## 1 Introduction
A piezoelectric patch was used as the sensor to obtain the vibration amplitude. Through these sensors, the vibration of the glass plate was adjusted, which caused the continuous change of the tactile effect [12]. Many tactile feedback devices utilize position sensors to detect the spatial position of fingers to change the excitation frequency, so as to realize the continuous change of touch sensation. In realizing variable tactile sensations, this type of haptic device requires a closed-loop control system that needs to be supported by extra circuits. Researchers usually neglect the importance of structural dynamic design to implement more diverse tactile sensations under simple control. On the other hand, some applications of haptic devices are fabricated by array actuators. For example, a piezoelectric tactile feedback device developed by [PERSON] at the University in Canada had 64 piezoelectric exciters, 112 contact pins, and 36 grooves [13]. The tactile feedback actuator can realize the touch sensation of lines, surfaces, shapes, and geometric boundaries, but the structure of the device was very complex. In 2002, [PERSON] designed a texture reproduction tactile feedback device by means of piezoelectric sheet and pin array. The device connected the needle array excited by the piezoelectric plate and tactile plane as the skin tactile excitation, and the stylus array was arranged according to \(5\times 2\). The device used array touch to stimulate the human fingers, which produced different effects of tactile feedback [14]. In 2008, [PERSON] designed a broadband vibrotactile display, where a pin matrix tactile display composed of 12 piezoelectric bimorph actuators was used to elicit tactile sensations [15]. The piezoelectric bimorph actuator of the display possessed flat frequency characteristics in the perceivable bandwidth of vibratory sensations. In 2018, [PERSON] developed a vibrotactile pedestal device, which was a tactile-based information transmission device using multiple vibration actuators. The developed device consisted of 12 discrete vibrating tactile areas, mainly by using a large number of actuators to create the detailed haptics [16]. In 2015, [PERSON] of the University of Tokyo released a spatial ultrasonic tactile display device at the World Touch Technology Conference. The device uses a piezoelectric array driver to emit ultrasonic waves on a tactile plane to stimulate human skin to produce spatial tactile sensations [17]. The haptic feedback devices using array actuators have problems such as complex structure, they are not easy to carry, and have high cost. In the above-mentioned research report on the haptic feedback devices, it can be seen that few people have focused on the realization of a rich and diverse tactile pattern under open-loop control using the dynamic structural design of the haptic devices. To explore and solve the above-mentioned issues, [PERSON] presented a tactile feedback device fabricated by piezoelectric ciliary-like body beams [18; 19; 20]. The tactile feedback device can create a different rough or smooth feeling by changing the finger movement direction when the subject touches a point on the ciliary-like beam. In previous studies, the authors have investigated the free vibration characteristics of the ciliary-like beam. In addition, the anisotropic vibration tactile model of the ciliary-like beam was established for predicting the equivalent friction coefficient when locally covered and fully covered by skin. In [18], it was shown that the acceleration of the beam vibration is vital for effecting the equivalent friction coefficient, but the method of obtaining the forced acceleration response of the ciliary-like beam was not presented in detail. This paper presents the detailed solution of the forced response of the ciliary-like beam under piezoelectric excitation, and the instantaneous acceleration and the average acceleration effect on the skin are obtained. Meanwhile, the effect of the system parameters is also investigated.