DE102023126058A1 - Arrangement and method for generating sound and vibrations with a mechanical structure excited by a strain actuator - Google Patents

Abstract

The invention generally relates to an arrangement and a method for generating vibrations in a mechanical structure (19) and for generating airborne sound and for actively suppressing noise using an electromechanical strain actuator (3) connected to the structure at a contact surface (S _c ). The strain actuator uses piezoelectric material to convert an electrical signal u into a strain in the contact surface (S _c ). A structural element (21) of the structure generates a low slope of the eigenfunction on one side (7) of the boundary line of the contact surface (S _c ) and a high slope on the opposite side (9) of the boundary line in order to increase the excitation of modal vibrations at low frequencies. The method includes an iterative design procedure that optimizes the properties of the structure and the position of the strain actuator by maximizing an excitation metric calculated based on the eigenfunction at the boundary line of the contact surface (S _c ).

Description

FIELD OF THE INVENTION

The invention generally relates to an arrangement for generating airborne sound by means of a passive, mechanical structure which is excited to oscillate by means of an electromechanical expansion actuator and to a method for the structural design and optimal adaptation of these components in the arrangement.

STATE OF THE ART

Most loudspeakers and other electroacoustic sound transducers use special components such as membranes made of lightweight materials that are particularly well-suited for generating vibrations and radiating sound. The state-of-the-art flat panel speaker uses a flat plate, a curved shell, a window, a door, a cabinet, a monitor screen, a car body panel, and other structures with large, sound-radiating surfaces that were originally designed for other purposes. These structures are excited by an electromechanical actuator to produce mechanical vibrations that radiate sound. Fuller, C., Elliott, S., and Nelson, P. developed a physical theory for this arrangement that can be used to actively control these structures, see Active Control of Vibration, Associated Press, 1996, doi:https://doi.org/10.1016/b978-0-12-269440-0.x5000-6 .

The mechanical structure can be excited by a force applied perpendicularly to the surface of the mechanical structure, achieving a nearly constant effective excitation over a wide frequency range. There are a variety of electromechanical force actuators that generate a force at a relatively small contact area S _c . This group includes an electrodynamic transducer, which uses a voice coil in a magnetic field, exploiting the inertia of the magnet to generate the excitation force. Electrodynamic force actuators have some disadvantages, as the magnetic material is expensive and heavy and requires an iron path, which increases the thickness of flat panel displays and televisions.

The mechanical structure can also be excited by a strain actuator, an electromechanical transducer that generates a strain on the contact surface _Sc from an electrical input voltage u. Strain actuators can be relatively easily implemented using, for example, a piezoelectric ceramic plate or dielectric foils. These transducers are lightweight, extremely flat, robust, and can be easily attached to the mechanical structure.

M. Heilemann and Tre DiPassio presented a paper 10618 at the 153rd AES Conference in October 2022 with dem Title “Piezoelectric actuators for flat-panel loudspeakers “, which provides a comprehensive overview of the theory, important references and practical solutions that characterize the state of the art and are the basis for describing the special features of the invention described here. 1 shows a schematic representation of a typical flat panel loudspeaker comprising a piezoelectric strain actuator 3 attached to a rectangular thin isotropic plate 1 at an off-center position x ₀ and y _0. A z-polarized strain actuator made of a PVDF (polyvinylidene fluoride) film or piezoelectric ceramic plate 13 expands the electrostatic material in the x and y directions depending on the input voltage u applied between the upper and lower conductive contact foils 15 and 17. The strain actuator 3 in 1 has a rectangular shape, mounted at positions x ₀ and y ₀ on the upper side of plate 1 with parallel edges. The length 2l _x and the width 2l _y of the piezoelectric material determine the contact area S _c to the mechanical structure in strain actuators.

