Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases, The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Theoretical and Experimental Investigation of Flexural Vibration Transfer Properties of High-Pressure Periodic Pipe

According to the theory of phononic crystals, the hydraulic pipeline is designed to be a periodic structure composed of steel pipes and hoses to suppress the vibration of the hydraulic system with band gaps. We present theoretical and experimental investigations into the flexural vibration transfer properties of a high-pressure periodic pipe with the force on the inner pipe wall by oii pressure taken into consideration. The results show that the vibration attenuation of periodic pipe decreases along with the elevation of working pressure for the hydraulic system, and the band gaps in low frequency ranges move towards high frequency ranges. The periodic pipe has good vibration attenuation performance in the frequency range below 1000 Hz and the vibration of the hydraulic system is effectively suppressed. A11 the results are validated by experiment. The experimental results show a good agreement with the numerical calculations, thus the flexural vibration transfer properties of the high- pressure periodic pipe can be precisely calculated by taking the fluid structure interaction between the pipe and oil into consideration. This study provides an effective way for the vibration control of the hydraulic system.

Analysis of the flexural vibration of ship's tail shaft by transfer matrix method

A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock absorption for a ship's tail shaft.A mathematic model of tail shaft flexural vibrations was built using the transfer matrix method.The nature frequency of flexural vibration for an electrically propelled ship's tail shaft was then analyzed,and an effective method for calculating it was proposed:a genetic algorithm(GA),which calculates the nature frequency of vibration of a system.Sample calculations,with comparisons by the Prohl method under conditions bearing isotropic support,showed this method to be practical.It should have significant impact on engineering design theory.

Effects of ramp vibrational states on flexural intrinsic vibrations inBesocke-style scanners

For both the vibrating and steady supporting surfaces of a scanning disk in a Besocke-style piezoelectric scanner, a theoretical model is given by considering the nonlinear lateral friction at the micro-contact interface between the positioning legs and the supporting surface. Numerical simulations demonstrate that unexpected flexural vibrations can arise from a vibrating ramp, and their frequencies are lower than the eigenfrequencies of the scanner in the linearly elastic regime. The vibrations essentially depend on 1） the vibrational states of the supporting ramp and the steel ball tips on the three piezo- electric positioning legs, and 2） the tribological characteristics of the contacts between the tips and the ramp. The results give an insight into the intrinsic vibrations of the scanners, and are applicable in designing and optimizing piezoelectric scanning systems.

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners with nanometer resolution are studied by using an electro-mechanical coupling Timoshenko beam model. Meanwhile, the effects of friction, the first moment, and moment of inertia induced by mass loads are considered. The predicted resonance frequencies of the ceramic tubes are sensitive to not only the mechanical parameters of the scanners, but also the friction acting on the attached shaking ball and corresponding bending moment on the tubes. The theoretical results are in excellent agreement with the related experimental measurements. This model and corresponding results are applicable for optimizing the structures and performances of the scanners.

Modeling and solving for transverse vibration of gear with variational thickness

A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and fiexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.

Stability and vibration of a helical rod with circular cross section in a viscous medium

The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.

Principle and Experimental Verification of Novel Dual Driving Face Rotary Ultrasonic Motor

Existing rotary ultrasonic motors operating in extreme environments cannot meet the requirements of good environmental adaptability and compact structure at same time,and existing ultrasonic motors with Langevin transducers show better environmental adaptability,but size of these motors are usually big due to the radial arrangement of the Langevin transducers.A novel dual driving face rotary ultrasonic motor is proposed,and its working principle is experimentally verified.The working principle of the novel ultrasonic motor is firstly proposed.The 5th in-plane flexural vibration travelling wave,excited by the Langevin transducers around the stator ring,is used to drive the rotors.Then the finite element method is used in the determination of dimensions of the prototype motor,and the confirmation of its working principle.After that,a laser Doppler vibrometer system is used for measuring the resonance frequency and vibration amplitude of the stator.At last,output characteristics of the prototype motor are measured,environmental adaptability is tested and performance for driving a metal ball is also investigated.At room temperature and 200 V(zero to peak) driving voltage,the motor’s no-load speed is 80 r/min,the stalling torque is 0.35 N·m and the maximum output power is 0.85 W.The response time of this motor is 0.96 ms at the room temperature,and it decreases or increases little in cold environment.A metal ball driven by the motor can rotate at 210 r/min with the driving voltage 300 V(zero to peak).Results indicate that the prototype motor has a large output torque and good environmental adaptability.A rotary ultrasonic motor owning compact structure and good environmental adaptability is proposed,and lays the foundations of ultrasonic motors’ applications in extreme environments.

