads, as they are typical of highspeed railways. The phenomenon of resonance was observed by early investigators including Timoshenko, Bolotin, Frýba, Matsuura, etc. However, the phenomenon of cancellation was noted lately in 1997 by Yang et al. By letting the conditions of resonance and cancellation coincident, they proposed the optimal span length for suppressing the resonance of simple beams, which is equal to 1.5 times the car length. This 1.5 times rule has been verified and adopted in the design of some highspeed railways. In this article, the theoretical solution for the problem will be revisited for unveiling the key parameters such as the resonance speed (in temporal domain) and resonance wavelength (in spatial domain). Then a rather in-depth review will be given of existing works on the resonance and cancellation of railway bridges from the waves perspective. Some new developments along these lines will also be identified.

The dynamic characteristics, deformation and installation accuracy of the bridge structure will have a greater impact on the response of maglev system. This study performs the dynamic analysis of a flexible long-span continuous rigid frame bridge induced by high-speed maglev train. To achieve this, the spatial coupling analysis model is first established. Then, the influence of track irregularities and speed on the maglev system is analyzed. In addition, the mechanism of vertical resonance of the bridge and vehicle under the action of harmonic loads at low speed is also studied by a semi-analytical approach. The results show that the influence of the long-span bridge deformation on car-body vertical acceleration is greater than that of track irregularity. The resonance exists between train and the long-span bridge at low speed. When the frequency of the harmonic loads is consistent with the basic frequency of the bridge, it will cause the bridge resonance. The resonant speed range of the rigid car-body is 20–40km/h. During bridge design, it shall be avoided that the basic frequency of the bridge is consistent with that of the vehicle.

The paper deals with the problem of obtaining a given dynamic behavior of simply supported bridge beams from the impact of rolling stock. Resonant vibrations of beams become a reality at high speeds if the train is formed of identical cars, which is typical for passenger trains. The phenomenon of suppression of beam vibrations by a train, known from publications, is possible only with an exact ratio of the length of the car and the beam. This significantly reduces the possibilities of choosing the necessary spans of beams. Consideration of issues of interaction in the “bridge–track—train” system for security purposes requires the involvement of a rather complex mathematical apparatus and appropriate software. The paper proposes a new method for determining the specified dynamic behavior of bridge beams, suitable for any spans and available to engineers at the stage of pre-design assignment of dynamic parameters of beams. The requirements that are necessary and sufficient conditions for preventing the resonance of bridge beams on the HSR are determined. At the same time, it does not require the involvement of software based on a complex mathematical technique.

We examine the effect of adding a sinusoidal signal to a system of coupled noisy nonlinear oscillators. When the frequency of this "probe" signal is close to the frequency of the unprobed system we observe a resonance behavior, enabling us to determine the underlying frequency of the noisy system. Furthermore, in the prototype SQUID system we consider here, we find that the frequency of the underlying solution decreases with increasing coupling strength. Combining this finding with the resonance phenomenon we discuss ways to enhance the sensitive of SQUIDs to weak low frequency signals.

The paper discusses a combined effect of periodic and random perturbations on the onset of hysteresis in a generic two-state system. The interplay of both noises is investigated pointing out variations in signal tuning to the external driving force and their influence on the area and shape of the hysteresis. As an extension to former studies relating dynamic hysteresis to stochastic resonance and synchronization of passages in a double well system, in the present work the effect of the field asymmetry on the response of the system is analyzed.

This paper presents a new on-line technique for denoising impulsive vibration signals in noisy environments using Wavelet Packets. The proposed algorithm is based on localizing the frequency subbands of the resonances embedded in impulsive vibration signals. The performance of the algorithm is evaluated in denoising real vibration signals measured from faulty bearings. The results compared to the theoretical values and those obtained by the HFD algorithm show the effectiveness of the proposed algorithm while the computational cost reduces to half.

We give algorithms for the asymptotic expansions of the almost sure and moment Lyapunov exponents associated with the two-dimensional stochastic differential equation obtained as a small perturbation of the deterministic rotation with rate ω. The matrices in the perturbation terms are all assumed to be periodic functions of time with period l. The form of the algorithms depends on whether or not the periods 2π/ω and l of the unperturbed system and the perturbation coefficients are commensurable (i.e. the ratio of the periods is rational). In the commensurable case certain resonances may cause jumps in the Lyapunov exponents. We give an example of a stochastically perturbed Hill's oscillator which is almost surely stable when 2ω is not an integer, but is almost surely unstable at resonant frequencies ω = m/2. This work extends recent results of Imkeller and Milstein.

The pressure gain distribution along the ear canal is strongly dependent on boundary conditions, and, in normal conditions, the ear canal produces a 0–20-dB pressure gain close to the tympanic membrane in the 0.1–20kHz range. Additionally, the pressure gain distribution along the ear canal at high frequencies (over the second resonance of the ear canal at 8–9kHz) depends strongly on axis position; therefore, the middle ear transfer functions based on ear canal pressure are also strongly dependent on the measuring point.

Objective: The aim of this study is to evaluate the mechanical influence of the tympanic cavity, ossicular chain and tympanic membrane connections on the pressure in the ear canal in the frequency range of 0.1–20kHz when a pressure source is applied to the ear canal entrance.