mit der Heaviside-Stufenfunktion H(x) und der Dehnung ε_pe(u), abhängig von der Eingangsspannung u des Aktuators und einer Konstante C₀, die andere geometrische und Materialeigenschaften repräsentiert.The stress u applied to the strain actuator generates moments that produce bending waves in plate 1. A single strain actuator 3 mounted on one side of plate 1 also generates strain forces and longitudinal waves in the plate, which are neglected in further modeling. The moments on the contact surface S _c can be modeled as follows: $$\begin{array}{c}{M}_x=M_y=C_0{\epsilon }_{pe}\left(u\right)\left[H\left\{x-\left(x_0-l_x\right)\right\}-H\left\{x-\left(x_0-l_x\right)\right\}\right]\\ \left[H\left\{y-\left(y_0-l_y\right)\right\}-H\left\{y-\left(y_0+l_y\right)\right\}\right]\end{array}$$

with the Heaviside step function H(x) and the strain ε _pe (u), depending on the input voltage u of the actuator and a constant C ₀ representing other geometric and material properties.

unter Verwendung der Plattenbiegesteifigkeit D, des Nabla-Operators V , eines Dämpfungsparameters b und der Flächenmassendichte m''. Die partielle Ableitung II. Ordnung wandelt die gleichmäßig über die Kontaktfläche S_c verteilten Momente M_x und M_y in positive und negative Dipolkräfte an den Rändern der Kontaktfläche S_c um, dargestellt durch die Ableitungen der Dirac-Delta-Funktionen δ'(·) in Gleichung (2). Die Dipolkräfte können sich unter bestimmten Bedingungen gegenseitig aufheben, wodurch die Anregung der Biegewellen bei niedrigen Frequenzen zusätzlich verringert wird. The equation of motion based on the classical theory for thin plates can be written in the form of the displacement w as $$\begin{array}{l}D{\nabla }^{4}w+\dot{b}w+m\text{'}\text{'}\ddot{w}=\frac{{\partial }^2{M}_x}{\partial x^2}+\frac{{\partial }^2{M}_y}{\partial y^2}\hfill \\ =C_0{\epsilon }_{pe}\left(u\right)\left[\delta \text{'}\left\{x-\left(x_0-l_x\right)\right\}-\delta \text{'}\left\{x-\left(x_0-l_x\right)\right\}\right]\left[H\left\{y-\left(y_0-l_y\right)\right\}-H\left\{y-\left(y_0+l_y\right)\right\}\right]\hfill \\ +C_0{\epsilon }_{pe}\left(u\right)\left[H\left\{x-\left(x_0-l_x\right)\right\}-H\left\{x-\left(x_0+l_x\right)\right\}\right]\left[\delta \text{'}\left\{y-\left(y_0-l_y\right)\right\}-\delta \text{'}\left\{y-\left(y_0+l_y\right)\right\}\right]\hfill \end{array}$$

using the plate bending stiffness D, the nabla operator V , a damping parameter b and the surface mass density m''. The second-order partial derivative converts the moments M _x and M _y uniformly distributed over the contact area S _c into positive and negative dipole forces at the edges of the contact area S _c , represented by the derivatives of the Dirac delta functions δ'(·) in equation (2). The dipole forces can cancel each other under certain conditions, which further reduces the excitation of the bending waves at low frequencies.

The displacement w(x,y) in the z-direction at the coordinates x and y can be described by orthonormal eigenfunctions Φ _mn (x,y), which are scaled with the modal amplitude W _mn $$w\left(x,y,t\right)={\displaystyle \sum _{m=1}^{\infty }{\displaystyle \sum _{n=1}^{\infty }{W}_{mn}{\mathrm{\Phi }}_{mn}\left(x,y\right)}}{e}^{j\omega t}.$$

mit γ_m = mπ / L_x und γ_n = nπ / L_y. Die Indizes m und n stellen die Anzahl der Halbwellenlängen in x- und y-Richtung dar, die in die Längen L_x bzw. L_y der rechteckigen Platte 1 passen.Heilemann describes a rectangular plate with simply supported (hinged) edges 11, as in 1 shown, using analytical solutions for the eigenfunctions $${\mathrm{\Phi }}_{mn}\left(x,y\right)=\text{sin}\left({\gamma }_{m}x\right)\text{sin}\left({\gamma }_{n}y\right)$$

with γ _m = mπ / L _x and γ _n = nπ / L _y . The indices m and n represent the number of half-wavelengths in the x- and y-directions that fit into the lengths L _x and L _y of the rectangular plate 1, respectively.

