Piezoelectric beam type bidirectional micromechanical vibration energy collector with eccentric mass block

Abstract

The invention discloses a piezoelectric beam type bidirectional micro-mechanical vibration energy collector with an eccentric mass block. The piezoelectric beam type bidirectional micro-mechanical vibration energy collector comprises a substrate, a cantilever beam and the mass block with an eccentric distance R0, the cantilever beam is arranged on the substrate, a piezoelectric layer is arranged on the upper surface of the cantilever beam, the position starting point of the piezoelectric layer is at the root of the cantilever beam, and the width of the piezoelectric layer is equal to that of the cantilever beam; the eccentric distance of the mass block is # imgabs0 #, L is the length of the cantilever beam, and LE is the length of the piezoelectric layer. Compared with the prior art that the mass center of a mass block is close to the longitudinal axis of a cantilever beam and vibration energy in the horizontal direction cannot be collected, the vibration energy in the two directions is collected at the same time through the eccentric mass block, and the mass center of the mass block is large away from the longitudinal axis of the cantilever beam, so that the vibration energy in the horizontal direction is collected when a foundation vibrates horizontally. The mass block generates large horizontal inertia moment to cause vibration deformation of the cantilever beam, and vibration energy in the horizontal direction and the vertical direction is converted into electric energy at the same time.

Description

Technical Field

[0001] The present invention relates to a micro piezoelectric vibration energy collector in the field of silicon micromachining manufacturing technology, and in particular to a piezoelectric beam type bidirectional micromechanical vibration energy collector with an eccentric mass block which simultaneously converts vibration energy in horizontal and vertical directions into electrical energy. Background Art

[0002] A piezoelectric vibration energy harvester is a device that uses the piezoelectric effect to convert mechanical vibration energy into electrical energy. Piezoelectric vibration energy harvesters are divided into ordinary and miniature types according to their size. The overall size of ordinary devices is more than 5 mm, and the overall size of miniature devices is less than 5 mm. Commonly used piezoelectric vibration energy harvesters consist of a proof mass and a cantilever beam. A piezoelectric layer is provided on the cantilever beam. When the foundation vibrates, the cantilever beam undergoes bending vibration under the inertial force of the proof mass. The piezoelectric layer on the cantilever beam converts the strain energy of the beam into electrical energy output. Figure 1 It is a typical micro vibration energy collector that collects vertical vibration energy of the foundation. The micro device is made of silicon-based materials. Figure 2 This is the schematic diagram of the cantilever beam device with a piezoelectric layer. The foundation vibrates vertically, the device is fixed on the foundation, and the piezoelectric layer starts at the root of the beam, that is, the piezoelectric layer is located where the beam strain is larger. In order to collect more energy, the piezoelectric layer length L E Equal to the cantilever beam length L.

[0003] Many environmental vibration directions are multi-directional, not only vertically but also horizontally. However, for currently commonly used devices, such as Figure 2 The center of mass of its mass block is very close to the longitudinal axis of the cantilever beam (x-axis), and cannot generate a sufficiently large moment of inertia along the horizontal direction (x-axis direction). It is unidirectionally sensitive and cannot collect vibration energy in the horizontal direction (x-axis).

[0004] The most commonly used method to collect vibration energy in two directions at the same time is to place two Figure 1 The unidirectional sensitive device in the device collects vibration energy at the same time, that is, the energy in two directions is collected independently by two unidirectional collecting devices that are close together.

[0005] How to improve the existing technology and use a mass block to collect energy in two directions at the same time is a technical problem that needs to be solved urgently. Summary of the invention

[0006] Purpose of the invention: In view of the shortcomings of the prior art that the center of mass of the device mass block is close to the x-axis of the longitudinal axis of the cantilever beam, cannot generate sufficient inertia moment along the horizontal x-axis, cannot collect vibration energy in the horizontal direction, and can only collect vibration energy in the vertical direction, the present invention proposes a piezoelectric beam type bidirectional micromechanical vibration energy collector with an eccentric mass block, which uses the eccentric mass block to simultaneously collect vibration energy in two directions. The center of mass of the mass block of the present invention is far away from the longitudinal axis of the cantilever beam. When the foundation vibrates horizontally, the mass block generates a large horizontal inertia moment, causing the cantilever beam to vibrate and deform; the energy collector of the present invention simultaneously converts the vibration energy in the horizontal and vertical directions into electrical energy.

