Multi-directional active vibration control of 1D smart structure inspired by automotive engine mounting system Hojoon Moon 1 Yeungnam University 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea Yang Qiu 2 Yeungnam University 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea Byeongil Kim 3

Yeungnam University 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, Republic of Korea

ABSTRACT Recently, active mounting system is being gradually applied to automotive engine mounts for mitigating structure-borne vibration effectively throughout the whole vehicle chassis. This paper presents modeling, analysis, and control of a source structure with an active mounting system in multi-directions, considering position and direction of actual automotive engine mounts. The active mount consists of a piezoelectric stack actuator in series with an elastomeric(rubber) mount. When harmonic excitation forces are employed, secondary force required for each active mount is calculated mathematically and the control signal can reduce the vibration through the destructive interference with input signal. In addition, the horizontal vibration can also be mitigated by setting a variable parameter through the dynamic relation of source structure. A series of simulation results demonstrate that the excitation vibration could be reduced along with this multi- directional(vertical and horizontal) active mounts. Based on this result, it can be expected that noise vibration harshness(NVH) performance can be improved by controlling the vibration of the actual automotive engine structure with rubber mount and secondary force of actuators in both vertical and horizontal directions.

1. INTRODUCTION

Nowadays, automobile development places importance on lightweight structure, high engine efficiency, and ride comfort. Therefore, research on an engine mounting system that supports the powertrain and insulates the excitation force transmitted to the vehicle chassis is becoming important. Most vehicles are fitted with passive mounts (rubber or hydraulic). However, the rubber

1 answns5@naver.com

2 positive0919@ynu.ac.kr

3 bikim@yu.ac.kr

mounts cannot mitigate vibration due to increased dynamic stiffness in the high frequency domain, and hydraulic mounts cannot mitigate vibration in the high frequency domain, although vibration is exceptionally mitigated at the notch frequency. To solve this problem, research on semi-active and active mounts is being conducted.

Li Sui et al. [1] showed that the use of a PZT actuator as a vehicle engine mount reduces vibration due to engine excitation (low frequency-low amplitude) at engine idle and vibration due to engine excitation (high frequency-low amplitude) during driving by 80%.Liette et al. [2] conducted a study to reduce vibration using two active paths composed of a piezo stack actuator and a rubber mount, and to quantify the interaction between the dynamic characteristics of the passive system and the active path. Based on the 6DOF model of the beam structure, vibration isolation was verified through simulations and experiments. Hong et al. [3] designed a 9-DOF model of the plate structure to consider the effect of rotational displacement in addition to previous studies, and performed realistic simulations as a result.

Although research on such an engine mount continues, unlike an actual engine mount, only an actuator that connects the engine and the chassis vertically is in progress. Therefore, in this study, the effect of vibration mitigation in the vertical and horizontal directions using vertical and horizontal actuators for the engine and chassis was investigated. To connect the source and receiver in the horizontal direction, the source structure is designed as a beam structure bent in an 'L' shape. Therefore, this article does the following: 1) A lumped parameter model is proposed for the given structure and equations of motion are established. And 2) Performing simulations and analyze the results to propose how to improve the vehicle’s NVH performance

2. Modeling and Control force

2.1. Lumped parameter model

The model of source-path-receiver system considering actual automotive engine mounts was established based on the lumped parameter model, as shown in Figure.1

Figure 1: Source-paths-receiver modeling In Figure 1, source means vehicle engine, path means active mounts that consists of a piezoelectric actuator and a rubber mount, and receiver means the sub-frame. 𝑚 𝑖 means mass of beam, 𝑚 𝑎𝑐𝑖 means mass of piezoelectric stack actuator, 𝐼 𝑖

𝑦 means moment of inertia in y axis. 𝑙 𝑠𝑖 means length from center of gravity at source, 𝑙 𝑟𝑖 means length from center of gravity at receiver. 𝑑 means the length from center of gravity of source to the external force. 𝜀 𝑖