Taking advantage of the modal orthogonality of the eigenfunctions, the modal amplitude can be expressed as follows: $$\begin{array}{c}{W}_{mn}=\frac{C_{mn}{\epsilon }_{pe}\left(u\right)}{{\omega }_{mn}^2-{\omega }^2+j\frac{\omega {\omega }_{mn}}{Q_{mn}}}\left(\text{cos}\left({\gamma }_m\left(x_0-l_x\right)\right)-\text{cos}\left({\gamma }_m\left(x_0+l_x\right)\right)\right)\\ \left(\text{cos}\left({\gamma }_n\left(y_0-l_y\right)\right)-\text{cos}\left({\gamma }_n\left(y_0+l_y\right)\right)\right)\\ =\frac{4C_{mn}{\epsilon }_{pe}\left(u\right)}{{\omega }_{mn}^2-{\omega }^2+j\frac{\omega {\omega }_{mn}}{Q_{mn}}}\text{sin}\left({\gamma }_m{x}_0\right)\text{sin}\left({\gamma }_n{x}_0\right)\text{sin}\left({\gamma }_m{l}_x\right)\text{sin}\left({\gamma }_n{l}_y\right)\end{array}$$

The modal amplitude of a simply supported plate is zero when the center of the extension actuator, represented by the coordinates x ₀ and y ₀ , lies on a nodal line where the eigenfunction sin (γ _m x ₀ ) sin (γ _n γ ₀ ) = 0. This criterion also applies to the placement of force actuators with electrodynamic inertial transducers. Thus, both a force actuator and a extension actuator located at the center of the simply supported plate generate more amplitude W ₁₁ of the fundamental mode (m = 1 and n = 1) than at any other point on the plate.

2 shows the total amplitude of the modal acceleration of the simply supported plate in 1 , which is excited by the strain actuator at the off-center position, measured and simulated by Heilemann in AES Conference Paper 10618. Heilemann found that “piezoelectric strain actuators typically exhibit a weaker bass response due to the relatively weak coupling between the dimensions of the strain actuator and the half-wavelength of the fundamental bending mode of the plate reproduction." The piezoelectric transducer principle does not cause this problem directly, but is a general property of all strain actuators that generate dipole forces at the boundary line of the contact area S _c . Any strain actuator with a small contact area S _c attached to a simply supported, thin plate generates the term sin (γ _m l _x )sin (γ _n l _y ) in equation (5), which vanishes when the dimensions l _x and _ly are much smaller than the bending wavelength. This problem diminishes at higher frequencies because the bending wavelength decreases and the number of nodes and antinodes on the simply supported plate increases.

Heilemann concluded in this conference paper: “Since piezoelectric strain actuators are very good at exciting the vibration modes at high frequencies, they should best be used as tweeters in a two-way crossover flat panel loudspeaker, with the vibration modes at low frequencies being excited with electrodynamic force actuators.”

Heilemann et al. disclosed in the patent US 10,966,042 also a “method for generating localized vibrations on panels” that uses piezoelectric actuators for the excitation of panels, which were modeled as a plate with simply supported edges and sinusoidal eigenfunctions in equation (6) in column 9.

Tomohiko Kamimura et al. revealed in the US patent application 2006/0093165 on page 1 a plate loudspeaker in which “the plate edge is held to a frame with seals at certain sections, the seal (31 in the 3a and 5 ) at the plate edge, on the opposite side of the electromechanical actuator, has a higher hardness than the seal at other positions."

SUMMARY OF THE INVENTION

The invention discloses an arrangement and a method for generating mechanical vibrations and radiating sound using a strain actuator, for example, an electrostatic transducer attached to a contact surface on a mechanical structure. The strain actuator converts an electrical input signal u into dipole forces at the boundary line of the contact surface _Sc , as shown in equation (2). A key objective of the invention is to improve the mechanical excitation of vibration modes in large mechanical structures using strain actuators with a small contact surface _Sc .

The invention exploits the fact that the positive and negative dipole forces at the opposite points 7 and 9 of the edge 5 of the contact surface _Sc cancel each other out if the modal eigenfunction at these opposite points has the same value. Cancellation can occur in low-order modes generated in simply supported plates 1 at low frequencies if the distance between the opposite points 7 and 9 is much smaller than the bending wavelength.