[0007] Technical solution: The piezoelectric beam-type bidirectional micromechanical vibration energy collector with an eccentric mass block of the present invention includes a substrate, a cantilever beam, and a mass block with an eccentric distance R0; the cantilever beam is arranged on the substrate; a piezoelectric layer is provided on the upper surface of the cantilever beam; the position starting point of the piezoelectric layer is at the root of the cantilever beam, and the width of the piezoelectric layer is equal to the width of the cantilever beam.

[0008] Figure 3 It is the first device of the present invention, wherein the mass block is supported by a cantilever beam with a piezoelectric layer. Figure 4 It is the first device of the present invention when there is no foundation. The present invention does not include a foundation.

[0009] In order to have the same energy collection capability in the vertical and horizontal directions, it satisfies the following relationship: The eccentricity of the mass block is Where L is the length of the cantilever beam, L E is the length of the piezoelectric layer. E is equal to the length of the cantilever beam L, and the eccentricity of the mass block is

[0010] The vertical and horizontal open circuit voltages of the vibration energy harvester must be the same. The open circuit voltage calculation formula is:

[0011]

[0012] Where b is the width of the piezoelectric layer, which is also the beam width; h0 is the thickness of the piezoelectric layer, L E is the length of the piezoelectric layer, A=b×L E is the area of ​​the piezoelectric layer, h 31 is the piezoelectric constant, constant u(x,t) is the cantilever beam deformation curve:

[0013] u(x,t)=φ(x)q(t) (2)

[0014] Where φ(x) is the known deformation function and q(t) is the time function.

[0015] The deformation curve of the cantilever beam under the vertical inertia force F is:

[0016]

[0017] In the formula, F 垂直 =ma 垂直 is the vertical inertial force, m is the mass of the mass block, a 垂直 is the vertical acceleration, E is the Young's modulus of the beam material, and I is the section moment of inertia of the beam;

[0018] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

[0019]

[0020] The deformation curve of the cantilever beam under the action of horizontal inertia moment is:

[0021]

[0022] Where M 水平 =ma 水平 R0 is the horizontal moment of inertia, a 水平 is the vertical acceleration, m is the mass of the mass block, E is the Young's modulus of the beam material, and I is the section moment of inertia of the beam;

[0023] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

[0024]

[0025] The open circuit voltage must be equal to: a 水平 =a 垂直 and Using the above two equations, the eccentric moment R0 of the mass block is the length L of the beam and the length L of the piezoelectric layer. E relation

[0026]

[0027] In particular, when the length of the piezoelectric layer is equal to the length of the beam, the eccentric moment of the mass is exactly Figure 5 The invention discloses a cantilever beam type bidirectional vibration energy collector in which the length of the piezoelectric layer is equal to the length of the beam.

[0028] Figure 6 The second device of the present invention is a mass block supported by two identical cantilever beams with piezoelectric layers on the left and right sides of the mass block, respectively. The length of the piezoelectric layer is L E . Figure 7The bidirectional vibration energy collector supported by the double cantilever beam of the present invention without foundation. In order to have the same energy collection capacity in vertical and horizontal directions, it satisfies the following relationship: The eccentricity of the mass block is R0 = L E When the piezoelectric layer length L E Equal to the length L of the left cantilever beam and the right cantilever beam, the eccentricity of the mass block is R0=L.

[0029] For vertical excitation, the deformation curve of the left cantilever support beam is

[0030]

[0031] Where E is Young's modulus of the beam material, and I is the section moment of inertia of the beam.

