Non-linear parametric vibration responses of composite plates on Pasternak foundations using extended dynamic stiffness method

ABSTRACT

In this work, the non-linear parametric vibration responses of rectangular laminated composite plates subjected on Pasternak foundation, under in-plane periodic compressive load applied along two opposite edges, are theoretically studied using the extended dynamic stiffness method. The authors present the new method to establish the exact dynamic stiffness matrices of rectangular laminated composite plates subjected to in-plane periodic forces based on general Von-Kármán large deflection plate theory. A set of second-order ordinary differential non-linear equations of extended Mathieu–Hill type with periodic coefficients is formed to determine the regions of dynamic instability and non-linear parametric vibration responses based on Bolotin method. The effects of various parameters such as static load, dynamic load, aspect ratio, boundary conditions, orthotropy and foundation stiffness factor on the dynamic instability regions and non-linear parametric vibration characteristics are investigated and discussed. For linear theory, the present results are found to be in agreement with available conclusions in the literature which was obtained based on the linear analysis.

KEYWORDS:

• Dynamic instability
• non-linear parametric vibrations
• dynamic stiffness method
• composite plate
• non-linear responses

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Hung Quoc Huynh

Dr. Hung Quoc Huynh, leader of Faculty of Civil Engineering, Mien Trung University of Civil Engineering, Tuyhoa City, Vietnam. (I am lecturer at Mien Trung University of Civil Engineering in Phu Yen Province, Vietnam. And also I am leader of Faculty of Civil Engineering. I have been teaching many subjects such as: Reinforced Concrete buildings, …I graduated in Engineering and Philosophy of doctor (PhD) of Civil Enigineering from Bach Khoa University (formerly Ho Chi Minh city University of Technology) which is a large higher education institution in Vietnam).

Hien Luong Thi Nguyen

Associate Prof. Dr. Hien Luong Thi Nguyen, Supervisor, University of Technology Ho Chi Minh City.

Hai Nguyen

Dr. Hai Nguyen, Vietnamese and Canadian, Co-Supervisor, University of Technology Ho Chi Minh City. (In 1988, he obtained his Ph.D. at Ecole Polytechnique, Université de Montréal, Montreal (Quebec), Canada, on the dynamic instability and non-linear response of rectangular plates. He was a senior lecturer at University of Technology Ho Chi Minh city, Hochiminh City, Vietnam, from 1995. He currently returns to Canada for his retirement.)