Multimodal acoustic impedance and piston loading in a locally excited hydraulic-cylinder cavity

Localized high-frequency inlet excitation in large hydraulic cylinders can generate multidimensional pressure fields that depart from the cross-sectionally uniform behavior assumed in lumped-compliance and one-dimensional water-hammer models. This study develops a closed-form hydroacoustic formulation for multimodal propagation and piston-coupled loading in a finite, rigid-walled cylindrical cavity. The pressure field is expanded in axisymmetric Bessel modes, with modal amplitudes determined from a localized incident volumetric source, complex inlet-end reflection, and a moving rigid piston. The formulation yields the pressure field, source-induced blocked force, acoustic dynamic stiffness, and incident-source-to-piston-velocity transfer function. Axisymmetric finite-element benchmarks show close numerical agreement: at the representative benchmark condition, the fully reflecting case gives full-field and piston-face amplitude errors of 0.4866% and 0.005 74%, respectively, while the median piston-face L2 error over 34 frequency-resolved and position-resolved cases is 0.005 28%. The results distinguish radial cutoff, finite-cavity acoustic resonance, and coupled piston-response resonance. Reflection magnitude governs resonant amplification, reflection phase shifts resonance locations, and piston position modifies modal phase accumulation and acoustic loading. Higher-order modes remain important for local pressure nonuniformity despite their vanishing net-force contribution on an ideal full-face piston, while below-cutoff evanescent components remain influential over finite distances. Sensitivity analyses show that effective sound speed and piston mass mainly shift characteristic frequencies, source localization controls higher-order modal content, and acoustic loss and mechanical damping primarily regulate resonance amplitude and bandwidth. These results provide a physically interpretable framework that links inlet, cavity, and mechanical parameters to multimodal pressure redistribution and the piston-coupled response.