Although there have been numerous efforts into harnessing the snap through dynamics of bistable structures with piezoelectric transducers to achieve large energy conversion, these same dynamics are undesirable under morphing applications where stationary control of the structure’s configuration is paramount. To suppress cross-well vibrations that primarily result from periodic excitation at low frequencies, a novel control strategy is proposed and implemented on the piezoelectrically generated bistable laminate, which consists of only macro fiber composites (MFCs) in a [ 0 MFC / 90 MFC ] T layup. While under cross-well regimes such as subharmonic, chaotic, or limit cycle oscillations, a single MFC is actuated to the laminate’s limit voltage to eliminate one of its potential wells and force it into the remaining stable state. Simultaneously, a positive position feedback (PPF) controller suppresses the resulting single-well oscillations through the other MFC. This dual control strategy is numerically and experimentally demonstrated through the suppression of various cross-well regimes and results in significant reduction of amplitude. The active control capability of the laminate prevents snap through instability when under large enough external vibrations.

Seeking analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges is of significance for an insight into the performances of related engineering devices and structures as well as their rapid design. A challenging set of problems concern the vibrating plates with a free corner, i.e., those with two adjacent edges free and the other two edges clamped or simply supported or one of them clamped and the other one simply supported. The main difficulty in solving one of such problems is to find a solution meeting both the boundary conditions at each edge and the condition at the free corner, which is unattainable using a conventional analytic method. In this paper, for the first time, we extend a novel symplectic superposition method to free vibration of rectangular thick plates with a free corner. The analytic frequency and mode shape solutions are both obtained and presented via comprehensive numerical and graphic results. The rigorousness in mathematical derivation and rationality of the method (without any predetermination for the solutions) guarantee the validity of our analytic solutions, which themselves are also validated by the reported results and refined finite element analysis.

The natural vibration of rectangular plates with rounded corners is studied by using a family of homotopy shapes and an efficient Ritz method.

Light-driven photostrictive actuators can induce control actions for wireless non-contact actuation and control of precision structures and systems. Conventional distributed actuators laminated on shells and plates usually only introduce uniform control forces and moments. Structural actuation and control based on uniform control forces and moments have been investigated for over two decades. This paper is to exploit a new photostrictive actuator design, i.e., a skew-quad (SQ) actuator system. This new distributed SQ actuator system laminated on shells and plates can introduce non-uniform control forces and moments. The new SQ actuator system is composed of four pieces of photostrictive materials and the inner two edges of each piece are bonded to a cross fixture. Under the irradiation of high-energy lights, each piece generates non-uniform control forces and moments, due to its uneven non-symmetrical boundary conditions. Modal actuation characteristics of a cylindrical shell coupled with the center-placed and corner-placed SQ actuator systems are evaluated respectively. A paired-design regulating positive/negative control forces of each actuator region is also proposed and evaluated to improve the control effectiveness of the center-located SQ actuator system. Parametric analysis proves improved control effectiveness of unsymmetrical shell modes.

In comparison with the transverse vibrations of rectangular plates, far less attention has been paid to the in-plane vibrations even though they may play an equally important role in affecting the vibrations and power flows in a built-up structure. In this paper, a generalized Fourier method is presented for the in-plane vibration analysis of rectangular plates with any number of elastic point supports along the edges. Displacement constraints or rigid point supports can be considered as the special case when the stiffnesses of the supporting springs tend to infinity. In the current solution, each of the in-plane displacement components is expressed as a 2D Fourier series plus four auxiliary functions in the form of the product of a polynomial times a Fourier cosine series. These auxiliary functions are introduced to ensure and improve the convergence of the Fourier series solution by eliminating all the discontinuities potentially associated with the original displacements and their partial derivatives along the edges when they are periodically extended onto the entire x - y plane as mathematically implied by the Fourier series representation. This analytical solution is exact in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. Numerical examples are given about the in-plane modes of rectangular plates with different edge supports. It appears that these modal data are presented for the first time in literature, and may be used as a benchmark to evaluate other solution methodologies. Some subtleties are discussed about corner support arrangements.

The extreme sensitivity of a scanning probe microscope demands an exceptional noise cancellation device that could effectively cut off a wide range of vibration noise. Existing commercial devices, although excellent in canceling high frequency noise, commonly leave low frequency vibration unattenuated. We design an add-on active stage that can function together with a standalone existing active stage. The objective is to provide a higher level of noise cancellation by lowering the overall system cut-off frequency. This study is concerned with the theoretical aspects of the coupling characteristics involved in stacking independently designed stages together to form a two-stage isolator. Whether an add-on stage would pose a stability threat to the existing stage needs to be addressed. In addition, we explore the use of coupling effects to optimize the performance of the overall system.