[0032] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is

[0033]

[0034] For vertical excitation, the deformation curve of the right cantilever support beam of the mass block is equal to the deformation curve of the left cantilever support beam, which yields:

[0035]

[0036] The lengths of the left and right beams of the present invention are equal. Under the action of the horizontal inertia moment, the deformation curve of the left cantilever support beam is

[0037]

[0038] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is

[0039]

[0040] Deformation curve of the right cantilever support beam

[0041]

[0042] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is

[0043]

[0044] Using equations (11) and (12), we can get

[0045]

[0046] The open circuit voltage must be equal to: a 水平 =a 垂直 and D 水平 =D 垂直, then the eccentric moment R0 of the mass block is the length L of the beam and the length L of the piezoelectric layer E relation

[0047] R0=L E (16)

[0048] In particular, when the length of the piezoelectric layer is equal to the length of the beam, the eccentric moment of the mass R0=L. Figure 8 It is a mechanical principle diagram of a double cantilever beam type bidirectional vibration energy harvester in which the piezoelectric layer length is equal to the beam length.

[0049] Working principle: The center of mass of the mass block of the current device is very close to the longitudinal axis (x-axis) of the cantilever beam, and cannot generate sufficient moment of inertia along the horizontal direction (x-axis), and cannot collect vibration energy in the horizontal direction, but can only collect vibration energy in the vertical direction. The micromechanical vibration energy collector of the present invention utilizes a cantilever beam with an eccentric mass block to simultaneously complete vibration energy collection in both vertical and horizontal directions. The center of mass of the mass block of the present invention is relatively large from the longitudinal axis of the cantilever beam. When the foundation vibrates horizontally, the mass block also generates a large horizontal moment of inertia, causing the cantilever beam to vibrate and deform. The present invention is also applicable to macro-mechanical vibration energy collectors. The difference between the above-mentioned macro-mechanical vibration energy collector and the present invention is that the substrate and cantilever beam of the macro-mechanical vibration energy collector are made of other materials and processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a typical structure diagram of a micro-mechanical vibration (unidirectional) energy collector that collects vertical vibration energy from the foundation;

[0051] Figure 2 This is a schematic diagram of the working principle of the currently commonly used unidirectional cantilever beam vibration energy harvester;

[0052] Figure 3 The schematic diagram of the cantilever beam vibration energy collector of the present invention which can collect horizontal and vertical vibration energy simultaneously;

[0053] Figure 4 It is a cantilever beam type bidirectional vibration energy collector of the present invention (without foundation);

[0054] Figure 5 The structure diagram of the bidirectional vibration energy collector of the present invention in which the length of the piezoelectric layer is equal to the length of the cantilever beam;

[0055] Figure 6 It is a principle diagram (including foundation) of the bidirectional vibration energy collector supported by double cantilever beams of the present invention when it is working;

[0056] Figure 7 This is a diagram of a bidirectional vibration energy collector (without foundation) supported by a double cantilever beam of the present invention, wherein:

[0057] Figure 7 (a) is a front view of the bidirectional vibration energy collector (without foundation) supported by double cantilever beams of the present invention;

[0058] Figure 7 (b) is a top view of the bidirectional vibration energy collector (without foundation) supported by the double cantilever beam of the present invention;

[0059] Figure 8 It is a mechanical principle diagram of a double cantilever beam type bidirectional vibration energy harvester in which the piezoelectric layer length is equal to the beam length of the present invention;

[0060] Fig. 9 This is a structural diagram of a cantilever beam type bidirectional vibration energy collector in which the piezoelectric layer length is equal to the beam length of the present invention;

[0061] Fig.10 This is a diagram of an embodiment of the present invention (without substrate and foundation);

[0062] Fig.11 It is a comparison diagram of the voltage of the vertical vibration displacement (solid line) and the voltage of the horizontal vibration displacement (dashed line) of the present invention. DETAILED DESCRIPTION

[0063] The piezoelectric beam type bidirectional micromechanical vibration energy collector with an eccentric mass block of the present invention comprises a substrate 1, a cantilever beam 3, and a mass block 4 with an eccentric distance R0; the cantilever beam 3 is arranged on the substrate 1; the upper surface of the cantilever beam 3 has a piezoelectric layer 2, and the mass block 4 is supported by the cantilever beam 3. In order to collect more energy, the piezoelectric layer 2 is located at the root of the beam, and the length of the piezoelectric layer 2 is L E It is equal to the cantilever beam length L. The thickness of the piezoelectric layer h0 is very small relative to the thickness t of the beam and does not affect the vibration performance of the beam. The y direction is the direction of the thickness h0 and t.