𝑧 , 𝜀 𝑎𝑐𝑖

𝑧 mean the vertical motion of the beam and actuator. 𝜀 𝑎𝑐2

𝑦 means the rotational motions of beam. 𝑘 𝑚𝑖 , 𝑐 𝑚𝑖 means stiffness and damping values between beam and actuator. 𝑘 𝑏𝑖 , 𝑐 𝑏𝑖 means stiffness and damping values between beam and ground. 𝑓 𝑎𝑐1

𝑥 means the horizontal motion of actuator2. 𝜃 𝑖

𝑥 means control force from each actuators. 𝑊 𝑧 means external force. All of the above parameters are determined based on the data measured by the experiment. This model can be expressed motion equation using Newton’s 2 nd law.

𝑧 , 𝑓 𝑎𝑐2

𝑀𝑞̈(𝑡) + 𝐶𝑞̇(𝑡) + 𝐾𝑞(𝑡) = 𝑊(𝑡) + 𝐹(𝑡) , (1)

In equation (1), M, K, C are mass, damping, stiffness matrix and 𝑞(𝑡), 𝑊(𝑡), 𝐹(𝑡) are displacement, external force, control force vector. It is assumed that displacement exists in the x-direction and z- direction, and rotational motion exists in the y-direction. Thus, overall model has five translational motions and two rotational motions, indicating that it is a 7 DOF system.

𝑦 𝐼 2

𝑦 ]) (2)

𝑀= 𝑑𝑖𝑎𝑔([𝑚 1 𝑚 2 𝑚 𝑎𝑐1 𝑚 𝑎𝑐2 𝑚 𝑎𝑐2 𝐼 1

𝑧 + 𝑘 𝑚2

𝑧 0 −𝑘 𝑚1

𝑧 −𝑘 𝑚2

𝑧

[ 𝑘 𝑚1

𝑧 + 𝑘 𝑏2

𝑧 −𝑘 𝑚3

𝑧 + 𝑘 𝑚4

𝑧 + 𝑘 𝑏1

𝑧 −𝑘 𝑚4

𝑧

0 𝑘 𝑚3

𝑧 −𝑘 𝑚3

𝑧 𝑘 𝑚1

𝑧 + 𝑘 𝑚3

𝑧 0 −𝑘 𝑚2

−𝑘 𝑚1

𝑧 −𝑘 𝑚4

𝑧 0 𝑘 𝑚2

𝑧 + 𝑘 𝑚4

𝑧

𝐾=

𝑧𝑥 𝑘 𝑚4

𝑧𝑥 0 −𝑘 𝑚2

𝑧𝑥 −𝑘 𝑚4

𝑧𝑥

𝑘 𝑚2

𝑧 𝑙 𝑠2 −𝑘 𝑚2

𝑧𝑥 𝑙 𝑠3 −𝑘 𝑚1

𝑧 𝑙 𝑠1 0 𝑘 𝑚1

𝑧 𝑙 𝑠1 𝑘 𝑚2

𝑧𝑥 𝑙 𝑠3 −𝑘 𝑚2

𝑧 𝑙 𝑠2 0 𝑘 𝑚3

𝑘 𝑚2

𝑧 𝑙 𝑟1 + 𝑘 𝑏2

𝑧 𝑙 𝑟2 −𝑘 𝑚4

𝑧 𝑙 𝑟3 + 𝑘 𝑚4

𝑧 𝑙 𝑟4 −𝑘 𝑏1

𝑧𝑥 𝑙 𝑟5 −𝑘 𝑚3

𝑧 𝑙 𝑟3 −𝑘 𝑚4

𝑧 𝑙 𝑟4 + 𝑘 𝑚4

𝑧𝑥 𝑙 𝑟5

(3)