In this paper, the authors propose a new method for optimum design of embossed panel sections on vibrating panel-like structures to reduce noise. It is proposed in the method to use the mapping of sound pressure level on the vibrating panel’s surface for best positioning of an embossed panel section, which means a raised panel section, in other words, and to apply the particle swarm optimization algorithm for determining the best dimensions of the embossed panel section. The optimum design method is applied to a rectangular aluminum panel whose size is 0.45 m × 0.4 m with thickness 0.001 m under the boundary condition of clamping four edge lines. Then, according to the optimum design, an embossed section is actually made in each panel by embossing using a press machine, and experiments are carried out to the panels for verification. The application study is carried out for two cases of different positions of a point force excitation on the panels. The two applications demonstrate that the embossed panel sections designed by the optimization method can realize good reduction of sound power.

Important characteristics of acoustic wave propagation are encoded in their dispersion relations. Hence, a computational algorithm, which attempts to preserve these relations, was investigated. Considering the linearized, 2-D Euler equations, simulations were performed to validate this scheme and its boundary conditions. The results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a corner boundary. The time-domain data generated by such computations were often intractable until their spectra was analyzed. For this purpose, the relative merits of three spectral analysis methods were considered. For simple, periodic waves with steep-sloped spectra, the periodogram method produced better estimates than the Blackman-Tukey method, and the Hanning window was more effective when used with the former. For chaotic waves, however, the weighted-overlapped-segment-averaging and Blackman-Tukey methods were better than the periodogram method. Therefore, it was observed that the spectral representation of time-domain data was significantly dependent on the particular method employed.

This study presents a software design tool for solving active noise control problems in irregularly shaped cavities with continuous and noncontinuous design variables and appropriate constraints. The optimum amplitude, phase, and location of the secondary source were simultaneously determined by minimizing the total acoustic potential energy of the control volume in the cavity. The boundary element method was utilized for computing the sound field in the cavity. An optimizer based on sequential quadratic programming was selected for its accuracy, efficiency, and reliability. In order to cope with noncontinuous design variables, the optimizer was linked with a modified branch and bound procedure for practical applications. Simulations indicated that the optimal secondary source in an irregularly shaped car cabin could always be positioned in a region close to the primary source if the primary source was located in a corner of the cavity and the excitation frequency was not a resonance. However, different findings were obtained if the primary source was not located in a corner and the excitation frequency was a resonance. Optimal secondary source locations could appear at antinodal points of the dominant mode not necessarily near the primary source.

This is the first known work which explicitly considers the bending stress singularities that occur in the two opposite, obtuse corner angles of simply supported rhombic plates undergoing free, transverse vibration. The importance of these singularities increases as the rhombic plate becomes highly skewed (i.e., the obtuse angles increase). The analysis is carried out by the Ritz method using a hybrid set consisting of two types of displacement functions, e.g., (1) algebraic polynomials and (2) corner functions accounting for the singularities in the obtuse corners. It is shown that the corner functions accelerate the convergence of solution, and that these functions are required if accurate solutions are to be obtained for highly skewed plates. Accurate nondimensional frequencies and normalized contours of the vibratory transverse displacement are presented for simply supported rhombic plates with skew angles ranging to 75 deg. (i.e., obtuse angles of 165 deg.). Frequency and mode shapes of isosceles and right triangular plates with all edges simply supported are also available from the data presented.

In this experiment, a 10.6 dB reduction in the total radiated sound power for an extended radiator was achieved via active control through optimization of active sources. An acoustic boundary element program was used to determine the magnitude and phase of the active sources which minimized the total radiated sound power. This paper details the experimental verification of the numerically predicted active source strengths using a box-shaped acoustic radiator. The top and bottom of the radiator were thin steel plates which were driven in one of their structural modes by an electromagnetic shaker. The four corners of the top plate were removed to accommodate baffled loudspeakers, representing the active sources. To provide precise control of the experiment, the driving signals to the shakers and loudspeakers were generated and monitored by a control computer. The experimental results agreed closely with the analytical prediction, confirming that the optimum reduction had been achieved for the primary and active source configuration. The measured sound pressure reductions in the acoustic field of the radiator ranged from 8 dB to 19 dB for the 1,1 structural mode of the plates.