[0064] Figure 3 This is the first structural diagram of the bidirectional micromechanical vibration energy harvester of the present invention, in which the mass block is supported by a cantilever beam with a piezoelectric layer. When the energy harvester is working, the rigid substrate is tightly fixed on the vibrating foundation, and the vibration of the foundation causes the mass block to vibrate, resulting in the deformation of the cantilever beam.

[0065] In order to have the same energy collection capability in the vertical and horizontal directions, it satisfies the following relationship: The eccentricity of the mass block is Where L is the length of the cantilever beam, L E is the length of the piezoelectric layer. E is equal to the length of the cantilever beam L, and the eccentricity of the mass block is

[0066] Figure 4This is the bidirectional vibration energy collector of the present invention when there is no foundation. The length, width and thickness directions of the beam are respectively in the x, z and y directions. The center of mass of the mass block of the present invention is larger than the x-axis dimension R0. When the foundation vibrates vertically, the present invention Figure 1 However, when the foundation vibrates horizontally, the mass block of the present invention has a large inertial force arm, which generates a large horizontal inertial moment, causing the cantilever beam to vibrate and deform, causing the piezoelectric layer to generate electric charge, thus completing energy conversion. Figure 1 The center of mass of the current device mass block is very close to the x-axis, the inertial force arm is small, and it cannot generate sufficient horizontal inertial moment.

[0067] In order to make the energy harvester have the same vibration energy harvesting capability in the vertical and horizontal directions, the open circuit voltage in the vertical and horizontal directions should be equal. The open circuit voltage calculation formula is:

[0068]

[0069] Where b is the width of the piezoelectric layer, which is also the beam width, h0 is the thickness of the piezoelectric layer, and L E is the length of the piezoelectric layer, A=b×L E is the area of ​​the piezoelectric layer, h 31 is the piezoelectric constant, constant u(x,t) is the cantilever beam deformation curve, written as:

[0070] u(x,t)=φ(x)q(t) (2)

[0071] Where φ(x) is the known deformation function and q(t) is the time function.

[0072] The deformation curve of the cantilever beam under the vertical inertia force F is:

[0073]

[0074] In the formula, F 垂直 =ma 垂直 is the vertical inertial force, m is the mass of the mass block, a 垂直 is the vertical acceleration, E is the Young's modulus of the beam material, and I is the section moment of inertia of the beam.

[0075] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

[0076]

[0077] The deformation curve of the present invention under the action of horizontal inertia moment is:

[0078]

[0079] Where M 水平=ma 水平 R0 is the horizontal moment of inertia, a 水平 is the vertical acceleration, m is the mass of the mass block, E is the Young's modulus of the beam material, and I is the section moment of inertia of the beam.

[0080] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

[0081]

[0082] The open circuit voltage must be equal to: a 水平 =a 垂直 and Using the above two equations, the eccentric moment R0 of the mass block and the length L of the beam and the length L of the piezoelectric layer E relation:

[0083]

[0084] In particular, when the length of the piezoelectric layer is equal to the length of the beam, the eccentric moment of the mass is Figure 5 The invention discloses a bidirectional vibration energy collector in which the length of the piezoelectric layer is equal to the length of the cantilever beam.

[0085] Figure 6 The second device of the present invention is a mass block supported by two identical cantilever beams with piezoelectric layers on the left and right sides of the mass block, respectively. The length of the piezoelectric layer is L E In order to have the same energy collection capability in the vertical and horizontal directions, it satisfies the following relationship: The eccentricity of the mass block is R0 = L E When the piezoelectric layer length L E Equal to the length L of the left cantilever beam and the right cantilever beam, the eccentricity of the mass block is R0=L.

