Dr. Yu Guo was born on January 14, 1984. He is currently working at Midwestern State University Texas as an Associate Professor. He previously worked at Caterpillar Inc. as an engine structural and dynamics engineer. Dr. Guo was originally from China. He has his B.S. in Computer Engineering from South China University of Technology. He received his M.S. and Ph.D. in Mechanical Engineering at Southern Illinois University Edwardsville. Dr. Guo conducts research focusing on nonlinear vibration and impact dynamics. He has published 14 peer-reviewed journal papers, more than 15 conference articles, 4 book chapters, and 1 monograph. He has also conducted many professional presentations or invited lectures all over the world.

• Preface.- Introduction.- A Semi-Analytical Method.- Discretization of a Parametric Pendulum.- Bifurcation Trees.- Harmonic Frequency-Amplitude Characteristics.- Non-Travelable Periodic Motions.- Travelable Periodic Motions.- References.- Authors' Biographies.

Dr. Yu Guo was born on January 14, 1984. He is currently working at Midwestern State University Texas as an Associate Professor. He previously worked at Caterpillar Inc. as an engine structural and dynamics engineer. Dr. Guo was originally from China. He has his B.S. in Computer Engineering from South China University of Technology. He received his M.S. and Ph.D. in Mechanical Engineering at Southern Illinois University Edwardsville. Dr. Guo conducts research focusing on nonlinear vibration and impact dynamics. He has published 14 peer-reviewed journal papers, more than 15 conference articles, 4 book chapters, and 1 monograph. He has also conducted many professional presentations or invited lectures all over the world.

• Preface.- Introduction.- A Semi-Analytical Method.- Discretization of a Parametric Pendulum.- Bifurcation Trees.- Harmonic Frequency-Amplitude Characteristics.- Non-Travelable Periodic Motions.- Travelable Periodic Motions.- References.- Authors' Biographies.

Dr. Yu Guo was born on January 14, 1984. He is currently working at Midwestern State University Texas as an Associate Professor. He previously worked at Caterpillar Inc. as an engine structural and dynamics engineer. Dr. Guo was originally from China. He has his B.S. in Computer Engineering from South China University of Technology. He received his M.S. and Ph.D. in Mechanical Engineering at Southern Illinois University Edwardsville. Dr. Guo conducts research focusing on nonlinear vibration and impact dynamics. He has published 14 peer-reviewed journal papers, more than 15 conference articles, 4 book chapters, and 1 monograph. He has also conducted many professional presentations or invited lectures all over the world.

• Preface.- Introduction.- A Semi-Analytical Method.- Discretization of a Parametric Pendulum.- Bifurcation Trees.- Harmonic Frequency-Amplitude Characteristics.- Non-Travelable Periodic Motions.- Travelable Periodic Motions.- References.- Authors' Biographies.