𝑧𝑥 𝑘 𝑚2

𝑧 𝑙 𝑠2 −𝑘 𝑚1

𝑧 𝑙 𝑠1 −𝑘 𝑚2

𝑧𝑥 𝑙 𝑠3 0 𝑘 𝑚4

𝑘 𝑚2

𝑧 𝑙 𝑟1 + 𝑘 𝑏2

𝑧 𝑙 𝑟2 −𝑘 𝑚4

𝑧𝑥 0 𝑘 𝑚3

𝑧 𝑙 𝑟3 + 𝑘 𝑚4

𝑧 𝑙 𝑟4 −𝑘 𝑏1

𝑧𝑥 𝑙 𝑟5 0 𝑘 𝑚1

𝑧 𝑙 𝑠1 −𝑘 𝑚3

𝑧 𝑙 𝑟3 −𝑘 𝑚2

𝑧𝑥 −𝑘 𝑚4

𝑧𝑥 𝑘 𝑚2

𝑧𝑥 𝑙 𝑠3 −𝑘 𝑚2

𝑧 𝑙 𝑠2 𝑘 𝑚4

𝑧𝑥 𝑙 𝑟5 −𝑘 𝑚4

𝑧 𝑙 𝑟4 𝑘 𝑚2

𝑥 + 𝑘 𝑚4

𝑥 𝑘 𝑚2

𝑧𝑥 𝑙 𝑠2 −𝑘 𝑚2

𝑥 𝑙 𝑠3 𝑘 𝑚4

𝑧𝑥 𝑙 𝑟4 −𝑘 𝑚4

𝑥 𝑙 𝑟5 𝑘 𝑚2

2 + 𝑘 𝑚2

2 + 𝑘 𝑚2

2 −2𝑘 𝑚2

𝑧𝑥 𝑙 𝑠2 −𝑘 𝑚2

𝑥 𝑙 𝑠3 𝑘 𝑚1

𝑧 𝑙 𝑠1

𝑧 𝑙 𝑠2

𝑥 𝑙 𝑠3

𝑧𝑥 𝑙 𝑠2 𝑙 𝑠3 0 −𝑘 𝑚4

2 + 𝑘 𝑚4

2 + 𝑘 𝑚4

2 + 𝑘 𝑏1

2 + 𝑘 𝑏2

2 −2𝑘 𝑚4

𝑧 𝑙 𝑟1

𝑧 𝑙 𝑟2

𝑥 𝑙 𝑟5 + 𝑘 𝑚4

𝑧𝑥 𝑙 𝑟4 0 𝑘 𝑚3

𝑧 𝑙 𝑟3

𝑧 𝑙 𝑟4

𝑥 𝑙 𝑟5

𝑧𝑥 𝑙 𝑟5 𝑙 𝑟4 ]

