Response of plates with unconstrained layer damping treatment to random acoustic excitation,part II: Response evaluation

Theoretical and experimental investigations on the response of a plate with unconstrained layer damping treatment to random acoustic excitation have been carried out. The theoretical response evaluation consisted of determining the power spectral density of the acceleration response of the layered plate by the use of generalized harmonic analysis under a specific random acoustic excitation, with use being made of modal frequencies and associated loss factors estimated as described in Part I. A study was made on the contribution of cross coupling terms of the acceleration response for the two boundary conditions investigated: namely, all edges simply supported and all edges clamped. In the experimental investigation, plates with different damping layer thicknesses were subjected to high intensity random acoustic excitation generated by an exponential horn driven by an electropneumatic transducer. The acceleration responses were recorded and later analyzed to yield the power spectral densities. Experimental and theoretical results are compared.     

Response of unconstrained layer panels to random excitation at a point

The acceleration response of unconstrained layer rectangular panels under random point force excitation has been investigated theoretically and experimentally. In the theory the layer material was assumed to be viscoelastic in nature. Generalized harmonic analysis was used to evaluate the power spectral density and the rms values of acceleration response analytically. The theoretical results are compared with the results obtained from experiments for “all edges simply supported” and “all edges clamped” panel boundary conditions.     

Vibration and damping analysis of annular plates with constrained damping layer treatments

The natural frequencies and modal loss factors of annular plates with fully and partially constrained damping treatments are considered. The equations of free vibration of the plate including the transverse shear effects are derived by a discrete layer annular finite element method. The extensional and shear moduli of the viscoelastic material layer are described by the complex quantities. Complex eigenvalues are then found numerically, and from these, both frequencies and loss factors are extracted. The effects of viscoelastic layer stiffness and thickness, constraining layer stiffness and thickness, and treatment size on natural frequencies and modal loss factors are presented. Numerical results also show that the longer constrained damping treatment in radial length does not always provide better damping than the shorter ones.     

Dynamic response of composite plates with cut-outs,part I: Simply-supported plates

The effect of square cut-outs on the natural frequencies of square, simply-supported composite plates is investigated. The forced and free dynamic response of plates with cut-outs is formulated. Laminations are assumed to be symmetric about the mid-plane and the plates are considered analytically as homogeneous anisotropic plates. In the method of solution it is assumed that the effect of the cut-out is equivalent to an external loading on the plate. For free vibration, the method leads to an infinite system of frequency equations. Depending upon the accuracy required, a suitable size of the system of frequency equations is selected. Results are given for square, simply-supported composite plates with centrally located square cut-outs for different modulus ratios. A comparison of results obtained from this method for isotropic plates with cut-outs with available literature is made and excellent agreement is obtained.     

Dynamic response of composite plates with cut-outs,part II: Clamped-clamped plates

The forced and free dynamic response of plates with cut-outs formulated in Part I [1] is used to investigate the effect of cut-outs on the natural frequencies of clamped-clamped plates. The size, shape and location of the cut-out is expressed as a displacement dependent external loading. The plates considered are homogeneous and anisotropic. Lagrange's equations of motion lead to an infinite system of differential equations in time-dependent generalized co-ordinates with generalized forces which include the effects of the cut-outs. There is an infinite system of frequency equations for free vibrations. The infinite system is truncated to a finite system of equations depending upon the accuracy desired in frequency values. Results are given for square, clamped-clamped plates with centrally located square cut-outs for different modulus ratios. Good agreement is obtained when results for isotropic plates with cut-outs are compared with available theoretical and experimental results.     

A solvable model of microscopic frequency modulation: I. Conventional treatment of the damping operator

A solvable model of quantum-statistical mechanical frequency modulation is proposed and is solved for the cases of boson and two-state irrelevant subsystems to obtain the intensity distribution for a certain operator of the relevant subsystem. The damping theoretical approach, which is based on the time-independent projection operator method, to the model is also investigated.     

Time and frequency response of structures with frequency dependent,non-proportional linear damping

A method to compute the non-stationary time and frequency response of structures with a frequency-dependent non-proportional linear damping, called the resonance modes method, is presented in this paper. It consists of two main steps. The first step aims at spotting the structure resonance modes, which are the solutions of the matrix nonlinear eigenvalue problem obtained using the finite element method in the complex plane. This step requires a complex eigensolver and an iterative scheme, a perturbation technique or a combination of both. The second step uses the computed resonance modes and an analytical expression of the inverse Laplace transform to deduce the time or frequency response of structures to general excitations. The response of an aluminum plate damped with an elastomer treatment to a point-force excitation, computed with the classical modal approach, the direct solution and the presented method shows its precision and efficiency. An acoustic power computation finally validates the implementation of a fast variant, based on the perturbation technique, for vibroacoustic applications.     