The vibroacoustic response and sound absorption performance of multilayer, microperforated rib-stiffened plates

The vibroacoustic response and sound absorption performance of a structure composed of multilayer plates and one rigid back wall are theoretically analyzed. In this structure, all plates are two-dimensional, microperforated, and periodically rib-stiffened. To investigate such a structural system, semianalytical models of one-layer and multilayer plate structures considering the vibration effects are first developed. Then approaches of the space harmonic method and Fourier transforms are applied to a one-layer plate, and finally the cascade connection method is utilized for a multilayer plate structure. Based on fundamental acoustic formulas, the vibroacoustic responses of microperforated stiffened plates are expressed as functions of a series of harmonic amplitudes of plate displacement, which are then solved by employing the numerical truncation method. Applying the inverse Fourier transform, wave propagation, and linear addition properties, the equations of the sound pressures and absorption coefficients for the one-layer and multilayer stiffened plates in physical space are finally derived. Using numerical examples, the effects of the most important physical parameters-for example, the perforation ratio of the plate, sound incident angles, and periodical rib spacing-on sound absorption performance are examined. Numerical results indicate that the sound absorption performance of the studied structure is effectively enhanced by the flexural vibration of the plate in water. Finally, the proposed approaches are validated by comparing the results of stiffened plates of the present work with solutions from previous studies.

Modal Control of Cantilever Beam Using a Gyrostabilizer

In this paper,an experimental model of a horizontal cantilever beam with a rotating/oscillating attached to the shaker for harmonic excitation at the one end and a gyrostabilizer at the other end is built to verify the equations of the Lagrangian model.The primary focus of the study was to investigate the parameters of excitation amplitude,natural frequency,rotating mass(disk mass),and disk speed of gyro that would minimize the amplitude of the beam to identify these effects.Numerical and experimental results indicate that the angular momentum of the gyrostabilizer is the most effective parameter in the reduction of beam displacement.

Study on rectangular ultrasonic radiator of flexural resonant vibration in high modes

Based on the theory of coupling vibration and flexural vibration of thin rod of rectangular cross section, the flexural vibration of rectangular thin plate was studied. The frequency equation was derived under the condition of free boundaries. The normal modes and the relation between the normal modes and the resonant frequency were obtained. Experiments showed that the calculated resonant frequencies agree well with the measured results, and the rectangular thin plate in flexural vibration has abundant resonant frequencies. The radiator of flexural vibration used in ultrasonic cleaning and other techniques has the advantages of large acoustic radiating area, uniform acoustic field and easy adjustment of resonant frequencies, proving that it is a promising ultrasonic source.

AN ACCURATE TWO-DIMENSIONAL THEORY OF VIBRATIONS OF ISOTROPIC,ELASTIC PLATES

An infinite system of two-dimensional equations of motion of isotropic elastic plates with edge and corner conditions are deduced from the three-dimensional equations of elasticity by expansion of displacements in a series of trigonometrical functions and a linear function of the thickness coordinate of the plate. The linear term in the expansion is to accommodate the in-plane displacements induced by the rotation of the plate normal in low-frequency flexural motions. A system of first-order equations of flexural motions and accompanying boundary conditions are extracted from the infinite system. It is shown that the present system of equations is equivalent to the Mindlin＇s first-order equations, and the dispersion relation of straight-crested waves of the present theory is identical to that of the Mindlin＇s without introducing any corrections. Reduction of present equations and boundary conditions to those of classical plate theories of flexural motions is also presented.