The results of stress analysis of angled members subjected to pure flexure are presented. The stress analysis was performed using the ANSYS finite element program. Stress concentration factors varying from 1.25 to 2.5 can be expected at the reentrant corner of the member depending on the ratio of the fillet radius to the width and the deviating angle.

The low frequency reflection and transmission of vibrational energy at an L-junction of square section rods is investigated theoretically and experimentally. The theoretical description, in which thin rod theory is employed, is complete in that all modes of vibration are considered including compression, torsion, and bending both for the incident and generated waves. It is seen that bending vibration in the plane of the system is coupled to compressional waves and bending vibration normal to the plane of the system is coupled to torsional waves. The theory applies to junctions of semi-infinite rods and this condition was simulated experimentally by means of impulse response techniques in which the reflected waves were removed by truncating the time histories prior to frequency analysis. A novel combination of phase separation, time of flight methods, and filtering has allowed the various modes of vibration to be separated and the agreement between predicted and measured reflection and transmission loss, both for same mode and dissimilar mode coupling, is promising.

Grinding wheel corner wear plays a very significant role in certain cylindrical plunge grinding operations in which the corner radius is critical. The corner wear affects the tolerance specified on the plunged corner radius on the component. Monitoring of corner wear is essential to know when exactly the tolerance zone has been crossed. This paper deals with the nature and geometry of corner wear and its monitoring using the fluctuations in the airflow velocity around the grinding wheel.

This paper is concerned with the application of the Boundary Element Method (BEM) to interior acoustics problems governed by the reduced wave (Helmholtz) differential equation. The development of an integral equation valid at the boundary of the interior region follows a similar formulation for exterior problems, except for interior problems the Sommerfeld radiation condition is not invoked. The boundary integral equation for interior problems does not suffer from the nonuniqueness difficulty associated with the boundary integral equation formulation for exterior problems. The boundary integral equation, once obtained, is solved for a specific geometry using quadratic isoparametric surface elements. A simplification for axisymmetric cavities and boundary conditions permits the solution to be obtained using line elements on the generator of the cavity. The present formulation includes the case where a node may be placed at a position on the boundary where there is not a unique tangent plane (e.g., at an edge or a corner point). The BEM capability is demonstrated for two types of classical interior axisymmetric problems: the acoustic response of a cavity and the transmission loss of a muffler. For the cavity response comparison data are provided by an analytical solution. For the muffler problem the BEM solution is compared to data obtained by a finite element method analysis.

The flow and wall-pressure field around a wing-body junction has been experimentally investigated in a quiet, low-turbulence wind tunnel. Measurements were made along the centerline in front of the wing and along several spanwise locations. The flow field data indicated that the strong adverse pressure gradient on the upstream centerline causes three-dimensional flow separation at approximately one wing thickness upstream and this induced the formation of the horseshoe root vortex which wrapped around the wing and became deeply embedded within the boundary layer. The wall-pressure fluctuations were measured for their spectral content and the data indicate that the effect of the adverse pressure gradient is to increase the low-frequency content of the wall pressure and to decrease the high-frequency content. The wall pressure data in the separated region, which is dominated by the horseshoe vortex, shows a significant increase in the low-frequency content and this characteristic feature prevails around the corner of the wing. The outer edge of the horseshoe vortex is clearly identified by the locus of maximum values of RMS wall pressure.

It is observed in practice that the classic (conventional) method as well as the finite element method, when using beam elements, to evaluate the strength and stiffness of a pressframe, gives results differing substantially from actual values. This discrepancy between experimental and theoretical results can be considerably narrowed if the stress-deformed state of the corner zone is separately considered in the computation of the overall strength and stiffness of the pressframe. By means of the application of the theory of thin-wall curved beam with large curvature it is economically possible to analyze the stress-deformed behavior of the pressform in general and the corner zone element in particular with fair reliability. In the present paper this method is applied to a mechanical C-frame press.

This paper is concerned with a method for solving vibration problems of arbitrarily shaped plates. The frequency equation for determining eigenfrequencies of arbitrarily shaped plates is presented. A method of numerical calculation has been given for five examples of circular plates, elliptical plates, rectangular plates with rounded corners, and cardioidal plates. Numerical calculations are carried out for rectangular plates with semicircular sides, rectangular plates with rounded corners and cardioidal plates. The results obtained by this method are compared with previously published results for typical cases of circular and rectangular plates.