𝑧 + 𝑐 𝑚2

𝑧 0 −𝑐 𝑚1

𝑧 −𝑐 𝑚2

𝑧

[ 𝑐 𝑚1

𝑧 + 𝑐 𝑏2

𝑧 −𝑐 𝑚3

𝑧 + 𝑐 𝑚4

𝑧 + 𝑐 𝑏1

𝑧 −𝑐 𝑚4

𝑧

0 𝑐 𝑚3

𝑧 −𝑐 𝑚3

𝑧 𝑐 𝑚1

𝑧 + 𝑐 𝑚3

𝑧 0 −𝑐 𝑚2

−𝑐 𝑚1

𝑧 −𝑐 𝑚4

𝑧 0 𝑐 𝑚2

𝑧 + 𝑐 𝑚4

𝑧

𝐶=

𝑧𝑥 𝑐 𝑚4

𝑧𝑥 0 −𝑐 𝑚2

𝑧𝑥 −𝑐 𝑚4

𝑧𝑥

𝑐 𝑚2

𝑧 𝑙 𝑠2 −𝑐 𝑚2

𝑧𝑥 𝑙 𝑠3 −𝑐 𝑚1

𝑧 𝑙 𝑠1 0 𝑐 𝑚1

𝑧 𝑙 𝑠1 𝑐 𝑚2

𝑧𝑥 𝑙 𝑠3 −𝑐 𝑚2

𝑧 𝑙 𝑠2 0 𝑐 𝑚3

𝑐 𝑚2

𝑧 𝑙 𝑟1 + 𝑐 𝑏2

𝑧 𝑙 𝑟2 −𝑐 𝑚4

𝑧 𝑙 𝑟3 + 𝑐 𝑚4

𝑧 𝑙 𝑟4 −𝑐 𝑏1

𝑧𝑥 𝑙 𝑟5 −𝑐 𝑚3

𝑧 𝑙 𝑟3 −𝑐 𝑚4

𝑧 𝑙 𝑟4 + 𝑐 𝑚4

𝑧𝑥 𝑙 𝑟5

(4)

𝑧𝑥 𝑐 𝑚2

𝑧 𝑙 𝑠2 −𝑐 𝑚1

𝑧 𝑙 𝑠1 −𝑐 𝑚2

𝑧𝑥 𝑙 𝑠3 0 𝑐 𝑚4

𝑐 𝑚2

𝑧 𝑙 𝑟1 + 𝑐 𝑏2

𝑧 𝑙 𝑟2 −𝑐 𝑚4

𝑧𝑥 0 𝑐 𝑚3

𝑧 𝑙 𝑟3 + 𝑐 𝑚4

𝑧 𝑙 𝑟4 −𝑐 𝑏1

𝑧𝑥 𝑙 𝑟5 0 𝑐 𝑚1

𝑧 𝑙 𝑠1 −𝑐 𝑚3

𝑧 𝑙 𝑟3 −𝑐 𝑚2

𝑧𝑥 −𝑐 𝑚4

𝑧𝑥 𝑐 𝑚2

𝑧𝑥 𝑙 𝑠3 −𝑐 𝑚2

𝑧 𝑙 𝑠2 𝑐 𝑚4

𝑧𝑥 𝑙 𝑟5 −𝑐 𝑚4

𝑧 𝑙 𝑟4 𝑐 𝑚2

𝑥 + 𝑐 𝑚4

𝑥 𝑐 𝑚2

𝑧𝑥 𝑙 𝑠2 −𝑐 𝑚2

𝑥 𝑙 𝑠3 𝑐 𝑚4

𝑧𝑥 𝑙 𝑟4 −𝑐 𝑚4

𝑥 𝑙 𝑟5 𝑐 𝑚2

2 + 𝑐 𝑚2

2 + 𝑐 𝑚2

2 −2𝑐 𝑚2

𝑧𝑥 𝑙 𝑠2 −𝑐 𝑚2

𝑥 𝑙 𝑠3 𝑐 𝑚1

𝑧 𝑙 𝑠1

𝑧 𝑙 𝑠2

𝑥 𝑙 𝑠3

𝑧𝑥 𝑙 𝑠2 𝑙 𝑠3 0 −𝑐 𝑚4

2 + 𝑐 𝑚4

2 + 𝑐 𝑚4

2 + 𝑐 𝑏1

2 + 𝑐 𝑏2

2 −2𝑐 𝑚4

𝑧 𝑙 𝑟1

𝑧 𝑙 𝑟2

𝑥 𝑙 𝑟5 + 𝑐 𝑚4

𝑧𝑥 𝑙 𝑟4 0 𝑐 𝑚3

𝑧 𝑙 𝑟3

𝑧 𝑙 𝑟4

𝑥 𝑙 𝑟5

𝑧𝑥 𝑙 𝑟5 𝑙 𝑟4 ]

𝑇

𝑦 (𝑡) 𝜃 2

𝑦 (𝑡)]

(5)

𝑥 (𝑡) 𝜃 1

𝑧 (𝑡) 𝜀 2

𝑧 (𝑡) 𝜀 𝑎𝑐1

𝑧 (𝑡) 𝜀 𝑎𝑐2

𝑧 (𝑡) 𝜀 𝑎𝑐2

𝑞(𝑡) = [𝜀 1

𝑊(𝑡) = [𝑊 𝑧 (𝑡) 0 0 0 0 𝑊 𝑧 (𝑡)𝑑 0] 𝑇 (6)

𝑥 (𝑡) 0 0] 𝑇 (7)

𝑧 (𝑡) 0 𝑓 𝑎𝑐2

𝐹(𝑡) = [0 0 𝑓 𝑎𝑐1

In order to focus on the effect of active mount, the displacement vector was changed using an appropriate transform matrix.

