本书稿是第一本专题讨论任意边界条件下层合梁、板、壳结构结构振动的专著。本书稿提供了一个完整的理论体系来分析任意边界条件下层合梁、板、壳结构的振动特性。内容如下：首先，本书稿系统地给出了不同结构理论下层合梁、板、壳结构有限变形过程中的应变、应力及它们之间的关系，建立了层合梁、板、壳结构的能量方程，并应用变分原理推导出其线性振动的控制方程和边界条件。其次，本书稿基于改进傅里叶级数提出了一种能够统一求解任意边界条件和任意层合形式下层合梁、板、壳结构振动问题的精确解法。最后本书稿以层合梁结构、板结构、柱壳和柱板结构、锥壳和锥板结构、球壳和球板结构、双曲浅壳结构等基础结构元为重点分析对象，详细给出了它们在不同边界条件、不同层合形式、不同几何和材料参数下的精确解，便于读者阅读、理解和应用。
1. Fundamental Equations of Laminated Beams，Plates and Shells.
1.1 Three-Dimensional Elasticity Theory in Curvilinear Coordinates
1.2 Fundamental Equations of Thin Laminated Shells
1.2.1 Kinematic Relations
1.2.2 Stress-Strain Relations and Stress Resultants
1.2.3 Energy Functions
1.2.4 Governing Equations and Boundary Conditions
1.3 Fundamental Equations of Thick Laminated Shells
1.3.1 Kinematic Relations
1.3.2 Stress-Strain Relations and Stress Resultants
1.3.3 Energy Functions
1.3.4 Governing Equations and Boundary Conditions
1.4 Lamé Parameters for Plates and Shells.
2. Modified Fourier Series and Rayleigh-Ritz Method
2.1 Modified Fourier Series
2.1.1 Traditional Fourier Series Solutions.
2.1.2 One-Dimensional Modified Fourier Series Solutions
2.1.3 Two-Dimensional Modified Fourier Series Solutions
2.2 Strong Form Solution Procedure
2.3 Rayleigh-Ritz Method (Weak Form Solution Procedure)
3. Straight and Curved Beams
3.1 Fundamental Equations of Thin Laminated Beams
3.1.1 Kinematic Relations
3.1.2 Stress-Strain Relations and Stress Resultants
3.1.3 Energy Functions
3.1.4 Governing Equations and Boundary Conditions
3.2 Fundamental Equations of Thick Laminated Beams.
3.2.1 Kinematic Relations
3.2.2 Stress-Strain Relations and Stress Resultants
3.2.3 Energy Functions
3.2.4 Governing Equations and Boundary Conditions
3.3 Solution Procedures
3.3.1 Strong Form Solution Procedure
3.3.2 Weak Form Solution Procedure (Rayleigh-Ritz Procedure)
3.4 Laminated Beams with General Boundary Conditions
3.4.1 Convergence Studies and Result Verification
3.4.2 Effects of Shear Deformation and Rotary Inertia
3.4.3 Effects of the Deepness Term (1+z/R).
3.4.4 Isotropic and Laminated Beams with General Boundary Conditions.
4 Plates
4.1 Fundamental Equations of Thin Laminated Rectangular Plates.
4.1.1 Kinematic Relations
4.1.2 Stress-Strain Relations and Stress Resultants
4.1.3 Energy Functions
4.1.4 Governing Equations and Boundary Conditions
4.2 Fundamental Equations of Thick Laminated Rectangular Plates.
4.2.1 Kinematic Relations
4.2.2 Stress-Strain Relations and Stress Resultants
4.2.3 Energy Functions
4.2.4 Governing Equations and Boundary Conditions
4.3 Vibration of Laminated Rectangular Plates
4.3.1 Convergence Studies and Result Verification
4.3.2 Laminated Rectangular Plates with Arbitrary Classical Boundary Conditions
4.3.3 Laminated Rectangular Plates with Elastic Boundary Conditions.
4.3.4 Laminated Rectangular Plates with Internal Line Supports.
4.4 Fundamental Equations of Laminated Sectorial， Annular and Circular Plates
4.4.1 Fundamental Equations of Thin Laminated Sectorial， Annular and Circular Plates
4.4. 2 Fundamental Equations of Thick Laminated Sectorial， Annular and Circular Plates
4.5 Vibration of Laminated Sectorial， Annular and Circular Plates
4.5.1 Vibration of Laminated Annular and Circular Plates
4.5.2 Vibration of Laminated Sectorial Plates
5 Cylindrical Shells
5.1 Fundamental Equations of Thin Laminated Cylindrical Shells
5.1.1 Kinematic Relations
5.1.2 Stress-Strain Relations and Stress Resultants
5.1.3 Energy Functions
5.1.4 Governing Equations and Boundary Conditions
5.2 Fundamental Equations of Thick Laminated Cylindrical Shells
5.2.1 Kinematic Relations
5.2.2 Stress-Strain Relations and Stress Resultants
5.2.3 Energy Functions
5.2.4 Governing Equations and Boundary Conditions
5.3 Vibration of Laminated Closed Cylindrical Shells
5.3.1 Convergence Studies and Result Verification
5.3.2 Effects of Shear Deformation and Rotary Inertia
5.3.3 Laminated Closed Cylindrical Shells with General End Conditions
5.3.4 Laminated Closed Cylindrical Shells with Intermediate Ring Supports
5.4 Vibration of Laminated Open Cylindrical Shells
5.4.1 Convergence Studies and Result Verification
5.4.2 Laminated Open Cylindrical Shells with General End Conditions
6 Conical Shells.
6.1 Fundamental Equations of Thin Laminated Conical Shells
6.1.1 Kinematic Relations
6.1.2 Stress-Strain Relations and Stress Resultants
6.1.3 Energy Functions
6.1.4 Governing Equations and Boundary Conditions
6.2 Fundamental Equations of Thick Laminated Conical Shells
6.2.1 Kinematic Relations
6.2.2 Stress-Strain Relations and Stress Resultants
6.2.3 Energy Functions
6.2.4 Governing Equations and Boundary Conditions
6.3 Vibration of Laminated Closed Conical Shells
6.3.1 Convergence Studies and Result Verification
6.3.2 Laminated Closed Conical Shells with General Boundary Conditions.
6.4 Vibration of Laminated Open Conical Shells
6.4.1 Convergence Studies and Result Verification
6.4.2 Laminated Open Conical Shells with General Boundary Conditions.
7 Spherical Shells
7.1 Fundamental Equations of Thin Laminated
……
8 Shallow Shells
References and Further Reading