According to the invention, the geometry or material of the mechanical structure 1 is to be modified, or the boundary conditions are to be changed by additional mechanical or acoustic elements in order to generate different slopes in the eigenfunction at the opposite points of the boundary of the contact area S _c . Clamping the edge of the mechanical structure and placing the strain actuator with one side of the boundary at the clamped edge are very effective embodiments of the invention. Another embodiment places the strain actuator at a specific position where the mechanical structure has a strong curvature in the shell, a varying thickness, or a transition between different materials, thereby generating different slopes in the eigenfunctions at opposite boundary points.

The invention can be used for a design method in which an excitation metric E _nm evaluates the slopes of the eigenfunction at opposite points on the boundary line of the contact surface S _c . A small value of the excitation metric (E _nm <<1) indicates poor mechanical excitation of the modal vibration. The excitation metric helps to determine the best position of the strain actuator and to evaluate design changes to the mechanical structure. The method is an iterative procedure in which the mutual interaction between the strain actuator and the structure, which influences the resulting eigenfunction, is taken into account. A high value of the excitation metric (E _nm ≈1) indicates that an optimal design solution has been found and the iterative procedure can be terminated.

BRIEF DESCRIPTION OF THE DRAWINGS

• 1 shows the position and size of a piezoelectric strain actuator attached to a simply supported plate in an off-center position used by Heilemann according to the state of the art.
• 2 shows the acceleration measured and simulated by Heilemann in the state of the art on the simply supported plate as state of the art, which is excited with a strain actuator in an off-center position.
• 3 shows a strain actuator attached to a structure and a structural component attached to the boundary line of the contact surface S _c according to the invention.
• 4 shows the first embodiment of the invention in a flat panel loudspeaker using a piezoelectric strain actuator attached to a plate by placing the contact surface S _c close to the clamped edges of the plate.
• 5 shows the second embodiment of the invention in a flat panel loudspeaker using two piezoelectric strain actuators mounted on a plate near the central clamping area.
• 6 shows the third embodiment of the invention in an active control system for suppressing unwanted vibrations on a housing using a piezoelectric strain actuator attached to the housing at a point where the housing shell has a strong curvature.
• 7 shows a flowchart detailing the steps for optimizing a flat panel speaker.

DETAILED DESCRIPTION OF THE INVENTION

bestehend aus Produkten zweier unabhängiger modaler Unterfunktionen φ_m(x) und φ_n(y), die die Abhängigkeit von x und y beschreiben. 3 shows the general elements and properties of the arrangement in the present invention. This arrangement uses a thin mechanical structure 19, such as a flat plate or curved shell, with other elements influencing the boundary conditions. This structure uses a specific geometry, materials, or a structural component 21 to clamp the structure at the boundary line of the contact surface S _c to reduce some of the dipole forces generated by the local derivatives of the direct delta functions δ'(·) in equation (2). These local properties of the mechanical structure prevent the effect of the dipole forces from partially canceling out, and the effective excitation of the bending waves at low frequencies is significantly smaller than at high frequencies. This arrangement cannot be modeled by the sinusoidal eigenfunctions Φ _mn (x, y) in equation (4) according to the prior art, which is only valid for a simply supported plate 1, but requires a more general definition of the eigenfunctions. $$w\left(x,y\right)={\displaystyle \sum _{m=1}^{\infty }{\displaystyle \sum _{n=1}^{\infty }{W}_{mn}}}{\mathrm{\Phi }}_{mn}\left(x,y\right)={\displaystyle \sum _{m=1}^{\infty }{\displaystyle \sum _{n=1}^{\infty }{W}_{mn}{\phi }_m\left(x\right){\phi }_n\left(y\right)}}$$

consisting of products of two independent modal subfunctions φ _m (x) and φ _n (y), which describe the dependence of x and y.