𝑥 (𝑡) 𝜉 𝑚3

𝑧 (𝑡) 𝜉 𝑚2

𝑧 (𝑡) 𝜀 𝑎𝑐1

𝑧 (𝑡) 𝜀 𝑎𝑐2

𝑧 (𝑡) 𝜀 𝑎𝑐2

𝑧 (𝑡) 𝜉 𝑚4

𝑧 (𝑡)] 𝑇 (8)

𝜉(𝑡) = [𝜉 𝑚1

2.2. Dynamic relation equation

Horizontal displacement can be known through the dynamic relationship of the structure. The horizontal displacement of the source close to the horizontal active mount is defined by Equation (9).

𝑦

𝑥 (𝑡) = (𝑡𝑎𝑛 𝜃 1

2 + 𝑙 𝑠3

𝑧 (𝑡) (9)

𝜉 𝑚2

) 𝜉 𝑚2

𝑙 𝑠2

𝑦 , θ 2

𝑦 ≪1 , Equation (9) is linearized and defined by Equation (10).

Assuming that θ 1

𝑦

𝑥 (𝑡) = ( 𝜃 1

2 + 𝑙 𝑠3

𝑧 (𝑡) (10)

𝜉 𝑚2

) 𝜉 𝑚2

𝑙 𝑠2

Likewise, the horizontal displacement of receiver is defined by Equation (11).

𝑦

𝑥 (𝑡) = 𝜃 2

𝑧 (𝑡) (11)

𝜉 𝑚4

2 𝜉 𝑚4

Therefore vertical displacement can be adjusted to control horizontal vibration at each position.

2.3. Theoretical control force

When using damping material, the stiffness value can be expressed in a complex value. Also the external force and control force are assumed to be harmonic force. It is defined by Equation (12),

𝑊 𝑧∗ (𝑡) = 𝑊 𝑧 𝑒 𝑖𝜔𝑡 , 𝑓 𝑎𝑐𝑖 (𝑡) = 𝐹 𝑎𝑐𝑖

∗ 𝑒 𝑖(𝜔𝑡+∅ 𝑎𝑐𝑖 ) (12)

ω is frequency of external force and ∅ aci is the phase value of each path. The phase between harmonic force and motion has an important relationship. Since the system is linear, the displacement for external force and control force is represented by Equation (13).

z |𝑒 𝑖(𝛽 𝑠𝑗.3 +𝜙 𝑎𝑐1 ) + |Ξ 𝑠𝑗.5

z |𝑒 𝑖𝛽 𝑠𝑗.1 + |Ξ 𝑠𝑗.3

𝑧 (𝑡) = (|Ξ 𝑠𝑗.1

z |𝑒 𝑖(𝛽 𝑠𝑗.5 +𝜙 𝑎𝑐2 ) )𝑒 𝑖𝜔𝑡 (13)

𝜉 𝑗

z is the amplitude of displacement due to an external force, Ξ 𝑠𝑗.3

z , Ξ 𝑠𝑗.5

z are the amplitude of displacement due to control force 𝑓 ac1 and 𝑓 𝑎𝑐2 . Likewise 𝛽 𝑠𝑗.1 is phase due to external force and 𝛽 𝑠𝑗.3 , 𝛽 𝑠𝑗.5 are phase due to control force, respectively. Compliance matrix is required to calculate the response. It is obtained by inverse matrix of dynamic stiffness matrix.