Methods: We have developed numerical simulations for seven different models using the finite element method (FEM). Starting with an external ear canal finite element model, additional elements are coupled or removed to evaluate their contributions. We modeled and simulated the tympanic membrane, ossicular chain, tympanic cavity and a simplified cochlea in seven different combinations.

Results: The pressure distribution along the external ear canal is obtained and represented in the 0.1–20kHz range for the seven model configurations.

We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian, 2 < p < ∞ ((p, 2)-equation) and with a reaction which exhibits asymmetric behavior at +∞ and at -∞ and is resonant. Using variational methods together with Morse theoretic arguments, we prove the existence of two and three nontrivial solutions.

We are concerned with a class of nonlinear Schrödinger-type equations with a reaction term and a differential operator that involves a variable exponent. By using related variational methods, we establish several existence results.

An ab initio spin-free valence bond code called Xiamen-99 has been developed based on an efficient algorithm called paired-permanent-determinant approach, where Hamiltonian and overlap matrix elements are expressed in terms of paired-permanent-determinants. With this tool, we probed the electronic delocalization phenomenon in a few typical examples including benzene, formamide and ethane. Our computations revealed that ab initio valence bond methods are able to estimate the energetic contribution from the delocalization effect to the stabilization of molecules, thus pave the way to illuminate the resonance theory at the quantitative level. In particular, we analyzed the cyclic electronic delocalization in benzene and showed that different understandings on the resonance may originate from the different usage of one-electron orbitals in the valence bond theory. Our investigation into the hyperconjugative interaction in ethane demonstrated that the hyperconjugation effect is not the dominating factor in the preference of the staggered conformer of ethane.

A theoretical framework is developed based on the premise that brains evolved into sufficiently complex adaptive systems capable of instantiating genomic consciousness through self-awareness and complex interactions that recognize qualitatively the controlling factors of biological processes. Furthermore, our hypothesis assumes that the collective interactions in neurons yield macroergic effects, which can produce sufficiently strong electric energy fields for electronic excitations to take place on the surface of endogenous structures via alpha-helical integral proteins as electro-solitons. Specifically the process of radiative relaxation of the electro-solitons allows for the transfer of energy via interactions with deoxyribonucleic acid (DNA) molecules to induce conformational changes in DNA molecules producing an ultra weak non-thermal spontaneous emission of coherent biophotons through a quantum effect. The instantiation of coherent biophotons confined in spaces of DNA molecules guides the biophoton field to be instantaneously conducted along the axonal and neuronal arbors and in-between neurons and throughout the cerebral cortex (cortico-thalamic system) and subcortical areas (e.g., midbrain and hindbrain). Thus providing an informational character of the electric coherence of the brain — referred to as quantum coherence. The biophoton field is realized as a conscious field upon the re-absorption of biophotons by exciplex states of DNA molecules. Such quantum phenomenon brings about self-awareness and enables objectivity to have access to subjectivity in the unconscious. As such, subjective experiences can be recalled to consciousness as subjective conscious experiences or qualia through co-operative interactions between exciplex states of DNA molecules and biophotons leading to metabolic activity and energy transfer across proteins as a result of protein-ligand binding during protein-protein communication. The biophoton field as a conscious field is attributable to the resultant effect of specifying qualia from the metabolic energy field that is transported in macromolecular proteins throughout specific networks of neurons that are constantly transforming into more stable associable representations as molecular solitons. The metastability of subjective experiences based on resonant dynamics occurs when bottom-up patterns of neocortical excitatory activity are matched with top-down expectations as adaptive dynamic pressures. These dynamics of on-going activity patterns influenced by the environment and selected as the preferred subjective experience in terms of a functional field through functional interactions and biological laws are realized as subjectivity and actualized through functional integration as qualia. It is concluded that interactionism and not information processing is the key in understanding how consciousness bridges the explanatory gap between subjective experiences and their neural correlates in the transcendental brain.

To read the signals of single molecules in vitro on a surface, or inside a living cell or organ, we introduce a coaxial atom tip (coat) and a coaxial atomic patch clamp (COAPAP). The metal-insulator-metal cavity of these probes extends to the atomic scale (0.1nm), it eliminates the cellular or environmental noise with a S/N ratio 10⁵. Five ac signals are simultaneously applied during a measurement by COAT and COAPAP to shield a true signal under environmental noise in five unique ways. The electromagnetic drive in the triaxial atomic tips is specifically designed to sense anharmonic vibrational and transmission signals for any system between 0.1nm and 50nm where the smallest nanopatch clamp cannot reach. COAT and COAPAP reliably pick up the atomic scale vibrations under the extreme noise of a living cell. Each protein’s distinct electromagnetic, mechanical, electrical and ionic vibrational signature studied in vitro in a protected environment is found to match with the ones studied inside a live neuron. Thus, we could confirm that by using our probe blindly we could hold on to a single molecule or its complex in the invisible domain of a living cell. Our decade long investigations on perfecting the tools to measure bio-resonance of all forms and simultaneously in all frequency domains are summarized. It shows that the ratio of emission to absorption resonance frequencies of a biomaterial is around $\pi$, only a few in the entire em spectrum are active that regulates all other resonances, like mechanical, ionic, etc.