unter Verwendung der Eigenfrequenzen ω_mn, der Gütefaktoren Q_mn und der Konstanten C_mn,c unter Berücksichtigung der geometrischen und materiellen Eigenschaften der Struktur, des Dehnungsaktuators und anderer akustischer Elemente (z.B. Gehäuse, Schallöffnungen) zur Erzeugung günstiger Anregungsbedingungen.Taking advantage of modal orthogonality, the modal amplitude W _mn can be calculated as $$\begin{array}{l}{W}_{mn}=\frac{C_{mn,c}{\epsilon }_{pe}\left(u\right)}{{\omega }_{mn}^2-{\omega }^2+j\frac{\omega {\omega }_{mn}}{Q_{mn}}}\left(\frac{\partial {\phi }_m\left(x_0-l_x\right)}{\partial x}-\frac{\partial {\phi }_m\left(x_0-l_x\right)}{\partial x}\right)\left(\frac{\partial {\phi }_n\left(y_0-l_y\right)}{\partial y}-\frac{\partial {\phi }_n\left(y_0+l_y\right)}{\partial y}\right)\hfill \\ =\frac{C_{mn,c}{\epsilon }_{pe}\left(u\right)}{{\omega }_{mn}^2-{\omega }^2+j\frac{\omega {\omega }_{mn}}{Q_{mn}}}\left(\phi {\text{'}}_m\left(x_0-l_x\right)-\phi {\text{'}}_m\left(x_0+l_x\right)\right)\left(\phi {\text{'}}_n\left(y_0-l_y\right)-\phi {\text{'}}_n\left(y_0-l_y\right)\right)\hfill \end{array}$$

using the natural frequencies ω _mn , the quality factors Q _mn and the constants C _mn,c taking into account the geometric and material properties of the structure, the strain actuator and other acoustic elements (e.g. housing, sound openings) to generate favorable excitation conditions.

If the dimensions 2l _x or 2l _y of the strain actuator 3 are much smaller than the bending wavelength λ _nm , the difference between the slopes φ' _m and φ' _n at the boundary line of the contact surface reduces the amplitude W _nm of the vibration modes. This effect is a characteristic property of the strain actuator 3 and can be evaluated by an excitation metric, which for a rectangular boundary can be expressed as follows: $$E_{mn}=\frac{\left|\phi {\text{'}}_m\left(x_0-l_x\right)-\phi {\text{'}}_m\left(x_0+l_x\right)\right|\left|\phi {\text{'}}_n\left(y_0-l_y\right)-\phi {\text{'}}_n\left(y_0+l_y\right)\right|}{\left(\left|\phi {\text{'}}_m\left(x_0-l_x\right)\right|+\left|\phi {\text{'}}_m\left(x_0+l_x\right)\right|\right)\left(\left|\phi {\text{'}}_n\left(y_0-l_y\right)\right|+\left|\phi {\text{'}}_n\left(y_0+l_y\right)\right|\right)}<1$$

The denominator in equation (8) provides a useful normalization to the maximum excitation, where the dimensions 2l _x or 2l _y of the strain actuator correspond to half the bending wavelength λ _nm .

beschreibt die mittlere Anregung in einem Frequenzband, das bei den Moden mit der Ordung N_H und M_H beginnt und die Anzahl N_D und M_D höherer Moden berücksichtigt.A second metric $${\overline{E}}_{mn}=\frac{1}{N_D{M}_D}{\displaystyle \sum _{n=N_H}^{N_H+N_D}{\displaystyle \sum _{m=M_H}^{M_H+M_D}{E}_{mn}}}$$

describes the average excitation in a frequency band that begins with the modes of order N _H and M _H and takes into account the number N _D and M _D of higher modes.

Both excitation metrics depend on the particular properties of the eigenfunctions φ _m (x) and φ _n (y), the placement of the strain actuator at x ₀ and y ₀ and the size of the strain actuator, represented by l _x and l _y .

According to the inventive idea, the geometry or material of the structure 19 is to be changed, or an additional component 21 is to be used in the structure 19, in order to reduce the slope of the eigenfunctions on one side 7 of the boundary of the contact area S _c , while the slope on the opposite side 9 is to be made as large as possible. Such a modified structure suppresses the dipole forces in equation (2) on one side 7 of the edge, but maintains the dipole forces on the opposite side 7 and prevents a cancellation effect at low frequencies. A strain actuator can also excite low-order modes at a nodal line φ _m = 0 or φ _n = 0 if the slope of the eigenfunction in the contact area S _c changes. A force actuator cannot excite vibration modes at the nodal line.