Ξ 𝑠𝑗.1

[ 𝐻 11 𝐻 12 𝐻 13 𝐻 14 𝐻 15 𝐻 16 𝐻 17 𝐻 21 𝐻 22 𝐻 23 𝐻 24 𝐻 25 𝐻 26 𝐻 27 𝐻 31 𝐻 32 𝐻 33 𝐻 34 𝐻 35 𝐻 36 𝐻 37 𝐻 41 𝐻 42 𝐻 43 𝐻 44 𝐻 45 𝐻 46 𝐻 47 𝐻 51 𝐻 52 𝐻 53 𝐻 54 𝐻 55 𝐻 56 𝐻 57 𝐻 61 𝐻 62 𝐻 63 𝐻 64 𝐻 65 𝐻 66 𝐻 67 𝐻 71 𝐻 72 𝐻 73 𝐻 74 𝐻 75 𝐻 76 𝐻 77 ]

(14)

𝐻=

𝑧 = (𝐻 𝑗1 + 𝐻 𝑗6 𝑑)𝑊 𝑧 , 𝛯 𝑠𝑗.3

𝑧 = 𝐻 𝑗3 𝐹 𝑎𝑐1 , 𝛯 𝑠𝑗.5

𝑧 = 𝐻 𝑗5 𝐹 𝑎𝑐2 𝛽 𝑠𝑗.1 = ∠(𝐻 𝑗1 + 𝐻 𝑗6 𝑑), 𝛽 𝑠𝑗.3 = ∠𝐻 𝑗3 , 𝛽 𝑠𝑗.5 = ∠𝐻 𝑗5 (15)

𝛯 𝑠𝑗.1

The phase value of Equation (13) is appropriately adjusted to the same value. Then the control force amplitude value that makes the displacement zero can be calculated. Governing equation of displacement is summarized in Equation (16).

𝑧 | + | 𝛯 𝑠𝑗.3

𝑧 | + | 𝛯 𝑠𝑗.5

𝑧 | = 0 (16)

𝑧 (𝑡) = | 𝛯 𝑠𝑗.1

𝜉 𝑗

Expressing Equation (16) in the form of a matrix is as follows.

|𝐻 𝑖1 + 𝑑𝐻 𝑖6 | |𝐻 𝑗1 + 𝑑𝐻 𝑗6 | } (17)

[ |𝐻 𝑖3 | |𝐻 𝑖5 | |𝐻 𝑗3 | |𝐻 𝑗5 | ] {𝐹 𝑎𝑐1

𝐹 𝑎𝑐2 } = −𝑊 𝑧 {

Through Equation (17), the control force amplitude value is calculated.

|𝐻 𝑖5 ||𝐻 𝑗1 + 𝑑𝐻 𝑗6 | −|𝐻 𝑗5 ||𝐻 𝑖1 + 𝑑𝐻 𝑖6 |

𝐹 𝑎𝑐1 = 𝑊 𝑧 (

|𝐻 𝑖3 ||𝐻 𝑗5 | −|𝐻 𝑖5 ||𝐻 𝑗3 | ) (18)

𝐹 𝑎𝑐2 = 𝑊 𝑧 ( |𝐻 𝑗3 ||𝐻 𝑖1 + 𝑑𝐻 𝑖6 | −|𝐻 𝑖5 ||𝐻 𝑗1 + 𝑑𝐻 𝑗6 |

|𝐻 𝑖3 ||𝐻 𝑗5 | −|𝐻 𝑖5 ||𝐻 𝑗3 | )

3. Simulation results and analysis

Based on the above definition, the vibration control method is divided into four cases: Case 1, Controls the two locations of the source. Case 2, Controls the two locations of the receiver. Case 3, Controls the source adjacent to the horizontal mount and the receiver adjacent to the vertical mount. Case 4, Controls the source adjacent to the vertical mount and receiver adjacent to the horizontal mount. In this study, it is assumed that the position of each mount matches the center of gravity of the receiver. The external force was given as a sine wave with an amplitude of 10N and a frequency of 400Hz. The uncontrolled results are shown in Figure 2.