Dynamic response of doubly curved honeycomb sandwich panels to random acoustic excitation. Part 1: Experimental study

A set of four doubly curved, composite honeycomb sandwich panels has been tested with broad band, random acoustic excitation in a progressive wave tube facility. This paper presents the experimental results in the form of dynamic face plate strain measurements taken from various points close to the centre of the panels, on both the inner and outer face plates. The panels were tested at overall sound pressure levels up to (ref. , over a frequency bandwidth of 60-). The response was found to be linear, with a maximum measured root mean square strain of 250με. The doubly curved geometry was found to have a profound effect on the ratio of inner-to-outer face plate strain, which was compared with ratios reported for flat and singly curved geometries. The second part of this study concentrates on three methods for predicting the response of the doubly curved panels to random acoustic excitation.     

Dynamic response of doubly curved honeycomb sandwich panels to random acoustic excitation. Part 2: Theoretical study

In this paper a single-degree-of-freedom model is developed to predict the dynamic response of an acoustially excited doubly curved sandwich panel. Three variants of the model are investigated, based on differing assumptions regarding the spatial distribution of the applied loading. When the loading is assumed to be uniform then the model reduces to the Miles approach, and when the loading is assumed to conform to the structural mode shape then the method is very similar to the Blevins approach. The third variant involves a more detailed consideration of the travelling wave characteristics of the applied loading, and this is found to give much improved agreement with experimental results obtained in a progressive wave tube facility. In addition, an approach using the finite element method is presented in which the response to grazing incidence excitation is computed, and this is also found to yield good agreement with the experimental results.     

Acoustoelasticity: General theory,acoustic natural modes and forced response to sinusoidal excitation,including comparisons with experiment

A comprehensive theoretical model has been developed for interior sound fields which are created by flexible wall motion resulting from exterior sound fields. Full coupling between the wall and interior acoustic cavity is permitted. An efficient computational method is used to determine acoustic natural frequencies of multiply connected cavities. Simplified formulae are developed for interior sound levels in terms of cavity, wall and external acoustic field parameters. Comparisons of theory and experiment show generally good agreement.     

Use of lagrange multipliers with polynomial series for dynamic analysis of constrained plates part I: Polynomial series

A theory for prediction of the dynamic response of a constrained plate is presented here. The boundaries of the plate may be partially fixed, its dynamic loading is due to elastically mounted vibrating machines and its constraints include beam-like stiffeners. The theory yields the eigenvalues and modal shapes of the plate and stiffeners which comprise the system. The solution, given in Part I, is based on Galerkin's method combined with use of special polynomial series presented by Kantorovich and Krylov. These eigenvalues are used in Part II [1] for response analysis of the complete system and the eigenvalues of the complete system will be obtained by the application of Lagrange equations and multipliers. The various coefficients used in the process are presented in the Appendices to the work. Comparisons with published results show good agreement.     

Multiple-order derivatives of a waveguide acoustic field with respect to sound speed, density, and frequency

An adjoint perturbative method is used to derive expressions for the first- through third-order derivatives of a pressure field with respect to sound speed, density, and frequency, for the restricted case of a laterally homogenous waveguide in which environmental parameters are only a function of depth. By using a normal-mode Green's function, the three-dimensional spatial correlation required by the standard acoustic adjoint equation can be reduced to a set of one-dimensional depth integrals. The resulting expressions for the first-order derivative are similar to those obtained by previous perturbative approaches based on the depth-separated wave equation, but the approach followed here permits straightforward extension to higher-order derivatives. Explicit evaluations of the expressions for a representative shallow-water waveguide model are in excellent agreement with numerical finite-difference computations. An analysis of the expressions as a function of source-receiver range finds the contributions to the mode amplitude derivatives to be non-negligible at ranges less than a few modal interference lengths, for parameters associated with the ocean bottom. Therefore, linear perturbative inversion methods that perturb only horizontal wavenumbers and not mode amplitudes should either be used with caution or modified to incorporate the expressions presented here.     