There are many practical ways to modify a given mechanical structure to meet these conditions, as illustrated in the following embodiments:

$$\phi {\text{'}}_m\left(x_0-l_x\right)=0$$

$${\phi }_n\left(y_0-l_y\right)=0$$

$${\phi }_m\left(x_0-l_x\right)=0$$

was den Wert der Anregungsmetrik E_nm für die Grund- und andere Moden erhöht. 4 shows the first embodiment of the invention in a flat panel loudspeaker using a piezoelectric strain actuator 3 mounted on a rectangular plate 1. In contrast to the 1 In the prior art shown, the strain actuator 3 is arranged at a corner of the plate 1 near the edges, where an additional clamp 23 has been applied. The clamp creates the boundary conditions at the edges of the contact surface S _c $${\phi }_m\left(x_0-l_x\right)=0$$

$$\phi {\text{'}}_m\left(x_0-l_x\right)=0$$

$${\phi }_n\left(y_0-l_y\right)=0$$

$${\phi }_m\left(x_0-l_x\right)=0$$

which increases the value of the excitation metric E _nm for the fundamental and other modes.

$${{\phi }^{\prime }}_m\left(x_l-l_x\right)\approx 0$$

$${\phi }_m\left(x_r-l_x\right)\approx 0$$

$${{\phi }^{\prime }}_m\left(x_r-l_x\right)\approx 0$$

5 shows the second embodiment of the invention in a rectangular flat plate 1, the outer edges 11 of which are simply supported. A rigid rail arranged on the vertical center line x _c on the back of the plate 1 establishes a center clamp 27, which generates independent modal systems of equal size on the left and right sides of the plate 1. Each structure is excited by a piezoelectric strain actuator 31 and 33, which is arranged on the left and right sides of the clamping rail at the positions x _l , y ₀ and x _r , y ₀ respectively. The center clamp 27 at the respective excitation position creates the following boundary conditions: $${\phi }_m\left(x_l-l_x\right)\approx 0$$

$${{\phi }^{\prime }}_m\left(x_l-l_x\right)\approx 0$$

$${\phi }_m\left(x_r-l_x\right)\approx 0$$

$${{\phi }^{\prime }}_m\left(x_r-l_x\right)\approx 0$$

$${{\phi }^{\prime }}_n\left(y_l+l_y,x_l-l_x<x<x_r+l_x\right)\approx 0$$

An additional edge clamp 29 is applied to plate 1, where the upper boundary line of both strain actuators lies. This results in the following boundary condition: $${\phi }_n\left(y_l+l_y,x_l-l_x<x<x_r+l_x\right)\approx 0$$

$${{\phi }^{\prime }}_n\left(y_l+l_y,x_l-l_x<x<x_r+l_x\right)\approx 0$$

The center clamp 27 and the edge clamp 29 increase the value of the excitation metric E _nm for the vibration modes.

$$u_r=\{\begin{array}{cc}{s}_l+s_r& f<f_c\\ s_r& f\ge f_c\end{array}$$

A stereo audio signal containing two sub-signals s _l and s _r is fed to a switch which generates the electrical input signals u _l and u _r for the strain actuators 31 and 32, respectively: $$u_l=\{\begin{array}{cc}{s}_l+s_r& f<f_c\\ s_l& f\ge f_c\end{array}$$

$$u_r=\{\begin{array}{cc}{s}_l+s_r& f<f_c\\ s_r& f\ge f_c\end{array}$$

Both expansion exciters 31 and 32 receive a mono signal at low frequencies, generated by summing the left and right partial signals. The high-frequency stereo signals are fed separately to the two expansion actuators. This design allows two fundamental modes to be excited on the left and right sides of the plate, which oscillate in phase and double the sound pressure output at low frequencies. The center clamp 27 enables the decoupling of the modal oscillation on the left and right sides of the plate at higher frequencies, which has a beneficial effect on the perceived width of the sound image.