Figure 2: Displacement at each position when uncontrolled As a result of calculating the control force for each case, in case 1, a vertical control of -4.96N and a horizontal control force of -12.33N were calculated. In case 2, control forces of -17.68N and - 19.82N, in case 3, 63.53N and -53.33N, in case 4, -4.96N and -12.33N were calculated. As a result of calculating the control force of each case, the case 2 and case 3 are not appropriate because they require very large control force compared to an external force. Figure 3illustrates the simulation results of the two case.

Figure 3: Displacement at each position when controlled. (a) Controls the two locations of the source,

(b) Controls the source adjacent to the vertical mount and receiver adjacent to the horizontal mount Table 1 and Table 2 show a root mean square (RMS) comparison of steady-state response for each cases. Table 1 : Displ acement and reduction rate through Case 1 [units: 𝛍𝐦 ]

Source Receiver

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒔

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒔

𝒙 𝑴𝒐𝒖𝒏𝒕𝟏 𝒓

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒓

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒓

𝒙

𝑴𝒐𝒖𝒏𝒕𝟏 𝒔

Uncontrolled 0.6022 1.0345 0.2924 0.0533 0.1878 1.39 × 10 −7

5.13 × 10 −7

Path 1 0 (100% ↓ )

0 (100% ↓ )

0 (100% ↓ )

0.1317 (147% ↑ )

0.3486 (86% ↑ )

(270% ↑ )

Path 2 0 (100% ↓ )

0 (100% ↓ )

0 (100% ↓ )

0.1319 (147% ↑ )

0.3486 (86% ↑ )

5.13 × 10 −7

(270% ↑ )

=

Table 2 : Displ acement and reduction rate through Case 4 [units: 𝛍𝐦 ]

Source Receiver

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒔

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒔

𝒙 𝑴𝒐𝒖𝒏𝒕𝟏 𝒓

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒓

𝒛 𝑴𝒐𝒖𝒏𝒕𝟐 𝒓

𝒙

𝑴𝒐𝒖𝒏𝒕𝟏 𝒔

Uncontrolled 0.6022 1.0345 0.2924 0.0533 0.1878 1.39 × 10 −7

4.59 × 10 −7

Path 1 0 (100% ↓ )

0.0639 (94% ↓ )

0.0181 (94% ↓ )

0.1209 (127% ↑ )

0.3314 (76% ↑ )

(231% ↑ )

Path 2 0.4772 (21% ↓ )

1.6355 (58% ↑ )

0.4623 (58% ↑ )

0.0705 (32% ↑ )

0 (100% ↓ )

0 (100% ↓ ) 4. CONCLUSIONS

As a result of the 7 DOF beam structure simulation, (1) If two locations of the source or receiver are controlled, the other are amplified. (2) Horizontal actuator requires a greater force than the vertical actuator to control vertical vibration. Reduced vibration of the receiver is required to improve vehicle NVH performance. Therefore, in order to improve the NVH performance of the actual automotive engine structure, the goal should be to mitigate the vibration of the source adjacent to the vertical mount and the receiver adjacent to the horizontal mount.

In the future research, experiments will be conducted through an experiment setup to experimentally verify the results of this study. 5. ACKNOWLEDGEMENTS

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2021R1A6A1A03039493) 6. REFERENCES

1. Li Sui, Xin Xiong, Gengchen Shi, Piezoelectric Actuator Design and Application on Active

Vibration Control. Physics Procedia 25 ( 2012 ) 1388 – 1396 2. Jared Liette, Jason T. Dreyer, Rajendra Singh, Interaction between two active structural paths

for source mass motion control over mid-frequency range. Journal of Sound and Vibration 333 (2014) 2369–2385 3. Hong, D. & Kim, B. Quantification of active structural path for vibration reduction control of

plate structure under sinusoidal excitation. Applied Sciences, 9(4), 711 (2019).