[0086] For vertical excitation, the deformation curve of the left cantilever support beam is:

[0087]

[0088] Where E is Young's modulus of the beam material, and I is the section moment of inertia of the beam.

[0089] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

[0090]

[0091] For vertical excitation, the deformation curve of the right cantilever support beam of the mass block is equal to the deformation curve of the left cantilever support beam, so:

[0092]

[0093] Where D垂直 Represents the integral in the vertical direction.

[0094] The lengths of the left and right beams of the present invention are equal. Under the action of the horizontal inertia moment, the deformation curve of the left cantilever support beam is:

[0095]

[0096] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

[0097]

[0098] Deformation curve of the right cantilever support beam:

[0099]

[0100] The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

[0101]

[0102] Using equations (11) and (12), we can obtain:

[0103]

[0104] The open circuit voltage must be equal to: a 水平 =a 垂直 and |D 水平 |=|D 垂直 |, the eccentric moment R0 of the mass block is related to the length L of the cantilever beam and the length L of the piezoelectric layer E relation:

[0105] R0=L E (16)

[0106] In particular, when the length of the piezoelectric layer is equal to the length of the beam, the eccentric moment of the mass R0=L. Figure 8 It is a mechanical working principle diagram of a double cantilever beam type bidirectional vibration energy harvester in which the piezoelectric layer length is equal to the beam length.

[0107] Example:

[0108] The specific effects of the present invention are shown in the following examples.

[0109] like Fig. 9 Consider a micro cantilever beam vibration energy harvester placed on a vibrating foundation, and the natural frequency of the vibration energy harvester is set to 500Hz. Assume that the vertical vibration of the foundation is equal to the horizontal vibration, both are 200Hz, and the amplitude is 10 microns, that is, y(t) = x(t) = a0sinω1t, where ω1 = 1256.6rad / s.

[0110] The mass block and the beam are made of single crystal silicon or polycrystalline silicon. In this embodiment, the mass block and the beam are made of single crystal silicon, with Young's modulus E = 130 GPa and density ρ = 2330 kgm -3 The length, width and thickness of the cantilever beam are in the x-direction, z-direction and y-direction respectively. The length L, width and thickness of the cantilever beam are 3000 μm, 1000 μm and 20 μm respectively. The mass of the mass block corresponding to the natural frequency is 9.757×10 -7 kg. The length and width of the piezoelectric layer are equal to the length and width of the cantilever beam. The thickness of the piezoelectric layer is 0.2μm, which is very small relative to the thickness of the beam and does not affect the vibration performance of the beam. The piezoelectric constant is 17pm / V.

[0111] In this embodiment, the mass block is a rectangular hexahedron. According to the working principle of the present invention, the size of the mass block is determined according to the following steps. First, the eccentricity of the mass block Therefore, the length of the mass block (dimension in the y direction) is equal to the length of the cantilever beam 3000μm; secondly, the width of the mass block (in the z direction) is equal to the width of the cantilever beam 1000μm; finally, according to the mass, length, width and density of the mass block, the thickness of the rectangular mass block (dimension in the x direction) is 1396μm. Fig.10 It is a main dimension diagram of the embodiment, in which the width direction of the beam is the z direction, excluding the substrate and foundation. Fig.11 is the output open-circuit voltage of this example under horizontal and vertical excitation respectively. Fig.11 It is concluded that under the same magnitude of excitation, the difference between the two voltages is less than 20%, so the horizontal and vertical directions have the same energy collection capabilities and can collect vibration energy in both directions at the same time.

[0112] If the length of the piezoelectric layer in this example is not equal to the cantilever beam length, for example: L E =2000μm, then since R0 = LL E / 2, so the length of the mass block (y-direction dimension) must be equal to the cantilever beam length 4000μm; the width of the mass block (z-direction) is equal to the cantilever beam width 1000μm. According to the mass, length, width and density of the mass block, the thickness of the rectangular mass block (x-direction dimension) is 1047μm.