6 shows a system for actively controlling the vibrations on the housing 35, which are excited by a force _FM generated by the motor 45 and transmitted to the housing via the platform 47 (Active Noise Control). The housing 35 behaves like a thin, curved shell, generating unwanted vibrations and noise that are radiated into the environment as noise. A sensor 37 measures the motion state signal a on the housing surface and generates an electrical input signal u in a control unit 49, which is fed to the piezoelectric strain actuator 39 attached to the housing 35. One side of the boundary of the contact surface _Sc is located at position 43, where the curvature and thickness of the shell and material properties such as density and local Young's modulus produce a low slope in the eigenfunction. The opposite side of the boundary is located at position 41, where the low curvature and the thin material produce a high slope in the eigenfunction. This embodiment of the invention exploits the given properties of the housing without using additional means for clamping or stiffening the mechanical structure and produces a high value in the excitation metric E _nm in equation (8).

The invention is also used as a method for the optimal design of mechanical shakers, loudspeakers and active systems for sound and vibration damping.

7 shows an optimization process as a flow chart in which the steps for optimizing sound reproduction using a television screen, for example, are listed.

The first step is to provide a preliminary version of a mechanical structure that meets the requirements of a primary application, such as the visual performance of a display.

In the second step, a strain actuator with a contact surface S _c is attached to the structure.

In the third step, the modal vibration of the structure is measured or simulated using the attached strain actuator.

In the fourth step, modal analysis is applied to the measured or simulated vibration data to extract the eigenfrequencies, the modal quality factor, and the eigenfunctions of the modes. The slopes of the eigenfunctions are calculated at the edges of the contact surface S _c .

In the fifth step, an excitation metric E _nm is calculated, which evaluates the difference between the slopes of the eigenfunctions in the x- or y-direction at opposite points on the boundary line of the contact surface S _c .

In the sixth step, the optimization is completed when the excitation metric E _nm reaches a predefined threshold (e.g., E _nm ≈1).

In the seventh step, design changes are made to the mechanical structure, e.g., by adding additional stiffeners, or the position of the strain actuator is changed taking into account the boundary conditions of the primary application and the previous steps 2 to 5 of the optimization procedure are repeated.

The iterative procedure takes into account the interactions between the modified structure, the effective excitation and the load exerted by the strain actuator at a specific position.

ADVANTAGES OF THE INVENTION

The invention is essential for the reproduction of audio signals as well as for the active suppression of noise generated by mechanical vibrations on thin-walled mechanical structures.

The invention can be applied to any mechanical structure, even if it was originally designed for another purpose where mechanical vibrations and sound radiation are unnecessary or undesirable. For example, a modern organic light-emitting diode (OLED) display in modern televisions and monitors is primarily designed to meet video requirements, but now also needs to be able to reproduce an audio sound signal. Electrostatic strain actuators and other thin and lightweight devices can be placed on the back of the display to reproduce audio signals with sufficient quality without compromising the video quality, visual appearance, and style of the consumer product.

Modern screens have a large radiating surface and sufficient modal vibration density, which is necessary for reproducing low audio frequencies. Strain actuators are advantageous for implementing multi-channel active control systems that generate a desired acoustic directivity at higher frequencies. The present invention enables a minimal number of small strain actuators for exciting lower-order vibration modes, which are required to reproduce the entire audio frequency band without additional woofers or force actuators. Thus, the invention reduces the cost, weight, and size of the audio components.

QUOTES CONTAINED IN THE DESCRIPTION

This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 10,966,042 [0014]
• US 2006/0093165 [0015]

Cited non-patent literature

• Active Control of Vibration, Associated Press, 1996, doi:https://doi.org/10.1016/b978-0-12-269440-0.x5000-6 [0002]
• M. Heilemann and Tre DiPassio presented a paper 10618 with [0005] at the 153rd AES Conference in October 2022.
• Title “Piezoelectric Actuators for Flat-Panel Loudspeakers [0005]

Claims (10)