Contributions of suppression and excitation to simultaneous masking: effects of signal frequency and masker-signal frequency relation

This study investigated the contributions of suppression and excitation to simultaneous masking for a range of masker frequencies both below and above three different signal frequencies (750, 2000, and 4850 Hz). A two-stage experiment was employed. In stage I, the level of each off-frequency simultaneous masker necessary to mask a signal at 10 or 30 dB sensation level was determined. In stage II, three different forward-masking conditions were tested: (1) an on-frequency condition, in which the signals in stage I were used to mask probes of the same frequency; (2) an off-frequency condition, in which the off-frequency maskers (at the levels determined in stage I) were used to mask the probes; and (3) a combined condition, in which the on- and off-frequency maskers were combined to mask the probes. If the off-frequency maskers simultaneously masked the signal via spread of excitation in stage I, then the off-frequency and combined maskers should produce considerable forward masking in stage II. If, on the other hand, they masked via suppression, they should produce little or no forward masking. The contribution of suppression was found to increase with increasing signal frequency; it was absent at 750 Hz, but dominant at 4850 Hz. These results have implications for excitation pattern analyses and are consistent with stronger nonlinear processing at high rather than at low frequencies.     

Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability

This paper initiates the theoretical analysis of microscale resonators containing internal flow, modelled here as microfabricated pipes conveying fluid, and investigates the effects of flow velocity on damping, stability, and frequency shift. The analysis is conducted within the context of classical continuum mechanics, and the effects of structural dissipation (including thermoelastic damping in hollow beams), boundary conditions, geometry, and flow velocity on vibrations are discussed. A scaling analysis suggests that slender elastomeric micropipes are susceptible to instability by divergence (buckling) and flutter at relatively low flow velocities of ∼10 m/s.     

Statistics of a random plus constant vector with application to acoustic and electromagnetic-wave scattering

A two-dimensional random-walk problem is investigated, where a vector fixed in amplitude (magnitude) is added to one that is random in phase (direction angle). This problem can arise from a study of the effect of multipath interference from an acoustic or electromagnetic-wave source, where an arrival of constant amplitude is combined with an incoherent background of randomly scattered components of the incident field. The source is considered to have harmonic time dependence. This study follows from an earlier paper, in which the required properties of the incoherent background were derived. In the present study, the joint distribution of the resultant amplitude and of the phase angle between the resultant and the fixed arrival is determined. Further, expressions are developed for the first and second moments of the resultant phase, amplitude, decibel-amplitude, and intensity. Many properties of these moments are described.This work was supported in part by Acoustic Programs, US Office of Naval Research and in part by the Electric Boat Division of General Dynamics.     

On the prediction of impact noise,part VI: Distribution of acceleration noise with frequency with application to bottle impacts

The spectral distribution of the acceleration noise, as defined in Part I of this series, is obtained using both the pressure waveform expressions and the spatial averaged velocity on the surface of the body, together with a radiation efficiency associated with the rigid body movement of the object. This distribution with frequency is shown to be mainly dependent on the size of the body and the duration of the transient and is independent of the body shape detail and the exact shape of the transient. The spectral distribution of acceleration noise is important in the case of impact of structures whose first ringing natural frequency is within the frequency range under investigation. Under such circumstances, it is important to estimate the response of the structure below this resonant frequency. In this paper this is investigated to show that the response, and hence the noise radiated from a structure below the first ringing frequency, is low and the noise in this frequency range is mostly due to acceleration noise. These results are verified in the case of bottle clashes.     

Dynamic and acoustic response of bidirectionally stiffened plates with eccentric stiffeners subject to airborne and structure-borne excitations

An analytical method based on the modal expansion technique was developed to predict the vibro-acoustic response of both unidirectionally and bidirectionally stiffened flat panel. This paper presents the response to diffuse acoustic field (DAF) and turbulent boundary layer (TBL) excitations in terms of their joint acceptance. Numerical results for the dynamic and acoustic responses are compared with finite element method (FEM) and boundary element (BEM) results for stiffened panel with complex and eccentrically shaped stiffeners subject to point force excitation. A theoretical prediction of the transmission loss (TL) is also compared with laboratory measurements conducted on flat panels representing aircraft models as well as with hybrid statistical energy analysis (SEA)-FEM periodic model. The results confirm that the stiffened panel has the same acoustic response as the skin without stiffeners at frequencies where the structural wavelengths are equal to the spacing between the stiffeners. In addition, the transmission loss is lowered by the presence of the stiffeners at some particular region of frequencies below the critical frequency with respect to the unstiffened panel.