Claims

1. A piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block, characterized in that: It comprises a substrate (1), a cantilever beam (3), and a mass block (4) having an eccentric distance R0; the cantilever beam (3) is arranged on the substrate (1); a piezoelectric layer (2) is provided on the upper surface of the cantilever beam (3); the starting point of the piezoelectric layer (2) is at the root of the cantilever beam, and the width of the piezoelectric layer (2) is equal to the width of the cantilever beam; The eccentricity of the mass block (4) is Where L is the length of the cantilever beam, L E is the length of the piezoelectric layer.

2. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 1, characterized in that: The length L of the piezoelectric layer (2) E is equal to the length of the cantilever beam L, and the eccentricity of the mass block (4) is 3. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 1, characterized in that: The two sides of the mass block (4) are supported by a left cantilever beam and a right cantilever beam with the same piezoelectric layer (2), and the length of the piezoelectric layer (2) is L. E , the eccentricity of the mass block (4) is R0 = L E .

4. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 1, characterized in that: The two sides of the mass block (4) are supported by a left cantilever beam and a right cantilever beam with the same piezoelectric layer (2), wherein the length of the piezoelectric layer (2) is L E Equal to the length L of the left cantilever beam and the right cantilever beam, the eccentricity of the mass block (4) is R0=L.

5. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 1, characterized in that: The mass block (4) and the cantilever beam (3) are made of single crystal silicon material.

6. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 1, characterized in that: The open circuit voltages of the vibration energy harvester in the vertical and horizontal directions are equal, and the open circuit voltage calculation formula is: Where b is the width of the piezoelectric layer, which is also the beam width; h0 is the thickness of the piezoelectric layer, L E is the length of the piezoelectric layer, A=b×L E is the area of ​​the piezoelectric layer, h 31 is the piezoelectric constant, constant u(x,t) is the cantilever beam deformation curve: u(x,t)=φ(x)q(t) (2) Where φ(x) is the known deformation function and q(t) is the time function.

7. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 1, characterized in that: The deformation curve of the cantilever beam under the action of the vertical inertia force F is: In the formula, F 垂直 =ma 垂直 is the vertical inertial force, m is the mass of the mass block, a 垂直 is the vertical acceleration, E is the Young's modulus of the beam material, and I is the section moment of inertia of the beam; The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is:

8. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 7, characterized in that: The deformation curve of the cantilever beam under the action of horizontal inertia moment is: Where M 水平 =ma 水平 R0 is the horizontal moment of inertia, a 水平 is the vertical acceleration, m is the mass of the mass block, E is the Young's modulus of the beam material, and I is the section moment of inertia of the beam; The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is: a 水平 =a 垂直 and When the open circuit voltage is equal, the eccentric moment R0 of the mass block is equal to the length L of the beam and the length L of the piezoelectric layer. E relation When the length of the piezoelectric layer is equal to the length of the beam, the eccentric moment of the mass is 9. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 4, characterized in that: The deformation curve of the left cantilever support beam under vertical excitation is: Where, E is the Young's modulus of the beam material, and I is the section moment of inertia of the beam; The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is For vertical excitation, the deformation curve of the right cantilever beam of the mass block is equal to the deformation curve of the left cantilever beam, which yields: Where D 垂直 Represents the integral in the vertical direction.

10. The piezoelectric beam type bidirectional micromechanical vibration energy harvester with an eccentric mass block according to claim 4, characterized in that: The deformation curve of the left cantilever support beam under the horizontal inertia moment is: The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is: The deformation curve of the right cantilever support beam is: The corresponding second-order derivative integral of the deformation curve in the open circuit voltage is: Through equations (11) and (12), we can get a 水平 =a 垂直 and D 水平 =D 垂直 , then the open circuit voltage is equal, and the eccentric moment R0 of the mass block is related to the length L of the cantilever beam and the length L of the piezoelectric layer. E relation R0=L E (16).

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