Vibration and Acoustic Radiation from Orthogonally Stiffened Infinite Circular Cylindrical Shells in Water

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic shells with ribs, by means of the Fourier integral transformation and the Fourier inverse transformation, as well as the stationary phase method, an analytic solution, which has satisfying computational effectiveness and precision, is derived for the solution to the vibration and acoustic radiation from a submerged stiffened infinite circular cylinder with both ring and axial ribs. It is easy to analyze the effect of stiffening supports in the acoustic radiation field by use of the formulas obtained by the presented method and corresponding numerical computation. It is shown that the axial-stiffeners can improve the mechanical and acoustical characteristics. Moreover, the present method can be used to study the acoustic radiation mechanism of the type of structure.

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface,in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell,by means of expanding field quantities as Legendre series,a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate,which has a satisfactory computational effectiveness and precision for an arbitrary frequency range.It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed.It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell,and give the coupling system a very rich resonance frequency spectrum.Moreover,the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.

Vibration and Acoustic Radiation from Submerged Spherical Double-Shell

Based on the motion differential equations of vibration and acoustic coupling system for a thin elastic spherical double-shell with several elastic plates attached to the shells, in which Dirac-δ functions are employed to introduce the forces and moments applied by the attachments, and by means of expanding field quantities as the Legendre series, a semi-analytic solution is derived for the solution to the vibration and acoustic radiation from a submerged spherical double-shell. This solution has a satisfying computational effectiveness and precision for arbitrary frequency range excitation. It is concluded that the internal plates attached to shells can change significantly the mechanical and acoustical characteristics of shells, and make the coupling system have a very rich resonance frequency spectrum. Moreover, the present method can be used to study the acoustic radiation mechanism of the type of structure.

Acoustic and Vibration Environment Prediction Technology of Instrument Cabin Based on Multi-Source Data

Noise characteristic is one of the important factors to be considered during the design of a launch vehicle system.In this paper,the acceptance conditions for the external noise environment of the instrument cabin are given based on multi-source data,including the measured data of the launch vehicle lift-off noise,the mechanical environment of the launch vehicle equipment,and the external noise environment of the instrument cabin deduced from empirical formula.Then an acoustic and vibration transfer model is established based on the response data of the instrument equipment used to conduct measurements in the noise test reverberation room.By using an external noise environment and a transfer model,the response of the instrument and equipment for the acceptance condition can be obtained.The acoustic and vibration prediction technology introduced in this paper can provide technical support in the environmental prediction analysis of heavy launch vehicles for the future.

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.

A new model for film bulk acoustic wave resonators

Based on cavity resonance and sandwich composite plate （3D） theoretical model for frequency dispersion characterization theory, this paper presents a universal three-dimensional and displacement profile shapes of the film bulk acoustic resonator （FBARs）. This model provides results of FBAR excited thickness-extensional and flexure modes, and the result of frequency dispersion is proposed in which the thicknesses and impedance of the electrodes and the piezoelectric material are taken into consideration; its further simplification shows good agreement with the modified Butterworth-Van-Dyke （MBVD） model. The displacement profile reflects the vibration stress distribution of electrode shapes and the lateral resonance effect, which depends on the axis ratio of the electrode shapes a/b. The results are consistent with the 3D finite element method modeling and laser interferometry measurement in general.

Fast Calculation of Electromagnetic Forces in IPMSMs Under PWM VSI Supply Based on Small-Signal Time-Harmonic Finite Element Method

This paper introduces a novel method for fast calculating the electromagnetic forces in interior permanent magnet synchronous machines(IPMSMs)under pulse width modulation(PWM)voltage source inverter(VSI)supply based on the small-signal time-harmonic finite element analysis(THFEA),which has been successfully utilized for fast calculating the PWMinduced losses in silicon steel sheets and permanent magnets.Based on the small-signal THFEA,the functional relationships between high-frequency harmonic voltages(HFHVs)and corresponding airgap flux densities are established,which are used for calculating the flux density spectra caused by each HFHV in the PWM voltage spectra.Then,the superposition principle is applied for calculating the flux density spectra caused by fundamental currents and all HFHVs,which are converted to the electromagnetic force spectra at last.The relative errors between the force density spectra calculated with the proposed method and those obtained from traditional time-stepping finite element analysis(TSFEA)using PWM voltages as input are within 3.1%,while the proposed method is 24 times faster than the traditional TSFEA.