Arrangement for generating sound and vibration on the basis of an electrical input signal u, comprising a mechanical structure and an electromechanical strain actuator which is connected to the mechanical structure via a contact surface S _c , wherein the strain actuator converts the electrical input signal u into a strain of the contact surface and excites the structure to mechanical vibrations via dipole moments at the boundary line of the contact surface S _c , which vibrations can be described by eigenfunctions φ _n ; the mechanical structure has at least one component which is designed such that it generates a different slope φ _n ' of the eigenfunction φ _n at opposite points on the boundary line of the contact surface S _c in order to increase the excitation of the structure by the dipole moments. Arrangement according to Claim 1 , wherein the mechanical structure has geometric and material properties required for the generation of bending waves; the size of the contact area S _c is smaller than the size of the sound-radiating area S; the electromechanical strain actuator uses piezoelectric material to generate the strain in the contact area S _c . Arrangement according to Claim 1 , wherein the constructive element causes a clamping of the mechanical structure which reduces the slope φ _n ' of the eigenfunction φ _n at points on the boundary line and produces a high slope φ _n ' of the eigenfunction φ _n at the opposite points on the boundary line. Arrangement according to Claim 3 , with the clamping being attached to the edge of the mechanical structure. Arrangement according to Claim 1 , where the structural element changes the stiffness or mass distribution of the structure so that the slope φ _n ' of the eigenfunction φ _n is reduced at points on the boundary line and at the same time a high slope φ _n ' of the eigenfunction φ _n is produced at opposite points on the boundary line. Arrangement according to Claim 1 , whereby the constructive element changes the sound pressure acting on the mechanical structure so that the slope φ _n ' of the eigenfunction φ _n is reduced at points on the boundary line and at the same time a high slope φ _n ' of the eigenfunction φ _n is generated at opposite points on the boundary line. Method for generating sound and vibrations based on an electrical input signal u using a mechanical structure and an electromechanical strain actuator according to the arrangement according to Claim 1 , comprising the following steps: I. Providing a first version of the mechanical structure that meets the requirements of a primary application; II. Attaching an electromechanical transducer to a contact surface S _c on the structure and generating a strain in the materials at the contact surface S _c with an electrical input signal u; III. Measuring or simulating the vibrations on the mechanical structure generated by the strain actuator; IV. Applying modal analysis to the measured or simulated vibration data to extract the natural frequencies, the modal quality factor and the eigenfunction of the low-order modes; V. Calculating the slope φ _n ' of the eigenfunction φ _n at the boundary line of the contact surface S _c ; VI. Calculating an excitation metric E _nm that evaluates the difference in the slope φ _n ' of the eigenfunction φ at opposite points on the boundary lines of the contact surface S _c ; VII. Completing the optimization procedure when the excitation metric E _nm reaches a predefined threshold; Otherwise, design changes to the mechanical structure or a change in the position of the strain actuator are made taking into account the requirements of the primary application and the previous steps II to VII of the optimization procedure are repeated. Procedure according to Claim 7 , further comprising the steps of: changing the stiffness or mass distribution in a contact surface S _c of the mechanical structure, wherein the slope φ _n ' of the eigenfunction φ _n at points on the boundary line of the contact surface S _c is reduced and at the same time a high slope φ _n ' of the eigenfunction φ _n at opposite points is generated on the boundary line; placing the strain actuator at the contact surface S _c of the mechanical structure. Procedure according to Claim 7 , further comprising the steps of: changing the boundary conditions of the mechanical structure by clamping components of the structure on the boundary line of the contact surface S _c , wherein the slope φ _n '=0 of the eigenfunction φ _n is reduced at the clamped points on the boundary line of the contact surface S _c and at the same time a high slope φ _n ' of the eigenfunction φ _n is generated at opposite points on the boundary line; placing the strain actuator on the contact surface S _c of the mechanical structure. Procedure according to Claim 7 , further comprising the steps of: changing the boundary conditions of the mechanical structure by acoustic components which influence the sound pressure on the contact surface S _c , whereby the slope φ _n '=0 of the eigenfunction φ _n is reduced at selected points on the boundary line of the contact surface S _c and at the same time a high slope φ _n ' of the eigenfunction φ _n is generated at opposite points on the boundary line; placing the strain actuator on the contact surface S _c of the mechanical structure.

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