FINITE ELEMENT APPROXIMATION OF EIGENVALUE PROBLEM FOR A COUPLED VIBRATION BETWEEN ACOUSTIC FIELD AND PLATE

We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babugka and Osborn. Some numerical example is shown for the problem for which the exact analytical solutions are calculated. The results shows that the convergence order is consistent with the one by the numerical analysis.

Calculation of vibrational energy transition rates in acoustic relaxation processes for excitable gas molecules

To research the correlation between vibrational energy transition rates and acoustic relaxation processes in excitable gases, the vibrational relaxation theory provided by Tanczos [J. Chem. Phy3. 25, 439 （1956）] is applied to calculate the energy transition rates of Vibrational- Vibrational （V-V） and Vibrational-Translational （V-T） energy transfer in gas mixtures. The results of calculation for the multi-relaxation processes in various gas mixtures, consisting of carbon dioxide, methane, chlorine, nitrogen, and oxygen at room temperature, demonstrate that the acoustic energy stagnated in every vibrational mode is coupled with each other through V-V energy exchanges. The vibrational excitation energy will relax through the V-T de-excitation path of the lowest mode because of its fastest V-T transition rate, resulting in that only one absorption peak can be measured for most of excitable gas mixtures. Thus, an effective model is provided to analyze how the vibrational energy transition rates affect the characteristics of acoustic relaxation processes and acoustic propagation in excitable gas mixtures.

Effects of installations on the low frequency vibration response of specimens in acoustic fatigue tests

The low frequency vibration response of a specimen in acoustic fatigue tests depends not only on the dynamic characteristics and the boundary conditions of the specimen itself, but also on the test unit which couples the specimen to a given sound field. Further, the latter can even be dominant instead the former in some circumstances. This fact is shown in the paper by using the experimental results and the theoretical analysis of the acoustic-induced vibration of a boundary clamped rectangular thin plate. In analysing the systems of acoustic fatigue test, an approach of electro-mechano-acoustical analogous circuit is used. The application of the approach can give an estimation of the effects on the low frequency vibration modes of various parameters in a system quantitatively. This supplies a theoretical basis and a means for the rational layout of acoustic fatigue tests.

A leakage particle-wall impingement based vibro-acoustic characterization of the leaked sand-gas pipe flow

Solid particle leakage detection in double-wall pipes is industrially important,especially in chemical and petroleum engineering.Here,we developed vibration and acoustic sensor approaches for the characterization and comparative study of the applicability of leakage sand particle detection from the flow of gas pipes.A specific wideband vibration sensor and pressure-field microphone were selected to identify the vibro-acoustic characteristics within 50 kHz of the particle leakage.The vibro-acoustic time-behaviours and characteristic frequencies of particle leakage were observed by the time-frequency method.The leakage gas flow noise was verified by coherence analysis and minimized by a digital bandpass and band-elimination filter.Corresponding experiments were performed,and good agreement was found between the release pressures(0.1-0.3 MPa)with different leak sizes(0-8 mm)under different sand masses(120μm)and vibro-acoustic Root-Mean-Square(RMS)levels.In the comparison of the two methods,the vibration method has a better frequency response for the leakage flow and is good for identifying whether there are particle leaks.The acoustic method has a time behaviour response and is good for establishing the relationship between the particle mass and signals.In addition,the acoustic method has frequency shift features with a better signal to noise ratio.The acoustic method lays the foundation for future work of more complex leakage detection combining the advantages of vibration and the acoustic method.

Local characteristics and acoustical energy of radiation on vibrating surface: Ⅰ. Theory

From a point of view of the auto-spectrum, the local characteristics and the acous-tical energy of radiating on a vibrating surface are theoretically studied in this paper. The point radiation impedance at any point on a vibrating surface is defined a-s the ratio of the sound pressure to the vibrating velocity, which establishes the relation between the vibration of the surface and the sound field. Applying the Cauchy iategral theorem, the chromatic disper-sion relation between the real and imaginary components of the point radiation impedance is given, and some characteristics are discussed. The discussion about two typical sound sotirces,pulsating and oscillating spheres, supports the arguments of this paper.

Local characteristics and acoustical energy of radiation on vibrating surface: Ⅱ. application

Applying the theory put forward in Ref. [3], the radiation mechanism of sound energy on a vibrating steel plate was studied. Between the point radiation resistance efficiency and the point radiation reactance efficiency exists the chromatic dispersion relation that is one to one. The chromatic dispersion relation fits not only smooth curves, but also the dispersed curves with sharp-pointed peaks. While the vibrating surface radiates the sound energy into field, it absorbs some energy from the field.